library(pacman); p_load(lavaan, psych)
data <- read.csv("NPSIQ.csv")
FITM <- c("chisq", "df", "nPar", "cfi", "rmsea", "rmsea.ci.lower", "rmsea.ci.upper", "aic", "bic")
describe(data)Schubert et al. (2022) assessed the relationship between the latent general factor of the latencies of event-related potentials (ERP) assessed during the administration of different elementary cognitive tasks and the latent general factor of the short version of the Berlin Intelligence Structure Test (BIS). Short versions of tests measure the same constructs as long-form versions. Valerius & Sparfeldt (2014) found the full version of the BIS measured the same g as the German Cognitive Ability Test (CogAT; r = 0.92) and the Cattell Culture Fair Test plus Raven’s Matrices (r = 0.99). Incidentally, the Cattell Culture Fair Test measures in common with the Sternberg Triarchic Abilities Test (Brody, 2003a, 2003b) and the Sternberg Triarchic Abilities Test is within the nomothetic network centered around g (Koke & Vernon, 2003). The Cattell Culture Fair Test without Raven’s Matrices also produced a g factor that was correlated at 0.88 with the g factor from the Test Battery of the Royal Dutch Navy, 0.79 with the Twents Instituut voor Bedrijfspsycologie’s (i.e., Factored Aptitude Series’) g, 0.77 with the g from the General Aptitude Test Battery, and 0.96 with the g from the Groninger Intelligence Test (Johnson, te Nijenhuis & Bouchard, 2008). This network of intercorrelations can be extended to other tests all day, but needless to say, the test used by Schubert et al. is a sufficiently valid measure of general intelligence, because the world of intelligence tests of large, but despite efforts to the contrary, their domain is small.
Schubert et al. presented what looks to be an incredibly interesting domain extension: an assessment of the degree to which intelligence, measured moderately-well, is measured by ERP measures. Their point for their analysis was to conduct a multiverse analysis of features to assess their impacts on the consistency of ERP component associations with intelligence. But the feature analysis wasn’t the most interesting part. The most interesting part was a little note underneath Figure 3 that read
Correlations for EEG data filtered with a 32 Hz low-pass filter are not shown because the variance of the latent ERP variable was not significant.
In other words, a general ERP factor was perfectly (anti)correlated with the g factor from an intelligence test. That is what’s implied when the variance drops to zero in the model they used (see Figure 1). Choosing not to present that result is odd because it is a very meaningful result, and it’s justifiable. In fact, because the sampling rate in their analysis was 1000 Hz (and thus the Nyquist frequency was 500/333 Hz), their choice to omit results with a low-pass filter at 32 Hz is strange. Sure, phase locking cannot be guaranteed, but they were probably still well-powered for a filter at ten times their cap. I am not sure why they chose to only present and discuss results for 8 and 16 Hz, truncating most of the available variance. Curiously, they did find that the latency reliabilities at these thresholds were 0.52 (SD = 17, 8 Hz), 0.45 (0.16, 16), and 0.48 (0.18, 32). There was no good reason to not present results at 32 Hz.
The number of offline references was just two: linked mastoid (LM) and average reference (AR). If I had to rank difference references, I would go REST > AR > LM, since REST has the best evidence that it just works the best, AR seems to produce results that are more comparable to REST in most cases I’ve seen, and LM produces results with a relatively muted signal. But this can be good if it promotes reliability. Since LM and AR were presented, they’re all we have to work with. In this data, it seems there’s some case for LM results to be preferred, since they were a bit more reliable (0.57, SD = 0.18) than AR ones (0.41, 0.13). But I do not want to sound like I’m conflating reliability with construct validity or relevance. Ideally, I would like to see cortical source estimates, but that’s hard to come by. For more on reference choices, I’d read Yang et al. (2017), Dong et al. (2019), and Yao et al. (2019). They’re linked in the references.
Here, I wish to avoid the multiverse results and just look at the outputs of Schubert et al.’s models, with a specific focus on the 32 Hz results, since those are valid and not nearly as restricted as the 8 and 16 Hz results. They’re more likely to give a “true” estimate of the relationship between intelligence and whatever this ERP-g is.
The below code is their own, with fits to follow. All models they fit are presented, with a break between models that control and do not control for age. As they noted, controlling for age had a minimal effect on their results, but I want to show all the model fits anyway.
## SEM: Average reference, 8 Hz low-pass filter, peak latency ----
model_avg_8Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_8Hz_avg + 1*zCRT_P2_PL_8Hz_avg + 1*zSternberg_P2_PL_8Hz_avg",
"N2 =~ 1*zPosner_N2_PL_8Hz_avg + 1*zCRT_N2_PL_8Hz_avg + 1*zSternberg_N2_PL_8Hz_avg",
"P3 =~ 1*zPosner_P3_PL_8Hz_avg + 1*zCRT_P3_PL_8Hz_avg + 1*zSternberg_P3_PL_8Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_PL_8Hz_avg + 1*zPosner_N2_PL_8Hz_avg + 1*zPosner_P3_PL_8Hz_avg",
"CRT =~ 1*zCRT_P2_PL_8Hz_avg + 1*zCRT_N2_PL_8Hz_avg + 1*zCRT_P3_PL_8Hz_avg",
"Sternberg =~ 1*zSternberg_P2_PL_8Hz_avg + 1*zSternberg_N2_PL_8Hz_avg + 1*zSternberg_P3_PL_8Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_8Hz_avg ~ 0",
"zPosner_N2_PL_8Hz_avg ~ 0",
"zPosner_P3_PL_8Hz_avg ~ 0",
"zCRT_P2_PL_8Hz_avg ~ 0",
"zCRT_N2_PL_8Hz_avg ~ 0",
"zCRT_P3_PL_8Hz_avg ~ 0",
"zSternberg_P2_PL_8Hz_avg ~ 0",
"zSternberg_N2_PL_8Hz_avg ~ 0",
"zSternberg_P3_PL_8Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_8Hz_avg ~~ v_P_P2*zPosner_P2_PL_8Hz_avg",
"zPosner_N2_PL_8Hz_avg ~~ v_P_N2*zPosner_N2_PL_8Hz_avg",
"zPosner_P3_PL_8Hz_avg~~ v_P_P3*zPosner_P3_PL_8Hz_avg",
"zCRT_P2_PL_8Hz_avg ~~ v_C_P2*zCRT_P2_PL_8Hz_avg",
"zCRT_N2_PL_8Hz_avg ~~ v_C_N2*zCRT_N2_PL_8Hz_avg",
"zCRT_P3_PL_8Hz_avg ~~ v_C_P3*zCRT_P3_PL_8Hz_avg",
"zSternberg_P2_PL_8Hz_avg ~~ v_S_P2*zSternberg_P2_PL_8Hz_avg",
"zSternberg_N2_PL_8Hz_avg ~~ v_S_N2*zSternberg_N2_PL_8Hz_avg",
"zSternberg_P3_PL_8Hz_avg ~~ v_S_P3*zSternberg_P3_PL_8Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_8Hz_PL <- sem(model_avg_8Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 148## SEM: Average reference, 8 Hz low-pass filter, 50 % FA latency ----
model_avg_8Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_8Hz_avg + 1*zCRT_P2_FA_8Hz_avg + 1*zSternberg_P2_FA_8Hz_avg",
"N2 =~ 1*zPosner_N2_FA_8Hz_avg + 1*zCRT_N2_FA_8Hz_avg + 1*zSternberg_N2_FA_8Hz_avg",
"P3 =~ 1*zPosner_P3_FA_8Hz_avg + 1*zCRT_P3_FA_8Hz_avg + 1*zSternberg_P3_FA_8Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_FA_8Hz_avg + 1*zPosner_N2_FA_8Hz_avg + 1*zPosner_P3_FA_8Hz_avg",
"CRT =~ 1*zCRT_P2_FA_8Hz_avg + 1*zCRT_N2_FA_8Hz_avg + 1*zCRT_P3_FA_8Hz_avg",
"Sternberg =~ 1*zSternberg_P2_FA_8Hz_avg + 1*zSternberg_N2_FA_8Hz_avg + 1*zSternberg_P3_FA_8Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_8Hz_avg ~ 0",
"zPosner_N2_FA_8Hz_avg ~ 0",
"zPosner_P3_FA_8Hz_avg ~ 0",
"zCRT_P2_FA_8Hz_avg ~ 0",
"zCRT_N2_FA_8Hz_avg ~ 0",
"zCRT_P3_FA_8Hz_avg ~ 0",
"zSternberg_P2_FA_8Hz_avg ~ 0",
"zSternberg_N2_FA_8Hz_avg ~ 0",
"zSternberg_P3_FA_8Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_8Hz_avg ~~ v_P_P2*zPosner_P2_FA_8Hz_avg",
"zPosner_N2_FA_8Hz_avg ~~ v_P_N2*zPosner_N2_FA_8Hz_avg",
"zPosner_P3_FA_8Hz_avg~~ v_P_P3*zPosner_P3_FA_8Hz_avg",
"zCRT_P2_FA_8Hz_avg ~~ v_C_P2*zCRT_P2_FA_8Hz_avg",
"zCRT_N2_FA_8Hz_avg ~~ v_C_N2*zCRT_N2_FA_8Hz_avg",
"zCRT_P3_FA_8Hz_avg ~~ v_C_P3*zCRT_P3_FA_8Hz_avg",
"zSternberg_P2_FA_8Hz_avg ~~ v_S_P2*zSternberg_P2_FA_8Hz_avg",
"zSternberg_N2_FA_8Hz_avg ~~ v_S_N2*zSternberg_N2_FA_8Hz_avg",
"zSternberg_P3_FA_8Hz_avg ~~ v_S_P3*zSternberg_P3_FA_8Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_8Hz_FA <- sem(model_avg_8Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some cases are empty and will be ignored:
## 148## SEM: Average reference, 16 Hz low-pass filter, peak latency ----
model_avg_16Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_16Hz_avg + 1*zCRT_P2_PL_16Hz_avg + 1*zSternberg_P2_PL_16Hz_avg",
"N2 =~ 1*zPosner_N2_PL_16Hz_avg + 1*zCRT_N2_PL_16Hz_avg + 1*zSternberg_N2_PL_16Hz_avg",
"P3 =~ 1*zPosner_P3_PL_16Hz_avg + 1*zCRT_P3_PL_16Hz_avg + 1*zSternberg_P3_PL_16Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_PL_16Hz_avg + 1*zPosner_N2_PL_16Hz_avg + 1*zPosner_P3_PL_16Hz_avg",
"CRT =~ 1*zCRT_P2_PL_16Hz_avg + 1*zCRT_N2_PL_16Hz_avg + 1*zCRT_P3_PL_16Hz_avg",
"Sternberg =~ 1*zSternberg_P2_PL_16Hz_avg + 1*zSternberg_N2_PL_16Hz_avg + 1*zSternberg_P3_PL_16Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_16Hz_avg ~ 0",
"zPosner_N2_PL_16Hz_avg ~ 0",
"zPosner_P3_PL_16Hz_avg ~ 0",
"zCRT_P2_PL_16Hz_avg ~ 0",
"zCRT_N2_PL_16Hz_avg ~ 0",
"zCRT_P3_PL_16Hz_avg ~ 0",
"zSternberg_P2_PL_16Hz_avg ~ 0",
"zSternberg_N2_PL_16Hz_avg ~ 0",
"zSternberg_P3_PL_16Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_16Hz_avg ~~ v_P_P2*zPosner_P2_PL_16Hz_avg",
"zPosner_N2_PL_16Hz_avg ~~ v_P_N2*zPosner_N2_PL_16Hz_avg",
"zPosner_P3_PL_16Hz_avg~~ v_P_P3*zPosner_P3_PL_16Hz_avg",
"zCRT_P2_PL_16Hz_avg ~~ v_C_P2*zCRT_P2_PL_16Hz_avg",
"zCRT_N2_PL_16Hz_avg ~~ v_C_N2*zCRT_N2_PL_16Hz_avg",
"zCRT_P3_PL_16Hz_avg ~~ v_C_P3*zCRT_P3_PL_16Hz_avg",
"zSternberg_P2_PL_16Hz_avg ~~ v_S_P2*zSternberg_P2_PL_16Hz_avg",
"zSternberg_N2_PL_16Hz_avg ~~ v_S_N2*zSternberg_N2_PL_16Hz_avg",
"zSternberg_P3_PL_16Hz_avg ~~ v_S_P3*zSternberg_P3_PL_16Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_16Hz_PL <- sem(model_avg_16Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Average reference, 16 Hz low-pass filter, 50 % FA latency ----
model_avg_16Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_16Hz_avg + 1*zCRT_P2_FA_16Hz_avg + 1*zSternberg_P2_FA_16Hz_avg",
"N2 =~ 1*zPosner_N2_FA_16Hz_avg + 1*zCRT_N2_FA_16Hz_avg + 1*zSternberg_N2_FA_16Hz_avg",
"P3 =~ 1*zPosner_P3_FA_16Hz_avg + 1*zCRT_P3_FA_16Hz_avg + 1*zSternberg_P3_FA_16Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_FA_16Hz_avg + 1*zPosner_N2_FA_16Hz_avg + 1*zPosner_P3_FA_16Hz_avg",
"CRT =~ 1*zCRT_P2_FA_16Hz_avg + 1*zCRT_N2_FA_16Hz_avg + 1*zCRT_P3_FA_16Hz_avg",
"Sternberg =~ 1*zSternberg_P2_FA_16Hz_avg + 1*zSternberg_N2_FA_16Hz_avg + 1*zSternberg_P3_FA_16Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_16Hz_avg ~ 0",
"zPosner_N2_FA_16Hz_avg ~ 0",
"zPosner_P3_FA_16Hz_avg ~ 0",
"zCRT_P2_FA_16Hz_avg ~ 0",
"zCRT_N2_FA_16Hz_avg ~ 0",
"zCRT_P3_FA_16Hz_avg ~ 0",
"zSternberg_P2_FA_16Hz_avg ~ 0",
"zSternberg_N2_FA_16Hz_avg ~ 0",
"zSternberg_P3_FA_16Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_16Hz_avg ~~ v_P_P2*zPosner_P2_FA_16Hz_avg",
"zPosner_N2_FA_16Hz_avg ~~ v_P_N2*zPosner_N2_FA_16Hz_avg",
"zPosner_P3_FA_16Hz_avg~~ v_P_P3*zPosner_P3_FA_16Hz_avg",
"zCRT_P2_FA_16Hz_avg ~~ v_C_P2*zCRT_P2_FA_16Hz_avg",
"zCRT_N2_FA_16Hz_avg ~~ v_C_N2*zCRT_N2_FA_16Hz_avg",
"zCRT_P3_FA_16Hz_avg ~~ v_C_P3*zCRT_P3_FA_16Hz_avg",
"zSternberg_P2_FA_16Hz_avg ~~ v_S_P2*zSternberg_P2_FA_16Hz_avg",
"zSternberg_N2_FA_16Hz_avg ~~ v_S_N2*zSternberg_N2_FA_16Hz_avg",
"zSternberg_P3_FA_16Hz_avg ~~ v_S_P3*zSternberg_P3_FA_16Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_16Hz_FA <- sem(model_avg_16Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Average reference, 32 Hz low-pass filter, peak latency ----
model_avg_32Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_32Hz_avg + 1*zCRT_P2_PL_32Hz_avg + 1*zSternberg_P2_PL_32Hz_avg",
"N2 =~ 1*zPosner_N2_PL_32Hz_avg + 1*zCRT_N2_PL_32Hz_avg + 1*zSternberg_N2_PL_32Hz_avg",
"P3 =~ 1*zPosner_P3_PL_32Hz_avg + 1*zCRT_P3_PL_32Hz_avg + 1*zSternberg_P3_PL_32Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_PL_32Hz_avg + 1*zPosner_N2_PL_32Hz_avg + 1*zPosner_P3_PL_32Hz_avg",
"CRT =~ 1*zCRT_P2_PL_32Hz_avg + 1*zCRT_N2_PL_32Hz_avg + 1*zCRT_P3_PL_32Hz_avg",
"Sternberg =~ 1*zSternberg_P2_PL_32Hz_avg + 1*zSternberg_N2_PL_32Hz_avg + 1*zSternberg_P3_PL_32Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_32Hz_avg ~ 0",
"zPosner_N2_PL_32Hz_avg ~ 0",
"zPosner_P3_PL_32Hz_avg ~ 0",
"zCRT_P2_PL_32Hz_avg ~ 0",
"zCRT_N2_PL_32Hz_avg ~ 0",
"zCRT_P3_PL_32Hz_avg ~ 0",
"zSternberg_P2_PL_32Hz_avg ~ 0",
"zSternberg_N2_PL_32Hz_avg ~ 0",
"zSternberg_P3_PL_32Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_32Hz_avg ~~ v_P_P2*zPosner_P2_PL_32Hz_avg",
"zPosner_N2_PL_32Hz_avg ~~ v_P_N2*zPosner_N2_PL_32Hz_avg",
"zPosner_P3_PL_32Hz_avg~~ v_P_P3*zPosner_P3_PL_32Hz_avg",
"zCRT_P2_PL_32Hz_avg ~~ v_C_P2*zCRT_P2_PL_32Hz_avg",
"zCRT_N2_PL_32Hz_avg ~~ v_C_N2*zCRT_N2_PL_32Hz_avg",
"zCRT_P3_PL_32Hz_avg ~~ v_C_P3*zCRT_P3_PL_32Hz_avg",
"zSternberg_P2_PL_32Hz_avg ~~ v_S_P2*zSternberg_P2_PL_32Hz_avg",
"zSternberg_N2_PL_32Hz_avg ~~ v_S_N2*zSternberg_N2_PL_32Hz_avg",
"zSternberg_P3_PL_32Hz_avg ~~ v_S_P3*zSternberg_P3_PL_32Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_32Hz_PL <- sem(model_avg_32Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Average reference, 32 Hz low-pass filter, 50 % FA latency ----
model_avg_32Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_32Hz_avg + 1*zCRT_P2_FA_32Hz_avg + 1*zSternberg_P2_FA_32Hz_avg",
"N2 =~ 1*zPosner_N2_FA_32Hz_avg + 1*zCRT_N2_FA_32Hz_avg + 1*zSternberg_N2_FA_32Hz_avg",
"P3 =~ 1*zPosner_P3_FA_32Hz_avg + 1*zCRT_P3_FA_32Hz_avg + 1*zSternberg_P3_FA_32Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_FA_32Hz_avg + 1*zPosner_N2_FA_32Hz_avg + 1*zPosner_P3_FA_32Hz_avg",
"CRT =~ 1*zCRT_P2_FA_32Hz_avg + 1*zCRT_N2_FA_32Hz_avg + 1*zCRT_P3_FA_32Hz_avg",
"Sternberg =~ 1*zSternberg_P2_FA_32Hz_avg + 1*zSternberg_N2_FA_32Hz_avg + 1*zSternberg_P3_FA_32Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_32Hz_avg ~ 0",
"zPosner_N2_FA_32Hz_avg ~ 0",
"zPosner_P3_FA_32Hz_avg ~ 0",
"zCRT_P2_FA_32Hz_avg ~ 0",
"zCRT_N2_FA_32Hz_avg ~ 0",
"zCRT_P3_FA_32Hz_avg ~ 0",
"zSternberg_P2_FA_32Hz_avg ~ 0",
"zSternberg_N2_FA_32Hz_avg ~ 0",
"zSternberg_P3_FA_32Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_32Hz_avg ~~ v_P_P2*zPosner_P2_FA_32Hz_avg",
"zPosner_N2_FA_32Hz_avg ~~ v_P_N2*zPosner_N2_FA_32Hz_avg",
"zPosner_P3_FA_32Hz_avg~~ v_P_P3*zPosner_P3_FA_32Hz_avg",
"zCRT_P2_FA_32Hz_avg ~~ v_C_P2*zCRT_P2_FA_32Hz_avg",
"zCRT_N2_FA_32Hz_avg ~~ v_C_N2*zCRT_N2_FA_32Hz_avg",
"zCRT_P3_FA_32Hz_avg ~~ v_C_P3*zCRT_P3_FA_32Hz_avg",
"zSternberg_P2_FA_32Hz_avg ~~ v_S_P2*zSternberg_P2_FA_32Hz_avg",
"zSternberg_N2_FA_32Hz_avg ~~ v_S_N2*zSternberg_N2_FA_32Hz_avg",
"zSternberg_P3_FA_32Hz_avg ~~ v_S_P3*zSternberg_P3_FA_32Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_32Hz_FA <- sem(model_avg_32Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 8 Hz low-pass filter, peak latency ----
model_mas_8Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_8Hz_mas + 1*zCRT_P2_PL_8Hz_mas + 1*zSternberg_P2_PL_8Hz_mas",
"N2 =~ 1*zPosner_N2_PL_8Hz_mas + 1*zCRT_N2_PL_8Hz_mas + 1*zSternberg_N2_PL_8Hz_mas",
"P3 =~ 1*zPosner_P3_PL_8Hz_mas + 1*zCRT_P3_PL_8Hz_mas + 1*zSternberg_P3_PL_8Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_PL_8Hz_mas + 1*zPosner_P3_PL_8Hz_mas",
"CRT =~ 1*zCRT_N2_PL_8Hz_mas + 1*zCRT_P3_PL_8Hz_mas",
"Sternberg =~ 1*zSternberg_N2_PL_8Hz_mas + 1*zSternberg_P3_PL_8Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_8Hz_mas ~ 0",
"zPosner_N2_PL_8Hz_mas ~ 0",
"zPosner_P3_PL_8Hz_mas ~ 0",
"zCRT_P2_PL_8Hz_mas ~ 0",
"zCRT_N2_PL_8Hz_mas ~ 0",
"zCRT_P3_PL_8Hz_mas ~ 0",
"zSternberg_P2_PL_8Hz_mas ~ 0",
"zSternberg_N2_PL_8Hz_mas ~ 0",
"zSternberg_P3_PL_8Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ v_n2*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_8Hz_mas ~~ v_P_P2*zPosner_P2_PL_8Hz_mas",
"zPosner_N2_PL_8Hz_mas ~~ v_P_N2*zPosner_N2_PL_8Hz_mas",
"zPosner_P3_PL_8Hz_mas~~ v_P_P3*zPosner_P3_PL_8Hz_mas",
"zCRT_P2_PL_8Hz_mas ~~ v_C_P2*zCRT_P2_PL_8Hz_mas",
"zCRT_N2_PL_8Hz_mas ~~ v_C_N2*zCRT_N2_PL_8Hz_mas",
"zCRT_P3_PL_8Hz_mas ~~ v_C_P3*zCRT_P3_PL_8Hz_mas",
"zSternberg_P2_PL_8Hz_mas ~~ v_S_P2*zSternberg_P2_PL_8Hz_mas",
"zSternberg_N2_PL_8Hz_mas ~~ v_S_N2*zSternberg_N2_PL_8Hz_mas",
"zSternberg_P3_PL_8Hz_mas ~~ v_S_P3*zSternberg_P3_PL_8Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + v_n2 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + v_n2 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (v_n2)/(v_erp + v_n2 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (v_n2)/(v_erp + v_n2 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (v_n2)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + v_n2 + v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + v_n2 + v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +v_n2 + v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_8Hz_PL <- sem(model_mas_8Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 8 Hz low-pass filter, 50 % FA latency ----
model_mas_8Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_8Hz_mas + 1*zCRT_P2_FA_8Hz_mas + 1*zSternberg_P2_FA_8Hz_mas",
"N2 =~ 1*zPosner_N2_FA_8Hz_mas + 1*zCRT_N2_FA_8Hz_mas + 1*zSternberg_N2_FA_8Hz_mas",
"P3 =~ 1*zPosner_P3_FA_8Hz_mas + 1*zCRT_P3_FA_8Hz_mas + 1*zSternberg_P3_FA_8Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_FA_8Hz_mas + 1*zPosner_P3_FA_8Hz_mas",
"CRT =~ 1*zCRT_N2_FA_8Hz_mas + 1*zCRT_P3_FA_8Hz_mas",
"Sternberg =~ 1*zSternberg_N2_FA_8Hz_mas + 1*zSternberg_P3_FA_8Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_8Hz_mas ~ 0",
"zPosner_N2_FA_8Hz_mas ~ 0",
"zPosner_P3_FA_8Hz_mas ~ 0",
"zCRT_P2_FA_8Hz_mas ~ 0",
"zCRT_N2_FA_8Hz_mas ~ 0",
"zCRT_P3_FA_8Hz_mas ~ 0",
"zSternberg_P2_FA_8Hz_mas ~ 0",
"zSternberg_N2_FA_8Hz_mas ~ 0",
"zSternberg_P3_FA_8Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ v_n2*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_8Hz_mas ~~ v_P_P2*zPosner_P2_FA_8Hz_mas",
"zPosner_N2_FA_8Hz_mas ~~ v_P_N2*zPosner_N2_FA_8Hz_mas",
"zPosner_P3_FA_8Hz_mas~~ v_P_P3*zPosner_P3_FA_8Hz_mas",
"zCRT_P2_FA_8Hz_mas ~~ v_C_P2*zCRT_P2_FA_8Hz_mas",
"zCRT_N2_FA_8Hz_mas ~~ v_C_N2*zCRT_N2_FA_8Hz_mas",
"zCRT_P3_FA_8Hz_mas ~~ v_C_P3*zCRT_P3_FA_8Hz_mas",
"zSternberg_P2_FA_8Hz_mas ~~ v_S_P2*zSternberg_P2_FA_8Hz_mas",
"zSternberg_N2_FA_8Hz_mas ~~ v_S_N2*zSternberg_N2_FA_8Hz_mas",
"zSternberg_P3_FA_8Hz_mas ~~ v_S_P3*zSternberg_P3_FA_8Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + v_n2 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + v_n2 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (v_n2)/(v_erp + v_n2 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (v_n2)/(v_erp + v_n2 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (v_n2)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + v_n2 + v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + v_n2 + v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +v_n2 + v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_8Hz_FA <- sem(model_mas_8Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 16 Hz low-pass filter, peak latency ----
model_mas_16Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_16Hz_mas + 1*zCRT_P2_PL_16Hz_mas + 1*zSternberg_P2_PL_16Hz_mas",
"N2 =~ 1*zPosner_N2_PL_16Hz_mas + 1*zCRT_N2_PL_16Hz_mas + 1*zSternberg_N2_PL_16Hz_mas",
"P3 =~ 1*zPosner_P3_PL_16Hz_mas + 1*zCRT_P3_PL_16Hz_mas + 1*zSternberg_P3_PL_16Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_PL_16Hz_mas + 1*zPosner_P3_PL_16Hz_mas",
"CRT =~ 1*zCRT_N2_PL_16Hz_mas + 1*zCRT_P3_PL_16Hz_mas",
"Sternberg =~ 1*zSternberg_N2_PL_16Hz_mas + 1*zSternberg_P3_PL_16Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_16Hz_mas ~ 0",
"zPosner_N2_PL_16Hz_mas ~ 0",
"zPosner_P3_PL_16Hz_mas ~ 0",
"zCRT_P2_PL_16Hz_mas ~ 0",
"zCRT_N2_PL_16Hz_mas ~ 0",
"zCRT_P3_PL_16Hz_mas ~ 0",
"zSternberg_P2_PL_16Hz_mas ~ 0",
"zSternberg_N2_PL_16Hz_mas ~ 0",
"zSternberg_P3_PL_16Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_16Hz_mas ~~ v_P_P2*zPosner_P2_PL_16Hz_mas",
"zPosner_N2_PL_16Hz_mas ~~ v_P_N2*zPosner_N2_PL_16Hz_mas",
"zPosner_P3_PL_16Hz_mas~~ v_P_P3*zPosner_P3_PL_16Hz_mas",
"zCRT_P2_PL_16Hz_mas ~~ v_C_P2*zCRT_P2_PL_16Hz_mas",
"zCRT_N2_PL_16Hz_mas ~~ v_C_N2*zCRT_N2_PL_16Hz_mas",
"zCRT_P3_PL_16Hz_mas ~~ v_C_P3*zCRT_P3_PL_16Hz_mas",
"zSternberg_P2_PL_16Hz_mas ~~ v_S_P2*zSternberg_P2_PL_16Hz_mas",
"zSternberg_N2_PL_16Hz_mas ~~ v_S_N2*zSternberg_N2_PL_16Hz_mas",
"zSternberg_P3_PL_16Hz_mas ~~ v_S_P3*zSternberg_P3_PL_16Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + 0 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + 0 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +0 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + 0 + v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + 0 + v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +0 + v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_16Hz_PL <- sem(model_mas_16Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 16 Hz low-pass filter, 50 % FA latency ----
model_mas_16Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_16Hz_mas + 1*zCRT_P2_FA_16Hz_mas + 1*zSternberg_P2_FA_16Hz_mas",
"N2 =~ 1*zPosner_N2_FA_16Hz_mas + 1*zCRT_N2_FA_16Hz_mas + 1*zSternberg_N2_FA_16Hz_mas",
"P3 =~ 1*zPosner_P3_FA_16Hz_mas + 1*zCRT_P3_FA_16Hz_mas + 1*zSternberg_P3_FA_16Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_FA_16Hz_mas + 1*zPosner_P3_FA_16Hz_mas",
"CRT =~ 1*zCRT_N2_FA_16Hz_mas + 1*zCRT_P3_FA_16Hz_mas",
"Sternberg =~ 1*zSternberg_N2_FA_16Hz_mas + 1*zSternberg_P3_FA_16Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_16Hz_mas ~ 0",
"zPosner_N2_FA_16Hz_mas ~ 0",
"zPosner_P3_FA_16Hz_mas ~ 0",
"zCRT_P2_FA_16Hz_mas ~ 0",
"zCRT_N2_FA_16Hz_mas ~ 0",
"zCRT_P3_FA_16Hz_mas ~ 0",
"zSternberg_P2_FA_16Hz_mas ~ 0",
"zSternberg_N2_FA_16Hz_mas ~ 0",
"zSternberg_P3_FA_16Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_16Hz_mas ~~ v_P_P2*zPosner_P2_FA_16Hz_mas",
"zPosner_N2_FA_16Hz_mas ~~ v_P_N2*zPosner_N2_FA_16Hz_mas",
"zPosner_P3_FA_16Hz_mas~~ v_P_P3*zPosner_P3_FA_16Hz_mas",
"zCRT_P2_FA_16Hz_mas ~~ v_C_P2*zCRT_P2_FA_16Hz_mas",
"zCRT_N2_FA_16Hz_mas ~~ v_C_N2*zCRT_N2_FA_16Hz_mas",
"zCRT_P3_FA_16Hz_mas ~~ v_C_P3*zCRT_P3_FA_16Hz_mas",
"zSternberg_P2_FA_16Hz_mas ~~ v_S_P2*zSternberg_P2_FA_16Hz_mas",
"zSternberg_N2_FA_16Hz_mas ~~ v_S_N2*zSternberg_N2_FA_16Hz_mas",
"zSternberg_P3_FA_16Hz_mas ~~ v_S_P3*zSternberg_P3_FA_16Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + 0 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + 0 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +0 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + 0 + v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + 0 + v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +0 + v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_16Hz_FA <- sem(model_mas_16Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 32 Hz low-pass filter, peak latency ----
model_mas_32Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_32Hz_mas + 1*zCRT_P2_PL_32Hz_mas + 1*zSternberg_P2_PL_32Hz_mas",
"N2 =~ 1*zPosner_N2_PL_32Hz_mas + 1*zCRT_N2_PL_32Hz_mas + 1*zSternberg_N2_PL_32Hz_mas",
"P3 =~ 1*zPosner_P3_PL_32Hz_mas + 1*zCRT_P3_PL_32Hz_mas + 1*zSternberg_P3_PL_32Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_PL_32Hz_mas + 1*zPosner_P3_PL_32Hz_mas",
"CRT =~ 1*zCRT_N2_PL_32Hz_mas + 1*zCRT_P3_PL_32Hz_mas",
"Sternberg =~ 1*zSternberg_N2_PL_32Hz_mas + 1*zSternberg_P3_PL_32Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_32Hz_mas ~ 0",
"zPosner_N2_PL_32Hz_mas ~ 0",
"zPosner_P3_PL_32Hz_mas ~ 0",
"zCRT_P2_PL_32Hz_mas ~ 0",
"zCRT_N2_PL_32Hz_mas ~ 0",
"zCRT_P3_PL_32Hz_mas ~ 0",
"zSternberg_P2_PL_32Hz_mas ~ 0",
"zSternberg_N2_PL_32Hz_mas ~ 0",
"zSternberg_P3_PL_32Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ v_n2*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_32Hz_mas ~~ v_P_P2*zPosner_P2_PL_32Hz_mas",
"zPosner_N2_PL_32Hz_mas ~~ v_P_N2*zPosner_N2_PL_32Hz_mas",
"zPosner_P3_PL_32Hz_mas~~ v_P_P3*zPosner_P3_PL_32Hz_mas",
"zCRT_P2_PL_32Hz_mas ~~ v_C_P2*zCRT_P2_PL_32Hz_mas",
"zCRT_N2_PL_32Hz_mas ~~ v_C_N2*zCRT_N2_PL_32Hz_mas",
"zCRT_P3_PL_32Hz_mas ~~ v_C_P3*zCRT_P3_PL_32Hz_mas",
"zSternberg_P2_PL_32Hz_mas ~~ v_S_P2*zSternberg_P2_PL_32Hz_mas",
"zSternberg_N2_PL_32Hz_mas ~~ v_S_N2*zSternberg_N2_PL_32Hz_mas",
"zSternberg_P3_PL_32Hz_mas ~~ v_S_P3*zSternberg_P3_PL_32Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + v_n2 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + v_n2 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (v_n2)/(v_erp + v_n2 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (v_n2)/(v_erp + v_n2 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (v_n2)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + v_n2 + v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + v_n2 + v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +v_n2 + v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_32Hz_PL <- sem(model_mas_32Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 32 Hz low-pass filter, 50 % FA latency ----
model_mas_32Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_32Hz_mas + 1*zCRT_P2_FA_32Hz_mas + 1*zSternberg_P2_FA_32Hz_mas",
"N2 =~ 1*zPosner_N2_FA_32Hz_mas + 1*zCRT_N2_FA_32Hz_mas + 1*zSternberg_N2_FA_32Hz_mas",
"P3 =~ 1*zPosner_P3_FA_32Hz_mas + 1*zCRT_P3_FA_32Hz_mas + 1*zSternberg_P3_FA_32Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_FA_32Hz_mas + 1*zPosner_P3_FA_32Hz_mas",
"CRT =~ 1*zCRT_N2_FA_32Hz_mas + 1*zCRT_P3_FA_32Hz_mas",
"Sternberg =~ 1*zSternberg_N2_FA_32Hz_mas + 1*zSternberg_P3_FA_32Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_32Hz_mas ~ 0",
"zPosner_N2_FA_32Hz_mas ~ 0",
"zPosner_P3_FA_32Hz_mas ~ 0",
"zCRT_P2_FA_32Hz_mas ~ 0",
"zCRT_N2_FA_32Hz_mas ~ 0",
"zCRT_P3_FA_32Hz_mas ~ 0",
"zSternberg_P2_FA_32Hz_mas ~ 0",
"zSternberg_N2_FA_32Hz_mas ~ 0",
"zSternberg_P3_FA_32Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_32Hz_mas ~~ v_P_P2*zPosner_P2_FA_32Hz_mas",
"zPosner_N2_FA_32Hz_mas ~~ v_P_N2*zPosner_N2_FA_32Hz_mas",
"zPosner_P3_FA_32Hz_mas~~ v_P_P3*zPosner_P3_FA_32Hz_mas",
"zCRT_P2_FA_32Hz_mas ~~ v_C_P2*zCRT_P2_FA_32Hz_mas",
"zCRT_N2_FA_32Hz_mas ~~ v_C_N2*zCRT_N2_FA_32Hz_mas",
"zCRT_P3_FA_32Hz_mas ~~ v_C_P3*zCRT_P3_FA_32Hz_mas",
"zSternberg_P2_FA_32Hz_mas ~~ v_S_P2*zSternberg_P2_FA_32Hz_mas",
"zSternberg_N2_FA_32Hz_mas ~~ v_S_N2*zSternberg_N2_FA_32Hz_mas",
"zSternberg_P3_FA_32Hz_mas ~~ v_S_P3*zSternberg_P3_FA_32Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + 0 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + 0 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +0 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + 0 + v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + 0 + v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +0 + v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_32Hz_FA <- sem(model_mas_32Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
"\n"## [1] "\n"round(cbind(RP8A = fitMeasures(fit_avg_8Hz_PL, FITM),
RP85 = fitMeasures(fit_avg_8Hz_FA, FITM),
RP16A = fitMeasures(fit_avg_16Hz_PL, FITM),
RP165 = fitMeasures(fit_avg_16Hz_FA, FITM),
RP32A = fitMeasures(fit_avg_32Hz_PL, FITM),
RP325 = fitMeasures(fit_avg_32Hz_FA, FITM),
FP8A = fitMeasures(fit_mas_8Hz_PL, FITM),
FP85 = fitMeasures(fit_mas_8Hz_FA, FITM),
FP16A = fitMeasures(fit_mas_16Hz_PL, FITM),
FP165 = fitMeasures(fit_mas_16Hz_FA, FITM),
FP32A = fitMeasures(fit_mas_32Hz_PL, FITM),
FP325 = fitMeasures(fit_mas_32Hz_FA, FITM)), 3)## RP8A RP85 RP16A RP165 RP32A RP325 FP8A
## chisq 106.944 122.816 96.794 111.643 134.442 146.806 83.484
## df 78.000 78.000 78.000 78.000 78.000 78.000 78.000
## npar 26.000 26.000 26.000 26.000 26.000 26.000 26.000
## cfi 0.925 0.880 0.938 0.887 0.795 0.788 0.986
## rmsea 0.050 0.063 0.040 0.054 0.070 0.077 0.022
## rmsea.ci.lower 0.022 0.040 0.000 0.029 0.049 0.058 0.000
## rmsea.ci.upper 0.072 0.083 0.064 0.075 0.090 0.096 0.052
## aic 4717.221 4753.426 4876.855 4869.284 4936.775 4900.125 4657.456
## bic 4794.972 4831.177 4954.783 4947.211 5014.702 4978.052 4735.384
## FP85 FP16A FP165 FP32A FP325
## chisq 78.569 94.921 87.625 93.047 103.022
## df 78.000 79.000 79.000 78.000 79.000
## npar 26.000 25.000 25.000 26.000 25.000
## cfi 0.999 0.957 0.977 0.963 0.946
## rmsea 0.007 0.037 0.027 0.036 0.045
## rmsea.ci.lower 0.000 0.000 0.000 0.000 0.012
## rmsea.ci.upper 0.047 0.062 0.055 0.061 0.068
## aic 4627.284 4778.940 4778.522 4756.927 4728.444
## bic 4705.211 4853.871 4853.452 4834.854 4803.374Fits across filter levels and choice of peak latency versus 50% fractional area latency should obviously not be compared since the models usually have equal degrees of freedom and they just use different variables, or more hopefully, different measurements of the same variables. Differences in DFs seem to be due to missingness. This is not comparison fit-based comparison of models that are incomparable: the fits for 50% fractional area latency were worse across the board with AR and better at 8 and 16 Hz with LM, but worse at 32 Hz. Fits for LM were much better, and were actually acceptable, but with AR, they were generally not acceptable.
The best 32 Hz fit was for peak latency. Let’s check the parameters:
summary(fit_mas_32Hz_PL, fit.measures=TRUE,standardized = TRUE,rsquare=T, ci = TRUE)## lavaan 0.6.14 ended normally after 28 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 26
##
## Number of observations 148
## Number of missing patterns 14
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 93.047 93.202
## Degrees of freedom 78 78
## P-value (Chi-square) 0.118 0.115
## Scaling correction factor 0.998
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 486.090 476.278
## Degrees of freedom 78 78
## P-value 0.000 0.000
## Scaling correction factor 1.021
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.963 0.962
## Tucker-Lewis Index (TLI) 0.963 0.962
##
## Robust Comparative Fit Index (CFI) 0.961
## Robust Tucker-Lewis Index (TLI) 0.961
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2352.463 -2352.463
## Scaling correction factor 1.093
## for the MLR correction
## Loglikelihood unrestricted model (H1) -2305.940 -2305.940
## Scaling correction factor 1.022
## for the MLR correction
##
## Akaike (AIC) 4756.927 4756.927
## Bayesian (BIC) 4834.854 4834.854
## Sample-size adjusted Bayesian (SABIC) 4752.574 4752.574
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.036 0.036
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.061 0.061
## P-value H_0: RMSEA <= 0.050 0.795 0.792
## P-value H_0: RMSEA >= 0.080 0.001 0.001
##
## Robust RMSEA 0.039
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.065
## P-value H_0: Robust RMSEA <= 0.050 0.730
## P-value H_0: Robust RMSEA >= 0.080 0.003
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.073 0.073
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## P2 =~
## zPs_P2_PL_32H_ 1.000 1.000 1.000
## zCRT_P2_PL_32H 1.000 1.000 1.000
## zSt_P2_PL_32H_ 1.000 1.000 1.000
## N2 =~
## zPs_N2_PL_32H_ 1.000 1.000 1.000
## zCRT_N2_PL_32H 1.000 1.000 1.000
## zSt_N2_PL_32H_ 1.000 1.000 1.000
## P3 =~
## zPs_P3_PL_32H_ 1.000 1.000 1.000
## zCRT_P3_PL_32H 1.000 1.000 1.000
## zSt_P3_PL_32H_ 1.000 1.000 1.000
## ERP =~
## N2 1.000 1.000 1.000
## P3 1.000 1.000 1.000
## Posner =~
## zPs_N2_PL_32H_ 1.000 1.000 1.000
## zPs_P3_PL_32H_ 1.000 1.000 1.000
## CRT =~
## zCRT_N2_PL_32H 1.000 1.000 1.000
## zCRT_P3_PL_32H 1.000 1.000 1.000
## Sternberg =~
## zSt_N2_PL_32H_ 1.000 1.000 1.000
## zSt_P3_PL_32H_ 1.000 1.000 1.000
## gf =~
## zPC 1.000 1.000 1.000
## zPS 0.937 0.181 5.174 0.000 0.582 1.292
## zM 0.775 0.146 5.322 0.000 0.489 1.060
## zC 0.581 0.133 4.359 0.000 0.320 0.842
## Std.lv Std.all
##
## 0.654 0.656
## 0.654 0.634
## 0.654 0.673
##
## 0.260 0.254
## 0.260 0.260
## 0.260 0.262
##
## 0.402 0.402
## 0.402 0.403
## 0.402 0.412
##
## 0.890 0.890
## 0.575 0.575
##
## 0.792 0.776
## 0.792 0.791
##
## 0.493 0.492
## 0.493 0.495
##
## 0.805 0.813
## 0.805 0.825
##
## 0.743 0.745
## 0.696 0.698
## 0.576 0.577
## 0.432 0.433
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Posner ~~
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## CRT ~~
## Sternberg 0.000 0.000 0.000
## ERP ~~
## gf -0.167 0.046 -3.591 0.000 -0.257 -0.076
## .N2 ~~
## gf 0.000 0.000 0.000
## .P3 ~~
## gf 0.000 0.000 0.000
## Posner ~~
## gf 0.000 0.000 0.000
## CRT ~~
## gf 0.000 0.000 0.000
## Sternberg ~~
## gf 0.000 0.000 0.000
## P2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## ERP 0.000 0.000 0.000
## .N2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .P3 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## ERP ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## P2 ~~
## gf -0.069 0.063 -1.106 0.269 -0.192 0.053
## Std.lv Std.all
##
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
##
## -0.969 -0.969
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## -0.143 -0.143
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .zPs_P2_PL_32H_ 0.000 0.000 0.000
## .zPs_N2_PL_32H_ 0.000 0.000 0.000
## .zPs_P3_PL_32H_ 0.000 0.000 0.000
## .zCRT_P2_PL_32H 0.000 0.000 0.000
## .zCRT_N2_PL_32H 0.000 0.000 0.000
## .zCRT_P3_PL_32H 0.000 0.000 0.000
## .zSt_P2_PL_32H_ 0.000 0.000 0.000
## .zSt_N2_PL_32H_ 0.000 0.000 0.000
## .zSt_P3_PL_32H_ 0.000 0.000 0.000
## .zPC 0.000 0.000 0.000
## .zPS 0.000 0.000 0.000
## .zM 0.000 0.000 0.000
## .zC 0.000 0.000 0.000
## P2 0.000 0.000 0.000
## .N2 0.000 0.000 0.000
## .P3 0.000 0.000 0.000
## ERP 0.000 0.000 0.000
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## gf 0.000 0.000 0.000
## Std.lv Std.all
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ERP (v_rp) 0.053 0.048 1.122 0.262 -0.040 0.147
## CRT (v_cr) 0.243 0.077 3.167 0.002 0.093 0.393
## Strnb (v_st) 0.649 0.102 6.334 0.000 0.448 0.849
## Posnr (v_ps) 0.627 0.106 5.901 0.000 0.419 0.836
## P2 (v_p2) 0.428 0.073 5.875 0.000 0.285 0.571
## .N2 (v_n2) 0.014 0.030 0.462 0.644 -0.046 0.074
## .P3 (v_p3) 0.108 0.039 2.752 0.006 0.031 0.185
## .zP_P2 (v_P_P2) 0.567 0.103 5.514 0.000 0.365 0.768
## .zP_N2 (v_P_N) 0.348 0.087 4.004 0.000 0.177 0.518
## .zP_P3 (v_P_P3) 0.213 0.071 3.022 0.003 0.075 0.352
## .zCRT_ (v_C_P2) 0.637 0.123 5.201 0.000 0.397 0.878
## .zCRT_ (v_C_N) 0.691 0.129 5.359 0.000 0.439 0.944
## .zCRT_ (v_C_P3) 0.588 0.139 4.230 0.000 0.316 0.861
## .zS_P2 (v_S_P2) 0.517 0.125 4.134 0.000 0.272 0.762
## .zS_N2 (v_S_N) 0.264 0.059 4.483 0.000 0.149 0.380
## .zS_P3 (v_S_P3) 0.142 0.080 1.781 0.075 -0.014 0.299
## .zPC 0.444 0.102 4.348 0.000 0.244 0.644
## .zPS 0.511 0.098 5.226 0.000 0.319 0.702
## .zM 0.663 0.098 6.758 0.000 0.471 0.855
## .zC 0.807 0.097 8.320 0.000 0.617 0.998
## gf 0.553 0.139 3.972 0.000 0.280 0.825
## Std.lv Std.all
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 0.208 0.208
## 0.669 0.669
## 0.567 0.570
## 0.348 0.334
## 0.213 0.213
## 0.637 0.598
## 0.691 0.690
## 0.588 0.592
## 0.517 0.547
## 0.264 0.270
## 0.142 0.150
## 0.444 0.445
## 0.511 0.513
## 0.663 0.667
## 0.807 0.812
## 1.000 1.000
##
## R-Square:
## Estimate
## N2 0.792
## P3 0.331
## zPs_P2_PL_32H_ 0.430
## zPs_N2_PL_32H_ 0.666
## zPs_P3_PL_32H_ 0.787
## zCRT_P2_PL_32H 0.402
## zCRT_N2_PL_32H 0.310
## zCRT_P3_PL_32H 0.408
## zSt_P2_PL_32H_ 0.453
## zSt_N2_PL_32H_ 0.730
## zSt_P3_PL_32H_ 0.850
## zPC 0.555
## zPS 0.487
## zM 0.333
## zC 0.188
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## trait_Posnr_P2 0.000 0.000 0.000
## trait_Posnr_N2 0.051 0.046 1.118 0.264 -0.039 0.141
## trait_Posnr_P3 0.053 0.047 1.140 0.254 -0.038 0.145
## trait_CRT_P2 0.000 0.000 0.000
## trait_CRT_N2 0.053 0.047 1.128 0.259 -0.039 0.146
## trait_CRT_P3 0.054 0.048 1.114 0.265 -0.041 0.149
## trt_Strnbrg_P2 0.000 0.000 0.000
## trt_Strnbrg_N2 0.055 0.050 1.091 0.275 -0.043 0.153
## trt_Strnbrg_P3 0.056 0.050 1.128 0.259 -0.041 0.154
## comp_Posner_P2 0.430 0.066 6.526 0.000 0.301 0.559
## comp_Posner_N2 0.013 0.029 0.461 0.645 -0.044 0.071
## comp_Posner_P3 0.108 0.039 2.750 0.006 0.031 0.185
## comp_CRT_P2 0.402 0.066 6.067 0.000 0.272 0.531
## comp_CRT_N2 0.014 0.031 0.459 0.646 -0.046 0.074
## comp_CRT_P3 0.109 0.038 2.873 0.004 0.035 0.183
## cmp_Strnbrg_P2 0.453 0.087 5.193 0.000 0.282 0.624
## cmp_Strnbrg_N2 0.014 0.031 0.465 0.642 -0.046 0.075
## cmp_Strnbrg_P3 0.114 0.042 2.677 0.007 0.030 0.197
## task_Posner_P2 0.000 0.000 0.000
## task_Posner_N2 0.602 0.067 9.007 0.000 0.471 0.733
## task_Posner_P3 0.626 0.077 8.148 0.000 0.475 0.776
## task_CRT_P2 0.000 0.000 0.000
## task_CRT_N2 0.243 0.066 3.651 0.000 0.112 0.373
## task_CRT_P3 0.245 0.076 3.226 0.001 0.096 0.393
## tsk_Strnbrg_P2 0.000 0.000 0.000
## tsk_Strnbrg_N2 0.662 0.057 11.525 0.000 0.549 0.774
## tsk_Strnbrg_P3 0.681 0.094 7.269 0.000 0.497 0.864
## rel_Posner_P2 0.430 0.066 6.526 0.000 0.301 0.559
## rel_Posner_N2 0.666 0.062 10.762 0.000 0.545 0.788
## rel_Posner_P3 0.787 0.072 10.947 0.000 0.646 0.928
## rel_CRT_P2 0.402 0.066 6.067 0.000 0.272 0.531
## rel_CRT_N2 0.310 0.059 5.286 0.000 0.195 0.425
## rel_CRT_P3 0.408 0.092 4.443 0.000 0.228 0.587
## rel_Strnbrg_P2 0.453 0.087 5.193 0.000 0.282 0.624
## rel_Strnbrg_N2 0.730 0.049 14.791 0.000 0.634 0.827
## rel_Strnbrg_P3 0.850 0.079 10.775 0.000 0.696 1.005
## Std.lv Std.all
## 0.000 0.000
## 0.391 0.393
## 0.347 0.347
## 0.000 0.000
## 0.345 0.345
## 0.307 0.307
## 0.000 0.000
## 0.404 0.404
## 0.356 0.355
## 0.638 0.637
## 0.081 0.082
## 0.232 0.232
## 0.611 0.626
## 0.072 0.072
## 0.205 0.205
## 0.659 0.646
## 0.084 0.084
## 0.238 0.237
## 0.000 0.000
## 0.391 0.393
## 0.347 0.347
## 0.000 0.000
## 0.345 0.345
## 0.307 0.307
## 0.000 0.000
## 0.404 0.404
## 0.356 0.355
## 0.638 0.637
## 0.864 0.869
## 0.926 0.926
## 0.611 0.626
## 0.762 0.762
## 0.819 0.818
## 0.659 0.646
## 0.893 0.891
## 0.949 0.947summary(fit_mas_32Hz_FA, fit.measures=TRUE,standardized = TRUE,rsquare=T, ci = TRUE)## lavaan 0.6.14 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 25
##
## Number of observations 148
## Number of missing patterns 15
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 103.022 103.544
## Degrees of freedom 79 79
## P-value (Chi-square) 0.036 0.033
## Scaling correction factor 0.995
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 525.386 511.388
## Degrees of freedom 78 78
## P-value 0.000 0.000
## Scaling correction factor 1.027
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.946 0.943
## Tucker-Lewis Index (TLI) 0.947 0.944
##
## Robust Comparative Fit Index (CFI) 0.945
## Robust Tucker-Lewis Index (TLI) 0.946
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2339.222 -2339.222
## Scaling correction factor 1.126
## for the MLR correction
## Loglikelihood unrestricted model (H1) -2287.711 -2287.711
## Scaling correction factor 1.027
## for the MLR correction
##
## Akaike (AIC) 4728.444 4728.444
## Bayesian (BIC) 4803.374 4803.374
## Sample-size adjusted Bayesian (SABIC) 4724.258 4724.258
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.045 0.046
## 90 Percent confidence interval - lower 0.012 0.014
## 90 Percent confidence interval - upper 0.068 0.069
## P-value H_0: RMSEA <= 0.050 0.606 0.594
## P-value H_0: RMSEA >= 0.080 0.004 0.005
##
## Robust RMSEA 0.048
## 90 Percent confidence interval - lower 0.014
## 90 Percent confidence interval - upper 0.072
## P-value H_0: Robust RMSEA <= 0.050 0.528
## P-value H_0: Robust RMSEA >= 0.080 0.012
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.076 0.076
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## P2 =~
## zPs_P2_FA_32H_ 1.000 1.000 1.000
## zCRT_P2_FA_32H 1.000 1.000 1.000
## zSt_P2_FA_32H_ 1.000 1.000 1.000
## N2 =~
## zPs_N2_FA_32H_ 1.000 1.000 1.000
## zCRT_N2_FA_32H 1.000 1.000 1.000
## zSt_N2_FA_32H_ 1.000 1.000 1.000
## P3 =~
## zPs_P3_FA_32H_ 1.000 1.000 1.000
## zCRT_P3_FA_32H 1.000 1.000 1.000
## zSt_P3_FA_32H_ 1.000 1.000 1.000
## ERP =~
## N2 1.000 1.000 1.000
## P3 1.000 1.000 1.000
## Posner =~
## zPs_N2_FA_32H_ 1.000 1.000 1.000
## zPs_P3_FA_32H_ 1.000 1.000 1.000
## CRT =~
## zCRT_N2_FA_32H 1.000 1.000 1.000
## zCRT_P3_FA_32H 1.000 1.000 1.000
## Sternberg =~
## zSt_N2_FA_32H_ 1.000 1.000 1.000
## zSt_P3_FA_32H_ 1.000 1.000 1.000
## gf =~
## zPC 1.000 1.000 1.000
## zPS 0.923 0.178 5.196 0.000 0.575 1.271
## zM 0.767 0.148 5.194 0.000 0.478 1.057
## zC 0.573 0.131 4.374 0.000 0.316 0.830
## Std.lv Std.all
##
## 0.661 0.678
## 0.661 0.631
## 0.661 0.671
##
## 0.295 0.290
## 0.295 0.293
## 0.295 0.296
##
## 0.432 0.434
## 0.432 0.439
## 0.432 0.430
##
## 1.000 1.000
## 0.682 0.682
##
## 0.790 0.778
## 0.790 0.794
##
## 0.429 0.427
## 0.429 0.437
##
## 0.821 0.825
## 0.821 0.817
##
## 0.749 0.751
## 0.691 0.693
## 0.575 0.576
## 0.429 0.431
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Posner ~~
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## CRT ~~
## Sternberg 0.000 0.000 0.000
## ERP ~~
## gf -0.179 0.050 -3.578 0.000 -0.277 -0.081
## .N2 ~~
## gf 0.000 0.000 0.000
## .P3 ~~
## gf 0.000 0.000 0.000
## Posner ~~
## gf 0.000 0.000 0.000
## CRT ~~
## gf 0.000 0.000 0.000
## Sternberg ~~
## gf 0.000 0.000 0.000
## P2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## ERP 0.000 0.000 0.000
## .N2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .P3 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## ERP ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## P2 ~~
## gf -0.073 0.063 -1.160 0.246 -0.196 0.050
## Std.lv Std.all
##
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
##
## -0.812 -0.812
##
## NaN NaN
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## NaN NaN
## NaN NaN
## NaN NaN
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## -0.147 -0.147
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .zPs_P2_FA_32H_ 0.000 0.000 0.000
## .zPs_N2_FA_32H_ 0.000 0.000 0.000
## .zPs_P3_FA_32H_ 0.000 0.000 0.000
## .zCRT_P2_FA_32H 0.000 0.000 0.000
## .zCRT_N2_FA_32H 0.000 0.000 0.000
## .zCRT_P3_FA_32H 0.000 0.000 0.000
## .zSt_P2_FA_32H_ 0.000 0.000 0.000
## .zSt_N2_FA_32H_ 0.000 0.000 0.000
## .zSt_P3_FA_32H_ 0.000 0.000 0.000
## .zPC 0.000 0.000 0.000
## .zPS 0.000 0.000 0.000
## .zM 0.000 0.000 0.000
## .zC 0.000 0.000 0.000
## P2 0.000 0.000 0.000
## .N2 0.000 0.000 0.000
## .P3 0.000 0.000 0.000
## ERP 0.000 0.000 0.000
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## gf 0.000 0.000 0.000
## Std.lv Std.all
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ERP (v_rp) 0.087 0.047 1.826 0.068 -0.006 0.180
## CRT (v_cr) 0.184 0.083 2.230 0.026 0.022 0.346
## Strnb (v_st) 0.673 0.092 7.294 0.000 0.492 0.854
## Posnr (v_ps) 0.624 0.117 5.341 0.000 0.395 0.853
## P2 (v_p2) 0.436 0.074 5.881 0.000 0.291 0.582
## .N2 0.000 0.000 0.000
## .P3 (v_p3) 0.100 0.034 2.960 0.003 0.034 0.166
## .zP_P2 (v_P_P2) 0.513 0.102 5.028 0.000 0.313 0.713
## .zP_N2 (v_P_N) 0.319 0.066 4.861 0.000 0.190 0.447
## .zP_P3 (v_P_P3) 0.178 0.076 2.355 0.019 0.030 0.327
## .zCRT_ (v_C_P2) 0.660 0.125 5.291 0.000 0.416 0.905
## .zCRT_ (v_C_N) 0.738 0.120 6.154 0.000 0.503 0.973
## .zCRT_ (v_C_P3) 0.595 0.150 3.962 0.000 0.301 0.890
## .zS_P2 (v_S_P2) 0.532 0.147 3.612 0.000 0.243 0.820
## .zS_N2 (v_S_N) 0.229 0.049 4.627 0.000 0.132 0.326
## .zS_P3 (v_S_P3) 0.149 0.067 2.218 0.027 0.017 0.280
## .zPC 0.435 0.101 4.289 0.000 0.236 0.633
## .zPS 0.517 0.096 5.373 0.000 0.329 0.706
## .zM 0.664 0.098 6.768 0.000 0.472 0.857
## .zC 0.810 0.096 8.393 0.000 0.620 0.999
## gf 0.561 0.139 4.024 0.000 0.288 0.834
## Std.lv Std.all
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 0.000 0.000
## 0.535 0.535
## 0.513 0.540
## 0.319 0.310
## 0.178 0.180
## 0.660 0.602
## 0.738 0.731
## 0.595 0.616
## 0.532 0.549
## 0.229 0.231
## 0.149 0.148
## 0.435 0.436
## 0.517 0.520
## 0.664 0.668
## 0.810 0.815
## 1.000 1.000
##
## R-Square:
## Estimate
## N2 1.000
## P3 0.465
## zPs_P2_FA_32H_ 0.460
## zPs_N2_FA_32H_ 0.690
## zPs_P3_FA_32H_ 0.820
## zCRT_P2_FA_32H 0.398
## zCRT_N2_FA_32H 0.269
## zCRT_P3_FA_32H 0.384
## zSt_P2_FA_32H_ 0.451
## zSt_N2_FA_32H_ 0.769
## zSt_P3_FA_32H_ 0.852
## zPC 0.564
## zPS 0.480
## zM 0.332
## zC 0.185
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## trait_Posnr_P2 0.000 0.000 0.000
## trait_Posnr_N2 0.084 0.047 1.784 0.074 -0.008 0.177
## trait_Posnr_P3 0.088 0.048 1.813 0.070 -0.007 0.183
## trait_CRT_P2 0.000 0.000 0.000
## trait_CRT_N2 0.086 0.047 1.824 0.068 -0.006 0.178
## trait_CRT_P3 0.090 0.051 1.778 0.075 -0.009 0.189
## trt_Strnbrg_P2 0.000 0.000 0.000
## trt_Strnbrg_N2 0.088 0.048 1.811 0.070 -0.007 0.183
## trt_Strnbrg_P3 0.086 0.046 1.860 0.063 -0.005 0.177
## comp_Posner_P2 0.460 0.072 6.394 0.000 0.319 0.601
## comp_Posner_N2 0.000 0.000 0.000
## comp_Posner_P3 0.101 0.035 2.911 0.004 0.033 0.169
## comp_CRT_P2 0.398 0.063 6.364 0.000 0.275 0.521
## comp_CRT_N2 0.000 0.000 0.000
## comp_CRT_P3 0.103 0.034 3.055 0.002 0.037 0.170
## cmp_Strnbrg_P2 0.451 0.095 4.744 0.000 0.265 0.637
## cmp_Strnbrg_N2 0.000 0.000 0.000
## cmp_Strnbrg_P3 0.099 0.034 2.887 0.004 0.032 0.166
## task_Posner_P2 0.000 0.000 0.000
## task_Posner_N2 0.606 0.065 9.385 0.000 0.479 0.733
## task_Posner_P3 0.631 0.089 7.126 0.000 0.457 0.805
## task_CRT_P2 0.000 0.000 0.000
## task_CRT_N2 0.183 0.076 2.419 0.016 0.035 0.331
## task_CRT_P3 0.191 0.086 2.223 0.026 0.023 0.359
## tsk_Strnbrg_P2 0.000 0.000 0.000
## tsk_Strnbrg_N2 0.681 0.054 12.646 0.000 0.575 0.786
## tsk_Strnbrg_P3 0.667 0.074 9.030 0.000 0.523 0.812
## rel_Posner_P2 0.460 0.072 6.394 0.000 0.319 0.601
## rel_Posner_N2 0.690 0.044 15.667 0.000 0.604 0.777
## rel_Posner_P3 0.820 0.077 10.713 0.000 0.670 0.970
## rel_CRT_P2 0.398 0.063 6.364 0.000 0.275 0.521
## rel_CRT_N2 0.269 0.066 4.043 0.000 0.138 0.399
## rel_CRT_P3 0.384 0.097 3.971 0.000 0.194 0.573
## rel_Strnbrg_P2 0.451 0.095 4.744 0.000 0.265 0.637
## rel_Strnbrg_N2 0.769 0.040 19.126 0.000 0.690 0.847
## rel_Strnbrg_P3 0.852 0.063 13.596 0.000 0.730 0.975
## Std.lv Std.all
## 0.000 0.000
## 0.431 0.433
## 0.369 0.368
## 0.000 0.000
## 0.365 0.366
## 0.319 0.317
## 0.000 0.000
## 0.449 0.448
## 0.373 0.373
## 0.661 0.649
## 0.000 0.000
## 0.197 0.197
## 0.602 0.624
## 0.000 0.000
## 0.171 0.170
## 0.653 0.645
## 0.000 0.000
## 0.199 0.199
## 0.000 0.000
## 0.431 0.433
## 0.369 0.368
## 0.000 0.000
## 0.365 0.366
## 0.319 0.317
## 0.000 0.000
## 0.449 0.448
## 0.373 0.373
## 0.661 0.649
## 0.863 0.866
## 0.934 0.934
## 0.602 0.624
## 0.731 0.732
## 0.810 0.804
## 0.653 0.645
## 0.897 0.896
## 0.945 0.945The correlations between ERP-g and first-order BIS-g were -0.969 and -0.812. The CIs are fairly wide, so these aren’t distinguishable from -1, and the former should not be distinguished from -1.
Here are the age-controlled results:
# SEM analyses controlled for Age differences ----
## SEM: AverAge reference, 8 Hz low-pass filter, peak latency (controlled for Age differences) ----
model_avg_8Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_8Hz_avg + 1*zCRT_P2_PL_8Hz_avg + 1*zSternberg_P2_PL_8Hz_avg",
"N2 =~ 1*zPosner_N2_PL_8Hz_avg + 1*zCRT_N2_PL_8Hz_avg + 1*zSternberg_N2_PL_8Hz_avg",
"P3 =~ 1*zPosner_P3_PL_8Hz_avg + 1*zCRT_P3_PL_8Hz_avg + 1*zSternberg_P3_PL_8Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_PL_8Hz_avg + 1*zPosner_N2_PL_8Hz_avg + 1*zPosner_P3_PL_8Hz_avg",
"CRT =~ 1*zCRT_P2_PL_8Hz_avg + 1*zCRT_N2_PL_8Hz_avg + 1*zCRT_P3_PL_8Hz_avg",
"Sternberg =~ 1*zSternberg_P2_PL_8Hz_avg + 1*zSternberg_N2_PL_8Hz_avg + 1*zSternberg_P3_PL_8Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_8Hz_avg ~ 0",
"zPosner_N2_PL_8Hz_avg ~ 0",
"zPosner_P3_PL_8Hz_avg ~ 0",
"zCRT_P2_PL_8Hz_avg ~ 0",
"zCRT_N2_PL_8Hz_avg ~ 0",
"zCRT_P3_PL_8Hz_avg ~ 0",
"zSternberg_P2_PL_8Hz_avg ~ 0",
"zSternberg_N2_PL_8Hz_avg ~ 0",
"zSternberg_P3_PL_8Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_8Hz_avg ~~ v_P_P2*zPosner_P2_PL_8Hz_avg",
"zPosner_N2_PL_8Hz_avg ~~ v_P_N2*zPosner_N2_PL_8Hz_avg",
"zPosner_P3_PL_8Hz_avg~~ v_P_P3*zPosner_P3_PL_8Hz_avg",
"zCRT_P2_PL_8Hz_avg ~~ v_C_P2*zCRT_P2_PL_8Hz_avg",
"zCRT_N2_PL_8Hz_avg ~~ v_C_N2*zCRT_N2_PL_8Hz_avg",
"zCRT_P3_PL_8Hz_avg ~~ v_C_P3*zCRT_P3_PL_8Hz_avg",
"zSternberg_P2_PL_8Hz_avg ~~ v_S_P2*zSternberg_P2_PL_8Hz_avg",
"zSternberg_N2_PL_8Hz_avg ~~ v_S_N2*zSternberg_N2_PL_8Hz_avg",
"zSternberg_P3_PL_8Hz_avg ~~ v_S_P3*zSternberg_P3_PL_8Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_8Hz_PL <- sem(model_avg_8Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: AverAge reference, 8 Hz low-pass filter, 50 % FA latency (controlled for Age differences) ----
model_avg_8Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_8Hz_avg + 1*zCRT_P2_FA_8Hz_avg + 1*zSternberg_P2_FA_8Hz_avg",
"N2 =~ 1*zPosner_N2_FA_8Hz_avg + 1*zCRT_N2_FA_8Hz_avg + 1*zSternberg_N2_FA_8Hz_avg",
"P3 =~ 1*zPosner_P3_FA_8Hz_avg + 1*zCRT_P3_FA_8Hz_avg + 1*zSternberg_P3_FA_8Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_FA_8Hz_avg + 1*zPosner_N2_FA_8Hz_avg + 1*zPosner_P3_FA_8Hz_avg",
"CRT =~ 1*zCRT_P2_FA_8Hz_avg + 1*zCRT_N2_FA_8Hz_avg + 1*zCRT_P3_FA_8Hz_avg",
"Sternberg =~ 1*zSternberg_P2_FA_8Hz_avg + 1*zSternberg_N2_FA_8Hz_avg + 1*zSternberg_P3_FA_8Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_8Hz_avg ~ 0",
"zPosner_N2_FA_8Hz_avg ~ 0",
"zPosner_P3_FA_8Hz_avg ~ 0",
"zCRT_P2_FA_8Hz_avg ~ 0",
"zCRT_N2_FA_8Hz_avg ~ 0",
"zCRT_P3_FA_8Hz_avg ~ 0",
"zSternberg_P2_FA_8Hz_avg ~ 0",
"zSternberg_N2_FA_8Hz_avg ~ 0",
"zSternberg_P3_FA_8Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_8Hz_avg ~~ v_P_P2*zPosner_P2_FA_8Hz_avg",
"zPosner_N2_FA_8Hz_avg ~~ v_P_N2*zPosner_N2_FA_8Hz_avg",
"zPosner_P3_FA_8Hz_avg~~ v_P_P3*zPosner_P3_FA_8Hz_avg",
"zCRT_P2_FA_8Hz_avg ~~ v_C_P2*zCRT_P2_FA_8Hz_avg",
"zCRT_N2_FA_8Hz_avg ~~ v_C_N2*zCRT_N2_FA_8Hz_avg",
"zCRT_P3_FA_8Hz_avg ~~ v_C_P3*zCRT_P3_FA_8Hz_avg",
"zSternberg_P2_FA_8Hz_avg ~~ v_S_P2*zSternberg_P2_FA_8Hz_avg",
"zSternberg_N2_FA_8Hz_avg ~~ v_S_N2*zSternberg_N2_FA_8Hz_avg",
"zSternberg_P3_FA_8Hz_avg ~~ v_S_P3*zSternberg_P3_FA_8Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_8Hz_FA <- sem(model_avg_8Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: AverAge reference, 16 Hz low-pass filter, peak latency (controlled for Age differences) ----
model_avg_16Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_16Hz_avg + 1*zCRT_P2_PL_16Hz_avg + 1*zSternberg_P2_PL_16Hz_avg",
"N2 =~ 1*zPosner_N2_PL_16Hz_avg + 1*zCRT_N2_PL_16Hz_avg + 1*zSternberg_N2_PL_16Hz_avg",
"P3 =~ 1*zPosner_P3_PL_16Hz_avg + 1*zCRT_P3_PL_16Hz_avg + 1*zSternberg_P3_PL_16Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_PL_16Hz_avg + 1*zPosner_N2_PL_16Hz_avg + 1*zPosner_P3_PL_16Hz_avg",
"CRT =~ 1*zCRT_P2_PL_16Hz_avg + 1*zCRT_N2_PL_16Hz_avg + 1*zCRT_P3_PL_16Hz_avg",
"Sternberg =~ 1*zSternberg_P2_PL_16Hz_avg + 1*zSternberg_N2_PL_16Hz_avg + 1*zSternberg_P3_PL_16Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_16Hz_avg ~ 0",
"zPosner_N2_PL_16Hz_avg ~ 0",
"zPosner_P3_PL_16Hz_avg ~ 0",
"zCRT_P2_PL_16Hz_avg ~ 0",
"zCRT_N2_PL_16Hz_avg ~ 0",
"zCRT_P3_PL_16Hz_avg ~ 0",
"zSternberg_P2_PL_16Hz_avg ~ 0",
"zSternberg_N2_PL_16Hz_avg ~ 0",
"zSternberg_P3_PL_16Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_16Hz_avg ~~ v_P_P2*zPosner_P2_PL_16Hz_avg",
"zPosner_N2_PL_16Hz_avg ~~ v_P_N2*zPosner_N2_PL_16Hz_avg",
"zPosner_P3_PL_16Hz_avg~~ v_P_P3*zPosner_P3_PL_16Hz_avg",
"zCRT_P2_PL_16Hz_avg ~~ v_C_P2*zCRT_P2_PL_16Hz_avg",
"zCRT_N2_PL_16Hz_avg ~~ v_C_N2*zCRT_N2_PL_16Hz_avg",
"zCRT_P3_PL_16Hz_avg ~~ v_C_P3*zCRT_P3_PL_16Hz_avg",
"zSternberg_P2_PL_16Hz_avg ~~ v_S_P2*zSternberg_P2_PL_16Hz_avg",
"zSternberg_N2_PL_16Hz_avg ~~ v_S_N2*zSternberg_N2_PL_16Hz_avg",
"zSternberg_P3_PL_16Hz_avg ~~ v_S_P3*zSternberg_P3_PL_16Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_16Hz_PL <- sem(model_avg_16Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: AverAge reference, 16 Hz low-pass filter, 50 % FA latency (controlled for Age differences) ----
model_avg_16Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_16Hz_avg + 1*zCRT_P2_FA_16Hz_avg + 1*zSternberg_P2_FA_16Hz_avg",
"N2 =~ 1*zPosner_N2_FA_16Hz_avg + 1*zCRT_N2_FA_16Hz_avg + 1*zSternberg_N2_FA_16Hz_avg",
"P3 =~ 1*zPosner_P3_FA_16Hz_avg + 1*zCRT_P3_FA_16Hz_avg + 1*zSternberg_P3_FA_16Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_FA_16Hz_avg + 1*zPosner_N2_FA_16Hz_avg + 1*zPosner_P3_FA_16Hz_avg",
"CRT =~ 1*zCRT_P2_FA_16Hz_avg + 1*zCRT_N2_FA_16Hz_avg + 1*zCRT_P3_FA_16Hz_avg",
"Sternberg =~ 1*zSternberg_P2_FA_16Hz_avg + 1*zSternberg_N2_FA_16Hz_avg + 1*zSternberg_P3_FA_16Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_16Hz_avg ~ 0",
"zPosner_N2_FA_16Hz_avg ~ 0",
"zPosner_P3_FA_16Hz_avg ~ 0",
"zCRT_P2_FA_16Hz_avg ~ 0",
"zCRT_N2_FA_16Hz_avg ~ 0",
"zCRT_P3_FA_16Hz_avg ~ 0",
"zSternberg_P2_FA_16Hz_avg ~ 0",
"zSternberg_N2_FA_16Hz_avg ~ 0",
"zSternberg_P3_FA_16Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_16Hz_avg ~~ v_P_P2*zPosner_P2_FA_16Hz_avg",
"zPosner_N2_FA_16Hz_avg ~~ v_P_N2*zPosner_N2_FA_16Hz_avg",
"zPosner_P3_FA_16Hz_avg~~ v_P_P3*zPosner_P3_FA_16Hz_avg",
"zCRT_P2_FA_16Hz_avg ~~ v_C_P2*zCRT_P2_FA_16Hz_avg",
"zCRT_N2_FA_16Hz_avg ~~ v_C_N2*zCRT_N2_FA_16Hz_avg",
"zCRT_P3_FA_16Hz_avg ~~ v_C_P3*zCRT_P3_FA_16Hz_avg",
"zSternberg_P2_FA_16Hz_avg ~~ v_S_P2*zSternberg_P2_FA_16Hz_avg",
"zSternberg_N2_FA_16Hz_avg ~~ v_S_N2*zSternberg_N2_FA_16Hz_avg",
"zSternberg_P3_FA_16Hz_avg ~~ v_S_P3*zSternberg_P3_FA_16Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_16Hz_FA <- sem(model_avg_16Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: AverAge reference, 32 Hz low-pass filter, peak latency (controlled for Age differences) ----
model_avg_32Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_32Hz_avg + 1*zCRT_P2_PL_32Hz_avg + 1*zSternberg_P2_PL_32Hz_avg",
"N2 =~ 1*zPosner_N2_PL_32Hz_avg + 1*zCRT_N2_PL_32Hz_avg + 1*zSternberg_N2_PL_32Hz_avg",
"P3 =~ 1*zPosner_P3_PL_32Hz_avg + 1*zCRT_P3_PL_32Hz_avg + 1*zSternberg_P3_PL_32Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_PL_32Hz_avg + 1*zPosner_N2_PL_32Hz_avg + 1*zPosner_P3_PL_32Hz_avg",
"CRT =~ 1*zCRT_P2_PL_32Hz_avg + 1*zCRT_N2_PL_32Hz_avg + 1*zCRT_P3_PL_32Hz_avg",
"Sternberg =~ 1*zSternberg_P2_PL_32Hz_avg + 1*zSternberg_N2_PL_32Hz_avg + 1*zSternberg_P3_PL_32Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_32Hz_avg ~ 0",
"zPosner_N2_PL_32Hz_avg ~ 0",
"zPosner_P3_PL_32Hz_avg ~ 0",
"zCRT_P2_PL_32Hz_avg ~ 0",
"zCRT_N2_PL_32Hz_avg ~ 0",
"zCRT_P3_PL_32Hz_avg ~ 0",
"zSternberg_P2_PL_32Hz_avg ~ 0",
"zSternberg_N2_PL_32Hz_avg ~ 0",
"zSternberg_P3_PL_32Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_32Hz_avg ~~ v_P_P2*zPosner_P2_PL_32Hz_avg",
"zPosner_N2_PL_32Hz_avg ~~ v_P_N2*zPosner_N2_PL_32Hz_avg",
"zPosner_P3_PL_32Hz_avg~~ v_P_P3*zPosner_P3_PL_32Hz_avg",
"zCRT_P2_PL_32Hz_avg ~~ v_C_P2*zCRT_P2_PL_32Hz_avg",
"zCRT_N2_PL_32Hz_avg ~~ v_C_N2*zCRT_N2_PL_32Hz_avg",
"zCRT_P3_PL_32Hz_avg ~~ v_C_P3*zCRT_P3_PL_32Hz_avg",
"zSternberg_P2_PL_32Hz_avg ~~ v_S_P2*zSternberg_P2_PL_32Hz_avg",
"zSternberg_N2_PL_32Hz_avg ~~ v_S_N2*zSternberg_N2_PL_32Hz_avg",
"zSternberg_P3_PL_32Hz_avg ~~ v_S_P3*zSternberg_P3_PL_32Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_32Hz_PL <- sem(model_avg_32Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: AverAge reference, 32 Hz low-pass filter, 50 % FA latency (controlled for Age differences) ----
model_avg_32Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_32Hz_avg + 1*zCRT_P2_FA_32Hz_avg + 1*zSternberg_P2_FA_32Hz_avg",
"N2 =~ 1*zPosner_N2_FA_32Hz_avg + 1*zCRT_N2_FA_32Hz_avg + 1*zSternberg_N2_FA_32Hz_avg",
"P3 =~ 1*zPosner_P3_FA_32Hz_avg + 1*zCRT_P3_FA_32Hz_avg + 1*zSternberg_P3_FA_32Hz_avg",
"ERP =~ 1*P2 + b_n2*N2 + b_p3*P3",
# task-specific factors
"Posner =~ 1*zPosner_P2_FA_32Hz_avg + 1*zPosner_N2_FA_32Hz_avg + 1*zPosner_P3_FA_32Hz_avg",
"CRT =~ 1*zCRT_P2_FA_32Hz_avg + 1*zCRT_N2_FA_32Hz_avg + 1*zCRT_P3_FA_32Hz_avg",
"Sternberg =~ 1*zSternberg_P2_FA_32Hz_avg + 1*zSternberg_N2_FA_32Hz_avg + 1*zSternberg_P3_FA_32Hz_avg",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*P2 + 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_32Hz_avg ~ 0",
"zPosner_N2_FA_32Hz_avg ~ 0",
"zPosner_P3_FA_32Hz_avg ~ 0",
"zCRT_P2_FA_32Hz_avg ~ 0",
"zCRT_N2_FA_32Hz_avg ~ 0",
"zCRT_P3_FA_32Hz_avg ~ 0",
"zSternberg_P2_FA_32Hz_avg ~ 0",
"zSternberg_N2_FA_32Hz_avg ~ 0",
"zSternberg_P3_FA_32Hz_avg ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_32Hz_avg ~~ v_P_P2*zPosner_P2_FA_32Hz_avg",
"zPosner_N2_FA_32Hz_avg ~~ v_P_N2*zPosner_N2_FA_32Hz_avg",
"zPosner_P3_FA_32Hz_avg~~ v_P_P3*zPosner_P3_FA_32Hz_avg",
"zCRT_P2_FA_32Hz_avg ~~ v_C_P2*zCRT_P2_FA_32Hz_avg",
"zCRT_N2_FA_32Hz_avg ~~ v_C_N2*zCRT_N2_FA_32Hz_avg",
"zCRT_P3_FA_32Hz_avg ~~ v_C_P3*zCRT_P3_FA_32Hz_avg",
"zSternberg_P2_FA_32Hz_avg ~~ v_S_P2*zSternberg_P2_FA_32Hz_avg",
"zSternberg_N2_FA_32Hz_avg ~~ v_S_N2*zSternberg_N2_FA_32Hz_avg",
"zSternberg_P3_FA_32Hz_avg ~~ v_S_P3*zSternberg_P3_FA_32Hz_avg",
# consistencies
"consistency_Posner_P2 := (v_erp)/(v_erp + v_p2 + v_posner + v_P_P2)",
"consistency_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"consistency_Posner_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"consistency_CRT_P2 := (v_erp)/(v_erp + v_p2 + v_crt + v_C_P2)",
"consistency_CRT_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"consistency_CRT_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"consistency_Sternberg_P2 := (v_erp)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"consistency_Sternberg_N2 := (b_n2^2*v_erp)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"consistency_Sternberg_P3 := (b_p3^2*v_erp)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(v_erp + v_p2 + v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(v_erp + v_p2 + v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (v_erp + v_p2 + v_posner)/(v_erp + v_p2 + v_posner + v_P_P2)",
"rel_Posner_N2 := (b_n2^2*v_erp + 0 + v_posner)/(b_n2^2*v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (b_p3^2*v_erp + v_p3 + v_posner)/(b_p3^2*v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (v_erp + v_p2 + v_crt)/(v_erp + v_p2 + v_crt + v_C_P2)",
"rel_CRT_N2 := (b_n2^2*v_erp + 0 + v_crt)/(b_n2^2*v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (b_p3^2*v_erp + v_p3 + v_crt)/(b_p3^2*v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (v_erp + v_p2 + v_sternberg)/(v_erp + v_p2 + v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (b_n2^2*v_erp +0 + v_sternberg)/(b_n2^2*v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (b_p3^2*v_erp + v_p3 + v_sternberg)/(b_p3^2*v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_avg_32Hz_FA <- sem(model_avg_32Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 8 Hz low-pass filter, peak latency (controlled for Age differences) ----
model_mas_8Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_8Hz_mas + 1*zCRT_P2_PL_8Hz_mas + 1*zSternberg_P2_PL_8Hz_mas",
"N2 =~ 1*zPosner_N2_PL_8Hz_mas + 1*zCRT_N2_PL_8Hz_mas + 1*zSternberg_N2_PL_8Hz_mas",
"P3 =~ 1*zPosner_P3_PL_8Hz_mas + 1*zCRT_P3_PL_8Hz_mas + 1*zSternberg_P3_PL_8Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_PL_8Hz_mas + 1*zPosner_P3_PL_8Hz_mas",
"CRT =~ 1*zCRT_N2_PL_8Hz_mas + 1*zCRT_P3_PL_8Hz_mas",
"Sternberg =~ 1*zSternberg_N2_PL_8Hz_mas + 1*zSternberg_P3_PL_8Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_8Hz_mas ~ 0",
"zPosner_N2_PL_8Hz_mas ~ 0",
"zPosner_P3_PL_8Hz_mas ~ 0",
"zCRT_P2_PL_8Hz_mas ~ 0",
"zCRT_N2_PL_8Hz_mas ~ 0",
"zCRT_P3_PL_8Hz_mas ~ 0",
"zSternberg_P2_PL_8Hz_mas ~ 0",
"zSternberg_N2_PL_8Hz_mas ~ 0",
"zSternberg_P3_PL_8Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ v_n2*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_8Hz_mas ~~ v_P_P2*zPosner_P2_PL_8Hz_mas",
"zPosner_N2_PL_8Hz_mas ~~ v_P_N2*zPosner_N2_PL_8Hz_mas",
"zPosner_P3_PL_8Hz_mas~~ v_P_P3*zPosner_P3_PL_8Hz_mas",
"zCRT_P2_PL_8Hz_mas ~~ v_C_P2*zCRT_P2_PL_8Hz_mas",
"zCRT_N2_PL_8Hz_mas ~~ v_C_N2*zCRT_N2_PL_8Hz_mas",
"zCRT_P3_PL_8Hz_mas ~~ v_C_P3*zCRT_P3_PL_8Hz_mas",
"zSternberg_P2_PL_8Hz_mas ~~ v_S_P2*zSternberg_P2_PL_8Hz_mas",
"zSternberg_N2_PL_8Hz_mas ~~ v_S_N2*zSternberg_N2_PL_8Hz_mas",
"zSternberg_P3_PL_8Hz_mas ~~ v_S_P3*zSternberg_P3_PL_8Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + v_n2 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + v_n2 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (v_n2)/(v_erp + v_n2 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (v_n2)/(v_erp + v_n2 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (v_n2)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + v_n2 + v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + v_n2 + v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +v_n2 + v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_8Hz_PL <- sem(model_mas_8Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 8 Hz low-pass filter, 50 % FA latency (controlled for Age differences) ----
model_mas_8Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_8Hz_mas + 1*zCRT_P2_FA_8Hz_mas + 1*zSternberg_P2_FA_8Hz_mas",
"N2 =~ 1*zPosner_N2_FA_8Hz_mas + 1*zCRT_N2_FA_8Hz_mas + 1*zSternberg_N2_FA_8Hz_mas",
"P3 =~ 1*zPosner_P3_FA_8Hz_mas + 1*zCRT_P3_FA_8Hz_mas + 1*zSternberg_P3_FA_8Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_FA_8Hz_mas + 1*zPosner_P3_FA_8Hz_mas",
"CRT =~ 1*zCRT_N2_FA_8Hz_mas + 1*zCRT_P3_FA_8Hz_mas",
"Sternberg =~ 1*zSternberg_N2_FA_8Hz_mas + 1*zSternberg_P3_FA_8Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_8Hz_mas ~ 0",
"zPosner_N2_FA_8Hz_mas ~ 0",
"zPosner_P3_FA_8Hz_mas ~ 0",
"zCRT_P2_FA_8Hz_mas ~ 0",
"zCRT_N2_FA_8Hz_mas ~ 0",
"zCRT_P3_FA_8Hz_mas ~ 0",
"zSternberg_P2_FA_8Hz_mas ~ 0",
"zSternberg_N2_FA_8Hz_mas ~ 0",
"zSternberg_P3_FA_8Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ v_n2*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_8Hz_mas ~~ v_P_P2*zPosner_P2_FA_8Hz_mas",
"zPosner_N2_FA_8Hz_mas ~~ v_P_N2*zPosner_N2_FA_8Hz_mas",
"zPosner_P3_FA_8Hz_mas~~ v_P_P3*zPosner_P3_FA_8Hz_mas",
"zCRT_P2_FA_8Hz_mas ~~ v_C_P2*zCRT_P2_FA_8Hz_mas",
"zCRT_N2_FA_8Hz_mas ~~ v_C_N2*zCRT_N2_FA_8Hz_mas",
"zCRT_P3_FA_8Hz_mas ~~ v_C_P3*zCRT_P3_FA_8Hz_mas",
"zSternberg_P2_FA_8Hz_mas ~~ v_S_P2*zSternberg_P2_FA_8Hz_mas",
"zSternberg_N2_FA_8Hz_mas ~~ v_S_N2*zSternberg_N2_FA_8Hz_mas",
"zSternberg_P3_FA_8Hz_mas ~~ v_S_P3*zSternberg_P3_FA_8Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + v_n2 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + v_n2 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (v_n2)/(v_erp + v_n2 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (v_n2)/(v_erp + v_n2 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (v_n2)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + v_n2 + v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + v_n2 + v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +v_n2 + v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_8Hz_FA <- sem(model_mas_8Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 16 Hz low-pass filter, peak latency (controlled for Age differences) ----
model_mas_16Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_16Hz_mas + 1*zCRT_P2_PL_16Hz_mas + 1*zSternberg_P2_PL_16Hz_mas",
"N2 =~ 1*zPosner_N2_PL_16Hz_mas + 1*zCRT_N2_PL_16Hz_mas + 1*zSternberg_N2_PL_16Hz_mas",
"P3 =~ 1*zPosner_P3_PL_16Hz_mas + 1*zCRT_P3_PL_16Hz_mas + 1*zSternberg_P3_PL_16Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_PL_16Hz_mas + 1*zPosner_P3_PL_16Hz_mas",
"CRT =~ 1*zCRT_N2_PL_16Hz_mas + 1*zCRT_P3_PL_16Hz_mas",
"Sternberg =~ 1*zSternberg_N2_PL_16Hz_mas + 1*zSternberg_P3_PL_16Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_16Hz_mas ~ 0",
"zPosner_N2_PL_16Hz_mas ~ 0",
"zPosner_P3_PL_16Hz_mas ~ 0",
"zCRT_P2_PL_16Hz_mas ~ 0",
"zCRT_N2_PL_16Hz_mas ~ 0",
"zCRT_P3_PL_16Hz_mas ~ 0",
"zSternberg_P2_PL_16Hz_mas ~ 0",
"zSternberg_N2_PL_16Hz_mas ~ 0",
"zSternberg_P3_PL_16Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_16Hz_mas ~~ v_P_P2*zPosner_P2_PL_16Hz_mas",
"zPosner_N2_PL_16Hz_mas ~~ v_P_N2*zPosner_N2_PL_16Hz_mas",
"zPosner_P3_PL_16Hz_mas~~ v_P_P3*zPosner_P3_PL_16Hz_mas",
"zCRT_P2_PL_16Hz_mas ~~ v_C_P2*zCRT_P2_PL_16Hz_mas",
"zCRT_N2_PL_16Hz_mas ~~ v_C_N2*zCRT_N2_PL_16Hz_mas",
"zCRT_P3_PL_16Hz_mas ~~ v_C_P3*zCRT_P3_PL_16Hz_mas",
"zSternberg_P2_PL_16Hz_mas ~~ v_S_P2*zSternberg_P2_PL_16Hz_mas",
"zSternberg_N2_PL_16Hz_mas ~~ v_S_N2*zSternberg_N2_PL_16Hz_mas",
"zSternberg_P3_PL_16Hz_mas ~~ v_S_P3*zSternberg_P3_PL_16Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + 0 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + 0 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +0 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + 0 + v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + 0 + v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +0 + v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_16Hz_PL <- sem(model_mas_16Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 16 Hz low-pass filter, 50 % FA latency (controlled for Age differences) ----
model_mas_16Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_16Hz_mas + 1*zCRT_P2_FA_16Hz_mas + 1*zSternberg_P2_FA_16Hz_mas",
"N2 =~ 1*zPosner_N2_FA_16Hz_mas + 1*zCRT_N2_FA_16Hz_mas + 1*zSternberg_N2_FA_16Hz_mas",
"P3 =~ 1*zPosner_P3_FA_16Hz_mas + 1*zCRT_P3_FA_16Hz_mas + 1*zSternberg_P3_FA_16Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_FA_16Hz_mas + 1*zPosner_P3_FA_16Hz_mas",
"CRT =~ 1*zCRT_N2_FA_16Hz_mas + 1*zCRT_P3_FA_16Hz_mas",
"Sternberg =~ 1*zSternberg_N2_FA_16Hz_mas + 1*zSternberg_P3_FA_16Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_16Hz_mas ~ 0",
"zPosner_N2_FA_16Hz_mas ~ 0",
"zPosner_P3_FA_16Hz_mas ~ 0",
"zCRT_P2_FA_16Hz_mas ~ 0",
"zCRT_N2_FA_16Hz_mas ~ 0",
"zCRT_P3_FA_16Hz_mas ~ 0",
"zSternberg_P2_FA_16Hz_mas ~ 0",
"zSternberg_N2_FA_16Hz_mas ~ 0",
"zSternberg_P3_FA_16Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_16Hz_mas ~~ v_P_P2*zPosner_P2_FA_16Hz_mas",
"zPosner_N2_FA_16Hz_mas ~~ v_P_N2*zPosner_N2_FA_16Hz_mas",
"zPosner_P3_FA_16Hz_mas~~ v_P_P3*zPosner_P3_FA_16Hz_mas",
"zCRT_P2_FA_16Hz_mas ~~ v_C_P2*zCRT_P2_FA_16Hz_mas",
"zCRT_N2_FA_16Hz_mas ~~ v_C_N2*zCRT_N2_FA_16Hz_mas",
"zCRT_P3_FA_16Hz_mas ~~ v_C_P3*zCRT_P3_FA_16Hz_mas",
"zSternberg_P2_FA_16Hz_mas ~~ v_S_P2*zSternberg_P2_FA_16Hz_mas",
"zSternberg_N2_FA_16Hz_mas ~~ v_S_N2*zSternberg_N2_FA_16Hz_mas",
"zSternberg_P3_FA_16Hz_mas ~~ v_S_P3*zSternberg_P3_FA_16Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + 0 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + 0 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +0 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + 0 + v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + 0 + v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +0 + v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_16Hz_FA <- sem(model_mas_16Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 32 Hz low-pass filter, peak latency (controlled for Age differences) ----
model_mas_32Hz_PL <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_PL_32Hz_mas + 1*zCRT_P2_PL_32Hz_mas + 1*zSternberg_P2_PL_32Hz_mas",
"N2 =~ 1*zPosner_N2_PL_32Hz_mas + 1*zCRT_N2_PL_32Hz_mas + 1*zSternberg_N2_PL_32Hz_mas",
"P3 =~ 1*zPosner_P3_PL_32Hz_mas + 1*zCRT_P3_PL_32Hz_mas + 1*zSternberg_P3_PL_32Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_PL_32Hz_mas + 1*zPosner_P3_PL_32Hz_mas",
"CRT =~ 1*zCRT_N2_PL_32Hz_mas + 1*zCRT_P3_PL_32Hz_mas",
"Sternberg =~ 1*zSternberg_N2_PL_32Hz_mas + 1*zSternberg_P3_PL_32Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_PL_32Hz_mas ~ 0",
"zPosner_N2_PL_32Hz_mas ~ 0",
"zPosner_P3_PL_32Hz_mas ~ 0",
"zCRT_P2_PL_32Hz_mas ~ 0",
"zCRT_N2_PL_32Hz_mas ~ 0",
"zCRT_P3_PL_32Hz_mas ~ 0",
"zSternberg_P2_PL_32Hz_mas ~ 0",
"zSternberg_N2_PL_32Hz_mas ~ 0",
"zSternberg_P3_PL_32Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ v_n2*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_PL_32Hz_mas ~~ v_P_P2*zPosner_P2_PL_32Hz_mas",
"zPosner_N2_PL_32Hz_mas ~~ v_P_N2*zPosner_N2_PL_32Hz_mas",
"zPosner_P3_PL_32Hz_mas~~ v_P_P3*zPosner_P3_PL_32Hz_mas",
"zCRT_P2_PL_32Hz_mas ~~ v_C_P2*zCRT_P2_PL_32Hz_mas",
"zCRT_N2_PL_32Hz_mas ~~ v_C_N2*zCRT_N2_PL_32Hz_mas",
"zCRT_P3_PL_32Hz_mas ~~ v_C_P3*zCRT_P3_PL_32Hz_mas",
"zSternberg_P2_PL_32Hz_mas ~~ v_S_P2*zSternberg_P2_PL_32Hz_mas",
"zSternberg_N2_PL_32Hz_mas ~~ v_S_N2*zSternberg_N2_PL_32Hz_mas",
"zSternberg_P3_PL_32Hz_mas ~~ v_S_P3*zSternberg_P3_PL_32Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + v_n2 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + v_n2 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (v_n2)/(v_erp + v_n2 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (v_n2)/(v_erp + v_n2 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (v_n2)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + v_n2 + v_posner)/(v_erp + v_n2 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + v_n2 + v_crt)/(v_erp + v_n2 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +v_n2 + v_sternberg)/(v_erp +v_n2 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_32Hz_PL <- sem(model_mas_32Hz_PL, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
## SEM: Linked mastoids reference, 32 Hz low-pass filter, 50 % FA latency (controlled for Age differences) ----
model_mas_32Hz_FA <- c(# hierarchical model
"P2 =~ 1*zPosner_P2_FA_32Hz_mas + 1*zCRT_P2_FA_32Hz_mas + 1*zSternberg_P2_FA_32Hz_mas",
"N2 =~ 1*zPosner_N2_FA_32Hz_mas + 1*zCRT_N2_FA_32Hz_mas + 1*zSternberg_N2_FA_32Hz_mas",
"P3 =~ 1*zPosner_P3_FA_32Hz_mas + 1*zCRT_P3_FA_32Hz_mas + 1*zSternberg_P3_FA_32Hz_mas",
"ERP =~ 1*N2 + 1*P3",
# task-specific factors
"Posner =~ 1*zPosner_N2_FA_32Hz_mas + 1*zPosner_P3_FA_32Hz_mas",
"CRT =~ 1*zCRT_N2_FA_32Hz_mas + 1*zCRT_P3_FA_32Hz_mas",
"Sternberg =~ 1*zSternberg_N2_FA_32Hz_mas + 1*zSternberg_P3_FA_32Hz_mas",
"Posner ~~ 0*CRT + 0*Sternberg",
"CRT ~~ 0*Sternberg",
# cognitive abilities
"gf =~ zPC + zPS + zM + zC",
# control for Age differences
"ERP ~ Age",
"gf ~ Age",
# structural model
"ERP ~~ gf",
"gf ~~ 0*N2 + 0*P3",
"gf ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P2 ~~ 0*Posner + 0*CRT + 0*Sternberg + 0*ERP",
"N2 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"P3 ~~ 0*Posner + 0*CRT + 0*Sternberg",
"ERP ~~ 0*Posner + 0*CRT + 0*Sternberg",
# fix intercepts to zero
"zPosner_P2_FA_32Hz_mas ~ 0",
"zPosner_N2_FA_32Hz_mas ~ 0",
"zPosner_P3_FA_32Hz_mas ~ 0",
"zCRT_P2_FA_32Hz_mas ~ 0",
"zCRT_N2_FA_32Hz_mas ~ 0",
"zCRT_P3_FA_32Hz_mas ~ 0",
"zSternberg_P2_FA_32Hz_mas ~ 0",
"zSternberg_N2_FA_32Hz_mas ~ 0",
"zSternberg_P3_FA_32Hz_mas ~ 0",
"zPC ~ 0",
"zPS ~ 0",
"zM ~ 0",
"zC ~ 0",
# variances
"ERP ~~ v_erp*ERP",
"CRT ~~ v_crt*CRT",
"Sternberg ~~ v_sternberg*Sternberg",
"Posner ~~ v_posner*Posner",
"P2 ~~ v_p2*P2",
"N2 ~~ 0*N2",
"P3 ~~ v_p3*P3",
"zPosner_P2_FA_32Hz_mas ~~ v_P_P2*zPosner_P2_FA_32Hz_mas",
"zPosner_N2_FA_32Hz_mas ~~ v_P_N2*zPosner_N2_FA_32Hz_mas",
"zPosner_P3_FA_32Hz_mas~~ v_P_P3*zPosner_P3_FA_32Hz_mas",
"zCRT_P2_FA_32Hz_mas ~~ v_C_P2*zCRT_P2_FA_32Hz_mas",
"zCRT_N2_FA_32Hz_mas ~~ v_C_N2*zCRT_N2_FA_32Hz_mas",
"zCRT_P3_FA_32Hz_mas ~~ v_C_P3*zCRT_P3_FA_32Hz_mas",
"zSternberg_P2_FA_32Hz_mas ~~ v_S_P2*zSternberg_P2_FA_32Hz_mas",
"zSternberg_N2_FA_32Hz_mas ~~ v_S_N2*zSternberg_N2_FA_32Hz_mas",
"zSternberg_P3_FA_32Hz_mas ~~ v_S_P3*zSternberg_P3_FA_32Hz_mas",
# trait specifities
"trait_Posner_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"trait_Posner_N2 := (v_erp)/(v_erp + 0 + v_posner + v_P_N2)",
"trait_Posner_P3 := (v_erp)/(v_erp + v_p3 + v_posner + v_P_P3)",
"trait_CRT_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"trait_CRT_N2 := (v_erp)/(v_erp + 0 + v_crt + v_C_N2)",
"trait_CRT_P3 := (v_erp)/(v_erp + v_p3 + v_crt + v_C_P3)",
"trait_Sternberg_P2 := (0*v_erp)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"trait_Sternberg_N2 := (v_erp)/(v_erp +0 + v_sternberg + v_S_N2)",
"trait_Sternberg_P3 := (v_erp)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# component specifities
"comp_Posner_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"comp_Posner_N2 := (0)/(v_erp + 0 + v_posner + v_P_N2)",
"comp_Posner_P3 := (v_p3)/(v_erp + v_p3 + v_posner + v_P_P3)",
"comp_CRT_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"comp_CRT_N2 := (0)/(v_erp + 0 + v_crt + v_C_N2)",
"comp_CRT_P3 := (v_p3)/(v_erp + v_p3 + v_crt + v_C_P3)",
"comp_Sternberg_P2 := (v_p2)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"comp_Sternberg_N2 := (0)/(v_erp +0 + v_sternberg + v_S_N2)",
"comp_Sternberg_P3 := (v_p3)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# task specifities
"task_Posner_P2 := (0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"task_Posner_N2 := (v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"task_Posner_P3 := (v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"task_CRT_P2 := (0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"task_CRT_N2 := (v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"task_CRT_P3 := (v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"task_Sternberg_P2 := (0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"task_Sternberg_N2 := (v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"task_Sternberg_P3 := (v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)",
# reliabilities
"rel_Posner_P2 := (0*v_erp + v_p2 + 0*v_posner)/(0*v_erp + v_p2 + 0*v_posner + v_P_P2)",
"rel_Posner_N2 := (v_erp + 0 + v_posner)/(v_erp + 0 + v_posner + v_P_N2)",
"rel_Posner_P3 := (v_erp + v_p3 + v_posner)/(v_erp + v_p3 + v_posner + v_P_P3)",
"rel_CRT_P2 := (0*v_erp + v_p2 + 0*v_crt)/(0*v_erp + v_p2 + 0*v_crt + v_C_P2)",
"rel_CRT_N2 := (v_erp + 0 + v_crt)/(v_erp + 0 + v_crt + v_C_N2)",
"rel_CRT_P3 := (v_erp + v_p3 + v_crt)/(v_erp + v_p3 + v_crt + v_C_P3)",
"rel_Sternberg_P2 := (0*v_erp + v_p2 + 0*v_sternberg)/(0*v_erp + v_p2 + 0*v_sternberg + v_S_P2)",
"rel_Sternberg_N2 := (v_erp +0 + v_sternberg)/(v_erp +0 + v_sternberg + v_S_N2)",
"rel_Sternberg_P3 := (v_erp + v_p3 + v_sternberg)/(v_erp + v_p3 + v_sternberg + v_S_P3)")
fit_mas_32Hz_FA <- sem(model_mas_32Hz_FA, data = data, estimator = "MLR" , missing="fiml", std.lv = FALSE)
round(cbind(RP8A = fitMeasures(fit_avg_8Hz_PL, FITM),
RP85 = fitMeasures(fit_avg_8Hz_FA, FITM),
RP16A = fitMeasures(fit_avg_16Hz_PL, FITM),
RP165 = fitMeasures(fit_avg_16Hz_FA, FITM),
RP32A = fitMeasures(fit_avg_32Hz_PL, FITM),
RP325 = fitMeasures(fit_avg_32Hz_FA, FITM),
FP8A = fitMeasures(fit_mas_8Hz_PL, FITM),
FP85 = fitMeasures(fit_mas_8Hz_FA, FITM),
FP16A = fitMeasures(fit_mas_16Hz_PL, FITM),
FP165 = fitMeasures(fit_mas_16Hz_FA, FITM),
FP32A = fitMeasures(fit_mas_32Hz_PL, FITM),
FP325 = fitMeasures(fit_mas_32Hz_FA, FITM)), 3)## RP8A RP85 RP16A RP165 RP32A RP325 FP8A
## chisq 156.576 181.949 154.501 177.899 178.192 197.743 143.141
## df 89.000 89.000 89.000 89.000 89.000 89.000 90.000
## npar 28.000 28.000 28.000 28.000 28.000 28.000 27.000
## cfi 0.843 0.781 0.814 0.750 0.712 0.703 0.879
## rmsea 0.072 0.084 0.071 0.082 0.082 0.091 0.063
## rmsea.ci.lower 0.053 0.066 0.051 0.064 0.065 0.074 0.043
## rmsea.ci.upper 0.090 0.101 0.089 0.100 0.100 0.108 0.082
## aic 4716.327 4751.682 4876.352 4867.857 4937.026 4900.024 4667.536
## bic 4800.249 4835.604 4960.274 4951.779 5020.948 4983.946 4748.461
## FP85 FP16A FP165 FP32A FP325
## chisq 142.549 167.119 160.838 142.264 167.071
## df 90.000 91.000 91.000 90.000 91.000
## npar 27.000 26.000 26.000 27.000 26.000
## cfi 0.889 0.822 0.836 0.883 0.848
## rmsea 0.063 0.075 0.072 0.063 0.075
## rmsea.ci.lower 0.042 0.057 0.053 0.042 0.057
## rmsea.ci.upper 0.082 0.093 0.090 0.082 0.093
## aic 4636.916 4784.147 4784.586 4757.291 4728.877
## bic 4717.841 4862.074 4862.513 4838.215 4806.805summary(fit_mas_32Hz_PL, fit.measures=TRUE,standardized = TRUE,rsquare=T, ci = TRUE)## lavaan 0.6.14 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 27
##
## Number of observations 148
## Number of missing patterns 14
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 142.264 139.311
## Degrees of freedom 90 90
## P-value (Chi-square) 0.000 0.001
## Scaling correction factor 1.021
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 536.943 516.084
## Degrees of freedom 91 91
## P-value 0.000 0.000
## Scaling correction factor 1.040
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.883 0.884
## Tucker-Lewis Index (TLI) 0.881 0.883
##
## Robust Comparative Fit Index (CFI) 0.884
## Robust Tucker-Lewis Index (TLI) 0.882
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2351.645 -2351.645
## Scaling correction factor 1.091
## for the MLR correction
## Loglikelihood unrestricted model (H1) -2280.513 -2280.513
## Scaling correction factor 1.037
## for the MLR correction
##
## Akaike (AIC) 4757.291 4757.291
## Bayesian (BIC) 4838.215 4838.215
## Sample-size adjusted Bayesian (SABIC) 4752.770 4752.770
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.063 0.061
## 90 Percent confidence interval - lower 0.042 0.040
## 90 Percent confidence interval - upper 0.082 0.080
## P-value H_0: RMSEA <= 0.050 0.143 0.178
## P-value H_0: RMSEA >= 0.080 0.067 0.048
##
## Robust RMSEA 0.065
## 90 Percent confidence interval - lower 0.043
## 90 Percent confidence interval - upper 0.085
## P-value H_0: Robust RMSEA <= 0.050 0.119
## P-value H_0: Robust RMSEA >= 0.080 0.118
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.092 0.092
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## P2 =~
## zPs_P2_PL_32H_ 1.000 1.000 1.000
## zCRT_P2_PL_32H 1.000 1.000 1.000
## zSt_P2_PL_32H_ 1.000 1.000 1.000
## N2 =~
## zPs_N2_PL_32H_ 1.000 1.000 1.000
## zCRT_N2_PL_32H 1.000 1.000 1.000
## zSt_N2_PL_32H_ 1.000 1.000 1.000
## P3 =~
## zPs_P3_PL_32H_ 1.000 1.000 1.000
## zCRT_P3_PL_32H 1.000 1.000 1.000
## zSt_P3_PL_32H_ 1.000 1.000 1.000
## ERP =~
## N2 1.000 1.000 1.000
## P3 1.000 1.000 1.000
## Posner =~
## zPs_N2_PL_32H_ 1.000 1.000 1.000
## zPs_P3_PL_32H_ 1.000 1.000 1.000
## CRT =~
## zCRT_N2_PL_32H 1.000 1.000 1.000
## zCRT_P3_PL_32H 1.000 1.000 1.000
## Sternberg =~
## zSt_N2_PL_32H_ 1.000 1.000 1.000
## zSt_P3_PL_32H_ 1.000 1.000 1.000
## gf =~
## zPC 1.000 1.000 1.000
## zPS 0.910 0.168 5.415 0.000 0.580 1.239
## zM 0.767 0.144 5.335 0.000 0.485 1.049
## zC 0.554 0.127 4.376 0.000 0.306 0.802
## Std.lv Std.all
##
## 0.653 0.658
## 0.653 0.631
## 0.653 0.672
##
## 0.257 0.252
## 0.257 0.257
## 0.257 0.259
##
## 0.402 0.402
## 0.402 0.404
## 0.402 0.411
##
## 0.893 0.893
## 0.571 0.571
##
## 0.790 0.776
## 0.790 0.790
##
## 0.492 0.492
## 0.492 0.494
##
## 0.806 0.815
## 0.806 0.825
##
## 0.743 0.751
## 0.676 0.682
## 0.570 0.575
## 0.411 0.414
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ERP ~
## Age 0.001 0.002 0.895 0.371 -0.002 0.004
## gf ~
## Age -0.004 0.002 -1.541 0.123 -0.008 0.001
## Std.lv Std.all
##
## 0.006 0.082
##
## -0.005 -0.068
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Posner ~~
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## CRT ~~
## Sternberg 0.000 0.000 0.000
## .ERP ~~
## .gf -0.159 0.043 -3.682 0.000 -0.244 -0.075
## .N2 ~~
## .gf 0.000 0.000 0.000
## .P3 ~~
## .gf 0.000 0.000 0.000
## Posner ~~
## .gf 0.000 0.000 0.000
## CRT ~~
## .gf 0.000 0.000 0.000
## Sternberg ~~
## .gf 0.000 0.000 0.000
## P2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .ERP 0.000 0.000 0.000
## .N2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .P3 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .ERP ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## Std.lv Std.all
##
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
##
## -0.941 -0.941
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .zPs_P2_PL_32H_ 0.000 0.000 0.000
## .zPs_N2_PL_32H_ 0.000 0.000 0.000
## .zPs_P3_PL_32H_ 0.000 0.000 0.000
## .zCRT_P2_PL_32H 0.000 0.000 0.000
## .zCRT_N2_PL_32H 0.000 0.000 0.000
## .zCRT_P3_PL_32H 0.000 0.000 0.000
## .zSt_P2_PL_32H_ 0.000 0.000 0.000
## .zSt_N2_PL_32H_ 0.000 0.000 0.000
## .zSt_P3_PL_32H_ 0.000 0.000 0.000
## .zPC 0.000 0.000 0.000
## .zPS 0.000 0.000 0.000
## .zM 0.000 0.000 0.000
## .zC 0.000 0.000 0.000
## P2 0.000 0.000 0.000
## .N2 0.000 0.000 0.000
## .P3 0.000 0.000 0.000
## .ERP 0.000 0.000 0.000
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .gf 0.000 0.000 0.000
## Std.lv Std.all
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .ERP (v_rp) 0.052 0.048 1.087 0.277 -0.042 0.147
## CRT (v_cr) 0.242 0.077 3.161 0.002 0.092 0.392
## Strnb (v_st) 0.650 0.103 6.314 0.000 0.449 0.852
## Posnr (v_ps) 0.625 0.108 5.789 0.000 0.413 0.836
## P2 (v_p2) 0.427 0.072 5.895 0.000 0.285 0.569
## .N2 (v_n2) 0.013 0.031 0.431 0.667 -0.047 0.074
## .P3 (v_p3) 0.109 0.040 2.754 0.006 0.031 0.186
## .zP_P2 (v_P_P2) 0.560 0.101 5.553 0.000 0.363 0.758
## .zP_N2 (v_P_N) 0.348 0.087 4.012 0.000 0.178 0.517
## .zP_P3 (v_P_P3) 0.214 0.071 3.018 0.003 0.075 0.352
## .zCRT_ (v_C_P2) 0.645 0.124 5.224 0.000 0.403 0.887
## .zCRT_ (v_C_N) 0.693 0.130 5.344 0.000 0.439 0.947
## .zCRT_ (v_C_P3) 0.587 0.139 4.218 0.000 0.314 0.860
## .zS_P2 (v_S_P2) 0.517 0.124 4.171 0.000 0.274 0.761
## .zS_N2 (v_S_N) 0.264 0.059 4.477 0.000 0.148 0.379
## .zS_P3 (v_S_P3) 0.143 0.080 1.790 0.073 -0.014 0.300
## .zPC 0.426 0.099 4.292 0.000 0.231 0.620
## .zPS 0.524 0.094 5.559 0.000 0.339 0.708
## .zM 0.659 0.098 6.739 0.000 0.467 0.851
## .zC 0.819 0.098 8.347 0.000 0.627 1.011
## .gf 0.549 0.130 4.212 0.000 0.294 0.805
## Std.lv Std.all
## 0.993 0.993
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 0.202 0.202
## 0.674 0.674
## 0.560 0.568
## 0.348 0.335
## 0.214 0.214
## 0.645 0.602
## 0.693 0.692
## 0.587 0.593
## 0.517 0.548
## 0.264 0.269
## 0.143 0.150
## 0.426 0.436
## 0.524 0.534
## 0.659 0.670
## 0.819 0.829
## 0.995 0.995
##
## R-Square:
## Estimate
## ERP 0.007
## N2 0.798
## P3 0.326
## zPs_P2_PL_32H_ 0.432
## zPs_N2_PL_32H_ 0.665
## zPs_P3_PL_32H_ 0.786
## zCRT_P2_PL_32H 0.398
## zCRT_N2_PL_32H 0.308
## zCRT_P3_PL_32H 0.407
## zSt_P2_PL_32H_ 0.452
## zSt_N2_PL_32H_ 0.731
## zSt_P3_PL_32H_ 0.850
## zPC 0.564
## zPS 0.466
## zM 0.330
## zC 0.171
## gf 0.005
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## trait_Posnr_P2 0.000 0.000 0.000
## trait_Posnr_N2 0.050 0.046 1.088 0.277 -0.040 0.141
## trait_Posnr_P3 0.052 0.047 1.108 0.268 -0.040 0.145
## trait_CRT_P2 0.000 0.000 0.000
## trait_CRT_N2 0.052 0.048 1.090 0.276 -0.042 0.146
## trait_CRT_P3 0.053 0.049 1.083 0.279 -0.043 0.148
## trt_Strnbrg_P2 0.000 0.000 0.000
## trt_Strnbrg_N2 0.053 0.050 1.057 0.291 -0.046 0.152
## trt_Strnbrg_P3 0.055 0.050 1.091 0.275 -0.044 0.153
## comp_Posner_P2 0.432 0.066 6.533 0.000 0.303 0.562
## comp_Posner_N2 0.013 0.030 0.429 0.668 -0.046 0.071
## comp_Posner_P3 0.109 0.040 2.754 0.006 0.031 0.186
## comp_CRT_P2 0.398 0.065 6.089 0.000 0.270 0.526
## comp_CRT_N2 0.013 0.031 0.429 0.668 -0.047 0.074
## comp_CRT_P3 0.110 0.038 2.884 0.004 0.035 0.185
## cmp_Strnbrg_P2 0.452 0.087 5.216 0.000 0.282 0.622
## cmp_Strnbrg_N2 0.014 0.031 0.434 0.664 -0.048 0.075
## cmp_Strnbrg_P3 0.114 0.043 2.674 0.007 0.030 0.198
## task_Posner_P2 0.000 0.000 0.000
## task_Posner_N2 0.602 0.067 9.017 0.000 0.471 0.733
## task_Posner_P3 0.625 0.077 8.120 0.000 0.474 0.776
## task_CRT_P2 0.000 0.000 0.000
## task_CRT_N2 0.242 0.066 3.638 0.000 0.112 0.372
## task_CRT_P3 0.244 0.076 3.217 0.001 0.095 0.393
## tsk_Strnbrg_P2 0.000 0.000 0.000
## tsk_Strnbrg_N2 0.664 0.058 11.505 0.000 0.551 0.777
## tsk_Strnbrg_P3 0.681 0.093 7.299 0.000 0.498 0.864
## rel_Posner_P2 0.432 0.066 6.533 0.000 0.303 0.562
## rel_Posner_N2 0.665 0.062 10.684 0.000 0.543 0.787
## rel_Posner_P3 0.786 0.073 10.793 0.000 0.643 0.929
## rel_CRT_P2 0.398 0.065 6.089 0.000 0.270 0.526
## rel_CRT_N2 0.307 0.059 5.200 0.000 0.192 0.423
## rel_CRT_P3 0.407 0.092 4.401 0.000 0.226 0.588
## rel_Strnbrg_P2 0.452 0.087 5.216 0.000 0.282 0.622
## rel_Strnbrg_N2 0.731 0.050 14.726 0.000 0.634 0.828
## rel_Strnbrg_P3 0.850 0.079 10.794 0.000 0.696 1.005
## Std.lv Std.all
## 0.000 0.000
## 0.391 0.393
## 0.345 0.345
## 0.000 0.000
## 0.344 0.344
## 0.305 0.305
## 0.000 0.000
## 0.404 0.403
## 0.353 0.353
## 0.641 0.638
## 0.079 0.080
## 0.234 0.234
## 0.608 0.624
## 0.070 0.070
## 0.207 0.207
## 0.659 0.646
## 0.082 0.082
## 0.240 0.239
## 0.000 0.000
## 0.393 0.395
## 0.347 0.347
## 0.000 0.000
## 0.346 0.346
## 0.307 0.307
## 0.000 0.000
## 0.407 0.406
## 0.356 0.355
## 0.641 0.638
## 0.863 0.868
## 0.926 0.926
## 0.608 0.624
## 0.760 0.760
## 0.820 0.818
## 0.659 0.646
## 0.893 0.891
## 0.949 0.947summary(fit_mas_32Hz_FA, fit.measures=TRUE,standardized = TRUE,rsquare=T, ci = TRUE)## lavaan 0.6.14 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 26
##
## Number of observations 148
## Number of missing patterns 15
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 167.071 166.179
## Degrees of freedom 91 91
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.005
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 591.001 572.083
## Degrees of freedom 91 91
## P-value 0.000 0.000
## Scaling correction factor 1.033
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.848 0.844
## Tucker-Lewis Index (TLI) 0.848 0.844
##
## Robust Comparative Fit Index (CFI) 0.847
## Robust Tucker-Lewis Index (TLI) 0.847
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2338.439 -2338.439
## Scaling correction factor 1.121
## for the MLR correction
## Loglikelihood unrestricted model (H1) -2254.903 -2254.903
## Scaling correction factor 1.031
## for the MLR correction
##
## Akaike (AIC) 4728.877 4728.877
## Bayesian (BIC) 4806.805 4806.805
## Sample-size adjusted Bayesian (SABIC) 4724.524 4724.524
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.075 0.075
## 90 Percent confidence interval - lower 0.057 0.056
## 90 Percent confidence interval - upper 0.093 0.092
## P-value H_0: RMSEA <= 0.050 0.014 0.015
## P-value H_0: RMSEA >= 0.080 0.341 0.326
##
## Robust RMSEA 0.079
## 90 Percent confidence interval - lower 0.060
## 90 Percent confidence interval - upper 0.098
## P-value H_0: Robust RMSEA <= 0.050 0.009
## P-value H_0: Robust RMSEA >= 0.080 0.475
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.099 0.099
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## P2 =~
## zPs_P2_FA_32H_ 1.000 1.000 1.000
## zCRT_P2_FA_32H 1.000 1.000 1.000
## zSt_P2_FA_32H_ 1.000 1.000 1.000
## N2 =~
## zPs_N2_FA_32H_ 1.000 1.000 1.000
## zCRT_N2_FA_32H 1.000 1.000 1.000
## zSt_N2_FA_32H_ 1.000 1.000 1.000
## P3 =~
## zPs_P3_FA_32H_ 1.000 1.000 1.000
## zCRT_P3_FA_32H 1.000 1.000 1.000
## zSt_P3_FA_32H_ 1.000 1.000 1.000
## ERP =~
## N2 1.000 1.000 1.000
## P3 1.000 1.000 1.000
## Posner =~
## zPs_N2_FA_32H_ 1.000 1.000 1.000
## zPs_P3_FA_32H_ 1.000 1.000 1.000
## CRT =~
## zCRT_N2_FA_32H 1.000 1.000 1.000
## zCRT_P3_FA_32H 1.000 1.000 1.000
## Sternberg =~
## zSt_N2_FA_32H_ 1.000 1.000 1.000
## zSt_P3_FA_32H_ 1.000 1.000 1.000
## gf =~
## zPC 1.000 1.000 1.000
## zPS 0.897 0.164 5.469 0.000 0.575 1.218
## zM 0.758 0.145 5.241 0.000 0.475 1.042
## zC 0.549 0.126 4.361 0.000 0.302 0.796
## Std.lv Std.all
##
## 0.660 0.680
## 0.660 0.628
## 0.660 0.672
##
## 0.292 0.288
## 0.292 0.291
## 0.292 0.293
##
## 0.430 0.433
## 0.430 0.439
## 0.430 0.428
##
## 1.000 1.000
## 0.678 0.678
##
## 0.788 0.779
## 0.788 0.794
##
## 0.426 0.425
## 0.426 0.435
##
## 0.823 0.827
## 0.823 0.818
##
## 0.748 0.757
## 0.671 0.678
## 0.567 0.572
## 0.411 0.413
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ERP ~
## Age 0.002 0.002 1.036 0.300 -0.001 0.005
## gf ~
## Age -0.004 0.002 -1.530 0.126 -0.008 0.001
## Std.lv Std.all
##
## 0.006 0.077
##
## -0.005 -0.067
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## Posner ~~
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## CRT ~~
## Sternberg 0.000 0.000 0.000
## .ERP ~~
## .gf -0.171 0.046 -3.682 0.000 -0.262 -0.080
## .N2 ~~
## .gf 0.000 0.000 0.000
## .P3 ~~
## .gf 0.000 0.000 0.000
## Posner ~~
## .gf 0.000 0.000 0.000
## CRT ~~
## .gf 0.000 0.000 0.000
## Sternberg ~~
## .gf 0.000 0.000 0.000
## P2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .ERP 0.000 0.000 0.000
## .N2 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .P3 ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .ERP ~~
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## Std.lv Std.all
##
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
##
## -0.788 -0.788
##
## NaN NaN
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## NaN NaN
## NaN NaN
## NaN NaN
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .zPs_P2_FA_32H_ 0.000 0.000 0.000
## .zPs_N2_FA_32H_ 0.000 0.000 0.000
## .zPs_P3_FA_32H_ 0.000 0.000 0.000
## .zCRT_P2_FA_32H 0.000 0.000 0.000
## .zCRT_N2_FA_32H 0.000 0.000 0.000
## .zCRT_P3_FA_32H 0.000 0.000 0.000
## .zSt_P2_FA_32H_ 0.000 0.000 0.000
## .zSt_N2_FA_32H_ 0.000 0.000 0.000
## .zSt_P3_FA_32H_ 0.000 0.000 0.000
## .zPC 0.000 0.000 0.000
## .zPS 0.000 0.000 0.000
## .zM 0.000 0.000 0.000
## .zC 0.000 0.000 0.000
## P2 0.000 0.000 0.000
## .N2 0.000 0.000 0.000
## .P3 0.000 0.000 0.000
## .ERP 0.000 0.000 0.000
## Posner 0.000 0.000 0.000
## CRT 0.000 0.000 0.000
## Sternberg 0.000 0.000 0.000
## .gf 0.000 0.000 0.000
## Std.lv Std.all
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
## 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .ERP (v_rp) 0.085 0.048 1.777 0.076 -0.009 0.178
## CRT (v_cr) 0.182 0.083 2.201 0.028 0.020 0.344
## Strnb (v_st) 0.677 0.093 7.280 0.000 0.495 0.859
## Posnr (v_ps) 0.621 0.118 5.270 0.000 0.390 0.852
## P2 (v_p2) 0.436 0.074 5.894 0.000 0.291 0.581
## .N2 0.000 0.000 0.000
## .P3 (v_p3) 0.100 0.034 2.951 0.003 0.034 0.166
## .zP_P2 (v_P_P2) 0.507 0.100 5.069 0.000 0.311 0.704
## .zP_N2 (v_P_N) 0.318 0.065 4.870 0.000 0.190 0.446
## .zP_P3 (v_P_P3) 0.179 0.076 2.362 0.018 0.030 0.327
## .zCRT_ (v_C_P2) 0.668 0.126 5.310 0.000 0.422 0.915
## .zCRT_ (v_C_N) 0.740 0.121 6.122 0.000 0.503 0.977
## .zCRT_ (v_C_P3) 0.594 0.151 3.945 0.000 0.299 0.889
## .zS_P2 (v_S_P2) 0.531 0.146 3.636 0.000 0.245 0.817
## .zS_N2 (v_S_N) 0.228 0.049 4.623 0.000 0.131 0.324
## .zS_P3 (v_S_P3) 0.150 0.067 2.228 0.026 0.018 0.281
## .zPC 0.417 0.098 4.270 0.000 0.226 0.608
## .zPS 0.530 0.093 5.726 0.000 0.348 0.711
## .zM 0.662 0.098 6.740 0.000 0.469 0.854
## .zC 0.819 0.098 8.382 0.000 0.628 1.011
## .gf 0.557 0.131 4.267 0.000 0.301 0.813
## Std.lv Std.all
## 0.994 0.994
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 1.000 1.000
## 0.000 0.000
## 0.540 0.540
## 0.507 0.538
## 0.318 0.311
## 0.179 0.181
## 0.668 0.605
## 0.740 0.735
## 0.594 0.618
## 0.531 0.549
## 0.228 0.230
## 0.150 0.148
## 0.417 0.427
## 0.530 0.541
## 0.662 0.673
## 0.819 0.829
## 0.995 0.995
##
## R-Square:
## Estimate
## ERP 0.006
## N2 1.000
## P3 0.460
## zPs_P2_FA_32H_ 0.462
## zPs_N2_FA_32H_ 0.689
## zPs_P3_FA_32H_ 0.819
## zCRT_P2_FA_32H 0.395
## zCRT_N2_FA_32H 0.265
## zCRT_P3_FA_32H 0.382
## zSt_P2_FA_32H_ 0.451
## zSt_N2_FA_32H_ 0.770
## zSt_P3_FA_32H_ 0.852
## zPC 0.573
## zPS 0.459
## zM 0.327
## zC 0.171
## gf 0.005
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## trait_Posnr_P2 0.000 0.000 0.000
## trait_Posnr_N2 0.083 0.047 1.748 0.080 -0.010 0.175
## trait_Posnr_P3 0.086 0.048 1.774 0.076 -0.009 0.181
## trait_CRT_P2 0.000 0.000 0.000
## trait_CRT_N2 0.084 0.048 1.767 0.077 -0.009 0.177
## trait_CRT_P3 0.088 0.051 1.741 0.082 -0.011 0.187
## trt_Strnbrg_P2 0.000 0.000 0.000
## trt_Strnbrg_N2 0.085 0.049 1.760 0.078 -0.010 0.181
## trt_Strnbrg_P3 0.084 0.046 1.804 0.071 -0.007 0.174
## comp_Posner_P2 0.462 0.072 6.440 0.000 0.322 0.603
## comp_Posner_N2 0.000 0.000 0.000
## comp_Posner_P3 0.102 0.035 2.910 0.004 0.033 0.170
## comp_CRT_P2 0.395 0.062 6.383 0.000 0.274 0.516
## comp_CRT_N2 0.000 0.000 0.000
## comp_CRT_P3 0.104 0.034 3.065 0.002 0.038 0.171
## cmp_Strnbrg_P2 0.451 0.095 4.759 0.000 0.265 0.637
## cmp_Strnbrg_N2 0.000 0.000 0.000
## cmp_Strnbrg_P3 0.099 0.034 2.871 0.004 0.031 0.166
## task_Posner_P2 0.000 0.000 0.000
## task_Posner_N2 0.607 0.065 9.363 0.000 0.480 0.734
## task_Posner_P3 0.631 0.089 7.109 0.000 0.457 0.805
## task_CRT_P2 0.000 0.000 0.000
## task_CRT_N2 0.181 0.076 2.387 0.017 0.032 0.329
## task_CRT_P3 0.189 0.086 2.196 0.028 0.020 0.358
## tsk_Strnbrg_P2 0.000 0.000 0.000
## tsk_Strnbrg_N2 0.684 0.054 12.688 0.000 0.579 0.790
## tsk_Strnbrg_P3 0.670 0.074 9.067 0.000 0.525 0.814
## rel_Posner_P2 0.462 0.072 6.440 0.000 0.322 0.603
## rel_Posner_N2 0.689 0.045 15.438 0.000 0.602 0.777
## rel_Posner_P3 0.819 0.077 10.639 0.000 0.668 0.969
## rel_CRT_P2 0.395 0.062 6.383 0.000 0.274 0.516
## rel_CRT_N2 0.265 0.068 3.899 0.000 0.132 0.398
## rel_CRT_P3 0.382 0.097 3.915 0.000 0.191 0.573
## rel_Strnbrg_P2 0.451 0.095 4.759 0.000 0.265 0.637
## rel_Strnbrg_N2 0.770 0.040 19.298 0.000 0.692 0.848
## rel_Strnbrg_P3 0.852 0.063 13.576 0.000 0.729 0.975
## Std.lv Std.all
## 0.000 0.000
## 0.430 0.431
## 0.366 0.366
## 0.000 0.000
## 0.364 0.364
## 0.318 0.315
## 0.000 0.000
## 0.447 0.447
## 0.370 0.371
## 0.663 0.650
## 0.000 0.000
## 0.199 0.199
## 0.599 0.623
## 0.000 0.000
## 0.173 0.171
## 0.653 0.646
## 0.000 0.000
## 0.201 0.201
## 0.000 0.000
## 0.432 0.434
## 0.369 0.368
## 0.000 0.000
## 0.366 0.366
## 0.320 0.317
## 0.000 0.000
## 0.450 0.450
## 0.373 0.373
## 0.663 0.650
## 0.862 0.865
## 0.934 0.933
## 0.599 0.623
## 0.729 0.731
## 0.810 0.804
## 0.653 0.646
## 0.898 0.897
## 0.944 0.945Controlling for age made all model fits unacceptable. As in Schubert et al.’s presented results, the effect of age on the relationship between ERP-g and BIS-g was minuscule, as they became -0.941 and -0.788.
Schubert et al. provided some fascinating data. It seems that intelligence can be measured from ERPs. So to answer the age-old question “What do the intelligence tests test?” We could say “neural latency”. But this should be considered carefully because that might make it seem like reduced neural latency is what drives intelligence, and this is not the case. Intelligence may be influenced by neural latency, but despite neural latency measures being capable of measuring it practically perfectly, successfully modifying speed does not impact intelligence (e.g., Stough et al., 1995; Schubert et al., 2018). The same is true for working memory and interventions on it (Sala et al., 2019).
This is very theoretically informative. If the causal structure of intelligence is validated and interventions produce real gains and they are not gains that transfer to g, we are dealing with a trait that demands reflective measurement. So, all measures of cognitive ability and sufficiently-advanced measures of potential underlying causes or influences on it may just be influenced by it. In other words, we have measurement with sufficiently-advanced indication coupled with unidirectional causation.
I will be using these estimates for my just one g meta-analysis.
Schubert, A.-L., Loeffler, C., Hagemann, D., & Sadus, K. (2023). How robust is the relationship between neural processing speed and cognitive abilities? Psychophysiology, 60(2), e14165. https://doi.org/10.1111/psyp.14165
Source: https://onlinelibrary.wiley.com/doi/10.1111/psyp.14165 Code: https://osf.io/7qruk
I am immensely thankful that Schubert et al. provided their code and data for reanalysis.
Valerius, S., & Sparfeldt, J. R. (2014). Consistent g- as well as consistent verbal-, numerical- and figural-factors in nested factor models? Confirmatory factor analyses using three test batteries. Intelligence, 44, 120–133. https://doi.org/10.1016/j.intell.2014.04.003
Brody, N. (2003). Construct validation of the Sternberg Triarchic Abilities Test: Comment and reanalysis. Intelligence, 31(4), 319–329. https://doi.org/10.1016/S0160-2896(01)00087-3
Brody, N. (2003). What Sternberg should have concluded. Intelligence, 31(4), 339–342. https://doi.org/10.1016/S0160-2896(02)00190-3
Koke, L. C., & Vernon, P. A. (2003). The Sternberg Triarchic Abilities Test (STAT) as a measure of academic achievement and general intelligence. Personality and Individual Differences, 35(8), 1803–1807. https://doi.org/10.1016/S0191-8869(03)00005-9
Johnson, W., Nijenhuis, J. te, & Bouchard, T. J. (2008). Still just 1 g: Consistent results from five test batteries. Intelligence, 36(1), 81–95. https://doi.org/10.1016/j.intell.2007.06.001
Yang, P., Fan, C., Wang, M., & Li, L. (2017). A Comparative Study of Average, Linked Mastoid, and REST References for ERP Components Acquired during fMRI. Frontiers in Neuroscience, 11. https://www.frontiersin.org/articles/10.3389/fnins.2017.00247
Dong, L., Liu, X., Zhao, L., Lai, Y., Gong, D., Liu, T., & Yao, D. (2019). A Comparative Study of Different EEG Reference Choices for Event-Related Potentials Extracted by Independent Component Analysis. Frontiers in Neuroscience, 13. https://www.frontiersin.org/articles/10.3389/fnins.2019.01068
Yao, D., Qin, Y., Hu, S., Dong, L., Bringas Vega, M. L., & Valdés Sosa, P. A. (2019). Which Reference Should We Use for EEG and ERP practice? Brain Topography, 32(4), 530–549. https://doi.org/10.1007/s10548-019-00707-x
Stough, C., Mangan, G., Bates, T., Kerkin, B., Pellett, O., & Frank, N. (1995). Effects of nicotine on perceptual speed. Psychopharmacology, 119(3), 305–310. https://doi.org/10.1007/BF02246296
Schubert, A.-L., Hagemann, D., Frischkorn, G. T., & Herpertz, S. C. (2018). Faster, but not smarter: An experimental analysis of the relationship between mental speed and mental abilities. Intelligence, 71, 66–75. https://doi.org/10.1016/j.intell.2018.10.005
Sala, G., Aksayli, N. D., Tatlidil, K. S., Tatsumi, T., Gondo, Y., & Gobet, F. (2019). Near and Far Transfer in Cognitive Training: A Second-Order Meta-Analysis. Collabra: Psychology, 5(1), 18. https://doi.org/10.1525/collabra.203 (It should also be noted that interventions produce fadeouts.)
sessionInfo()## R version 4.2.2 (2022-10-31 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 19045)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.utf8
## [2] LC_CTYPE=English_United States.utf8
## [3] LC_MONETARY=English_United States.utf8
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.utf8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] psych_2.2.9 lavaan_0.6-14 pacman_0.5.1
##
## loaded via a namespace (and not attached):
## [1] rstudioapi_0.14 knitr_1.42 MASS_7.3-58.1 mnormt_2.1.1
## [5] pbivnorm_0.6.0 lattice_0.20-45 R6_2.5.1 rlang_1.0.6
## [9] quadprog_1.5-8 fastmap_1.1.0 tools_4.2.2 parallel_4.2.2
## [13] grid_4.2.2 nlme_3.1-160 xfun_0.37 cli_3.6.0
## [17] jquerylib_0.1.4 htmltools_0.5.4 yaml_2.3.7 digest_0.6.31
## [21] vctrs_0.5.2 sass_0.4.5 cachem_1.0.6 evaluate_0.20
## [25] rmarkdown_2.20 compiler_4.2.2 bslib_0.4.2 stats4_4.2.2
## [29] jsonlite_1.8.4