assignment3
anjie
5/10/2021
library(psych)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4
## ✓ tibble 3.1.0 ✓ dplyr 1.0.5
## ✓ tidyr 1.1.1 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.4.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x ggplot2::%+%() masks psych::%+%()
## x ggplot2::alpha() masks psych::alpha()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(ggplot2)
library(corrplot)## corrplot 0.84 loadedlibrary(lavaan)## This is lavaan 0.6-8
## lavaan is FREE software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2covlibrary(semPlot)
library(here)## here() starts at /Users/caoanjie/Desktop/projects/psych262/assignment_3Reading in data
d <- read_csv(here("data/new_rt.csv"))## Parsed with column specification:
## cols(
## subject = col_character(),
## block_number = col_double(),
## block_type = col_character(),
## trial_number = col_double(),
## item_type = col_character(),
## trial_type = col_character(),
## trial_complexity = col_character(),
## item_id = col_character(),
## rt = col_double(),
## exposure_type = col_character(),
## half = col_character(),
## block_deviant_number = col_double(),
## trial_type_index = col_character(),
## first_dev_position = col_double(),
## second_dev_position = col_double()
## )data preprocessing
Here the data processing separates the original dataframe into two halves. The four factors of interests are the type of trials: background simple trial, background complex trial, deviant simple trial, and deviant complex trial. I separated the looking time data by half to examine whether the factorial invariances hold throughout the
d_first_half <- d %>%
filter(block_number < 6) %>%
group_by(subject, trial_complexity, item_type) %>%
summarise(rt = mean(rt)) %>%
unite(trial_type, trial_complexity, item_type) %>%
pivot_wider(names_from = trial_type,
values_from = rt,
names_prefix = "1_")## `summarise()` has grouped output by 'subject', 'trial_complexity'. You can override using the `.groups` argument.d_second_half <- d %>%
filter(block_number > 6 | block_number == 6) %>%
group_by(subject, trial_complexity, item_type) %>%
summarise(rt = mean(rt)) %>%
unite(trial_type, trial_complexity, item_type) %>%
pivot_wider(names_from = trial_type,
values_from = rt,
names_prefix = "2_")## `summarise()` has grouped output by 'subject', 'trial_complexity'. You can override using the `.groups` argument.d_processed <- left_join(d_first_half,
d_second_half,
by = "subject") %>%
drop_na() %>%
janitor::clean_names()describe(d_processed[, -1])## vars n mean sd median trimmed mad
## x1_complex_background 1 158 4347.57 2985.79 3849.77 4005.00 2688.26
## x1_complex_dissimilar_deviant 2 158 5001.80 3553.25 4288.57 4610.72 3177.34
## x1_simple_background 3 158 3916.27 2916.20 2986.15 3537.82 2429.04
## x1_simple_dissimilar_deviant 4 158 4321.52 3942.97 3342.61 3673.98 2781.77
## x2_complex_background 5 158 2895.70 1920.90 2544.34 2711.47 2014.10
## x2_complex_dissimilar_deviant 6 158 3480.01 3050.52 2876.37 3031.52 2491.88
## x2_simple_background 7 158 2629.62 2149.83 2032.67 2311.78 1674.62
## x2_simple_dissimilar_deviant 8 158 2820.68 2579.64 2232.56 2446.80 2346.30
## min max range skew kurtosis se
## x1_complex_background 184.19 15799.46 15615.27 1.31 2.33 237.54
## x1_complex_dissimilar_deviant 44.94 16776.66 16731.71 1.01 0.73 282.68
## x1_simple_background 225.62 16662.87 16437.25 1.44 2.58 232.00
## x1_simple_dissimilar_deviant 93.99 24488.67 24394.68 2.12 6.00 313.69
## x2_complex_background 183.11 9676.58 9493.48 0.92 0.67 152.82
## x2_complex_dissimilar_deviant 112.91 17792.69 17679.78 1.86 4.92 242.69
## x2_simple_background 163.92 12435.71 12271.78 1.87 4.78 171.03
## x2_simple_dissimilar_deviant 78.57 13313.68 13235.11 1.39 2.02 205.23corrplot(cor(d_processed[,-1]), order = "original", tl.col='black', tl.cex=.75) 
# configural invariance model
configural <- '
# Define the latent factors.
first_half_rt =~ NA*x1_complex_background + lambda1*x1_complex_background + x1_complex_dissimilar_deviant + x1_simple_background + x1_simple_dissimilar_deviant
second_half_rt =~NA*x2_complex_background + lambda1*x2_complex_background + x2_complex_dissimilar_deviant + x2_simple_background + x2_simple_dissimilar_deviant
# Intercepts
x1_complex_background ~ i1*1
x1_complex_dissimilar_deviant ~ 1
x1_simple_background ~ 1
x1_simple_dissimilar_deviant ~ 1
x2_complex_background ~ i1*1
x2_complex_dissimilar_deviant ~ 1
x2_simple_background ~ 1
x2_simple_dissimilar_deviant ~ 1
# Unique Variances
x1_complex_background ~~ x1_complex_background
x1_complex_dissimilar_deviant ~~ x1_complex_dissimilar_deviant
x1_simple_background ~~ x1_simple_background
x1_simple_dissimilar_deviant ~~ x1_simple_dissimilar_deviant
x2_complex_background ~~ x2_complex_background
x2_complex_dissimilar_deviant ~~ x2_complex_dissimilar_deviant
x2_simple_background ~~ x2_simple_background
x2_simple_dissimilar_deviant ~~ x2_simple_dissimilar_deviant
# Latent Variable Means
first_half_rt ~ 0*1
second_half_rt ~ 1
# Latent Variable Variances and Covariance
first_half_rt ~~ 1*first_half_rt
second_half_rt ~~ second_half_rt
first_half_rt ~~ second_half_rt
'fit_configural <- cfa(configural, data = d_processed, mimic = "mplus")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some observed variances are larger than 1000000
## lavaan NOTE: use varTable(fit) to investigate## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= -1.604676e-09) is smaller than zero. This may be a symptom that
## the model is not identified.summary(fit_configural, fit.measures = TRUE)## lavaan 0.6-8 ended normally after 226 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 27
## Number of equality constraints 2
##
## Number of observations 158
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 92.043
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 711.134
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.893
## Tucker-Lewis Index (TLI) 0.842
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11520.427
## Loglikelihood unrestricted model (H1) -11474.406
##
## Akaike (AIC) 23090.855
## Bayesian (BIC) 23167.420
## Sample-size adjusted Bayesian (BIC) 23088.283
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.156
## 90 Percent confidence interval - lower 0.125
## 90 Percent confidence interval - upper 0.189
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.054
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## first_half_rt =~
## x1_cmp_ (lmb1) 2252.806 207.933 10.834 0.000
## x1_cm__ 2729.991 245.118 11.137 0.000
## x1_smp_ 2265.608 199.989 11.329 0.000
## x1_sm__ 2917.764 277.109 10.529 0.000
## second_half_rt =~
## x2_cmp_ (lmb1) 2252.806 207.933 10.834 0.000
## x2_cm__ 3199.752 436.219 7.335 0.000
## x2_smp_ 2399.933 316.163 7.591 0.000
## x2_sm__ 2831.382 378.332 7.484 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## first_half_rt ~~
## second_half_rt 0.562 0.067 8.341 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_ (i1) 4347.569 236.784 18.361 0.000
## .x1_cmpl__ 5001.802 281.786 17.750 0.000
## .x1_smpl_b 3916.266 231.265 16.934 0.000
## .x1_smpl__ 4321.519 312.692 13.820 0.000
## .x2_cmplx_ (i1) 4347.569 236.784 18.361 0.000
## .x2_cmpl__ 5542.159 447.105 12.396 0.000
## .x2_smpl_b 4176.310 325.091 12.847 0.000
## .x2_smpl__ 4645.422 387.602 11.985 0.000
## frst_hlf_ 0.000
## scnd_hlf_ -0.644 0.110 -5.874 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_bckgr 3783408.245 0.123 30677043.728 0.000
## .x1_cmplx_dssm_ 5092843.263 0.029 176555677.856 0.000
## .x1_smpl_bckgrn 3317433.381 0.047 70933293.867 0.000
## .x1_smpl_dssml_ 6935285.200 0.015 450673522.922 0.000
## .x2_cmplx_bckgr 1255962.988 0.459 2733515.769 0.000
## .x2_cmplx_dssm_ 4383793.132 0.047 92437556.001 0.000
## .x2_smpl_bckgrn 1856821.298 0.158 11772348.015 0.000
## .x2_smpl_dssml_ 2804703.972 0.121 23114397.414 0.000
## first_half_rt 1.000
## second_half_rt 0.475 0.100 4.738 0.000semPaths(fit_configural, what="est",
sizeLat = 7, sizeMan = 7, edge.label.cex = .75)
configural invariance model with correlated uniqueness
corrunique <- '
# Define the latent factors.
first_half_rt =~ NA*x1_complex_background + lambda1*x1_complex_background + x1_complex_dissimilar_deviant + x1_simple_background + x1_simple_dissimilar_deviant
second_half_rt =~NA*x2_complex_background + lambda1*x2_complex_background + x2_complex_dissimilar_deviant + x2_simple_background + x2_simple_dissimilar_deviant
# Intercepts
x1_complex_background ~ i1*1
x1_complex_dissimilar_deviant ~ 1
x1_simple_background ~ 1
x1_simple_dissimilar_deviant ~ 1
x2_complex_background ~ i1*1
x2_complex_dissimilar_deviant ~ 1
x2_simple_background ~ 1
x2_simple_dissimilar_deviant ~ 1
# Unique Variances and Covariances
x1_complex_background ~~ x1_complex_background
x1_complex_dissimilar_deviant ~~ x1_complex_dissimilar_deviant
x1_simple_background ~~ x1_simple_background
x1_simple_dissimilar_deviant ~~ x1_simple_dissimilar_deviant
x2_complex_background ~~ x2_complex_background
x2_complex_dissimilar_deviant ~~ x2_complex_dissimilar_deviant
x2_simple_background ~~ x2_simple_background
x2_simple_dissimilar_deviant ~~ x2_simple_dissimilar_deviant
x1_complex_background ~~ x2_complex_background
x1_complex_dissimilar_deviant ~~ x2_complex_dissimilar_deviant
x1_simple_background ~~ x2_simple_background
x1_simple_dissimilar_deviant ~~ x2_simple_dissimilar_deviant
# Latent Variable Means
first_half_rt ~ 0*1
second_half_rt ~ 1
# Latent Variable Variances and Covariance
first_half_rt ~~ 1*first_half_rt
second_half_rt ~~ second_half_rt
first_half_rt ~~ second_half_rt
'fit_corrunique <- cfa(corrunique, data = d_processed, mimic = "mplus")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some observed variances are larger than 1000000
## lavaan NOTE: use varTable(fit) to investigate## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= -8.183856e-09) is smaller than zero. This may be a symptom that
## the model is not identified.summary(fit_corrunique, fit.measures = TRUE)## lavaan 0.6-8 ended normally after 227 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 31
## Number of equality constraints 2
##
## Number of observations 158
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 92.043
## Degrees of freedom 15
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 711.134
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.887
## Tucker-Lewis Index (TLI) 0.789
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11520.427
## Loglikelihood unrestricted model (H1) -11474.406
##
## Akaike (AIC) 23098.855
## Bayesian (BIC) 23187.670
## Sample-size adjusted Bayesian (BIC) 23095.871
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.180
## 90 Percent confidence interval - lower 0.146
## 90 Percent confidence interval - upper 0.217
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.054
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## first_half_rt =~
## x1_cmp_ (lmb1) 2252.807 207.933 10.834 0.000
## x1_cm__ 2729.992 245.118 11.137 0.000
## x1_smp_ 2265.609 199.989 11.329 0.000
## x1_sm__ 2917.765 277.109 10.529 0.000
## second_half_rt =~
## x2_cmp_ (lmb1) 2252.807 207.933 10.834 0.000
## x2_cm__ 3199.756 436.220 7.335 0.000
## x2_smp_ 2399.934 316.164 7.591 0.000
## x2_sm__ 2831.385 378.332 7.484 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .x1_complex_background ~~
## .x2_cmplx_bckgr 0.743 0.188 3.952 0.000
## .x1_complex_dissimilar_deviant ~~
## .x2_cmplx_dssm_ 0.493 0.018 27.265 0.000
## .x1_simple_background ~~
## .x2_smpl_bckgrn 0.756 0.068 11.100 0.000
## .x1_simple_dissimilar_deviant ~~
## .x2_smpl_dssml_ 0.489 0.017 29.080 0.000
## first_half_rt ~~
## second_half_rt 0.562 0.067 8.341 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_ (i1) 4347.569 236.784 18.361 0.000
## .x1_cmpl__ 5001.803 281.786 17.750 0.000
## .x1_smpl_b 3916.266 231.265 16.934 0.000
## .x1_smpl__ 4321.520 312.692 13.820 0.000
## .x2_cmplx_ (i1) 4347.569 236.784 18.361 0.000
## .x2_cmpl__ 5542.160 447.105 12.396 0.000
## .x2_smpl_b 4176.311 325.091 12.847 0.000
## .x2_smpl__ 4645.423 387.602 11.985 0.000
## frst_hlf_ 0.000
## scnd_hlf_ -0.644 0.110 -5.874 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_bckgr 3783407.800 0.123 30747903.856 0.000
## .x1_cmplx_dssm_ 5092843.877 0.028 179657753.169 0.000
## .x1_smpl_bckgrn 3317434.225 0.046 71606383.547 0.000
## .x1_smpl_dssml_ 6935280.360 0.015 450377019.404 0.000
## .x2_cmplx_bckgr 1255963.078 0.461 2726648.720 0.000
## .x2_cmplx_dssm_ 4383794.462 0.048 92225942.188 0.000
## .x2_smpl_bckgrn 1856820.366 0.158 11769475.236 0.000
## .x2_smpl_dssml_ 2804703.557 0.121 23172034.788 0.000
## first_half_rt 1.000
## second_half_rt 0.475 0.100 4.738 0.000semPaths(fit_corrunique, what="est",
sizeLat = 7, sizeMan = 7, edge.label.cex = .75)
weak invariance
weak <- '
# Define the latent factors.
first_half_rt =~ NA*x1_complex_background + lambda1*x1_complex_background + lambda2*x1_complex_dissimilar_deviant + lambda3*x1_simple_background + lambda4*x1_simple_dissimilar_deviant
second_half_rt =~NA*x2_complex_background + lambda1*x2_complex_background + lambda2*x2_complex_dissimilar_deviant + lambda3*x2_simple_background + lambda4*x2_simple_dissimilar_deviant
# Intercepts
x1_complex_background ~ i1*1
x1_complex_dissimilar_deviant ~ 1
x1_simple_background ~ 1
x1_simple_dissimilar_deviant ~ 1
x2_complex_background ~ i1*1
x2_complex_dissimilar_deviant ~ 1
x2_simple_background ~ 1
x2_simple_dissimilar_deviant ~ 1
# Unique Variances and Covariances
x1_complex_background ~~ x1_complex_background
x1_complex_dissimilar_deviant ~~ x1_complex_dissimilar_deviant
x1_simple_background ~~ x1_simple_background
x1_simple_dissimilar_deviant ~~ x1_simple_dissimilar_deviant
x2_complex_background ~~ x2_complex_background
x2_complex_dissimilar_deviant ~~ x2_complex_dissimilar_deviant
x2_simple_background ~~ x2_simple_background
x2_simple_dissimilar_deviant ~~ x2_simple_dissimilar_deviant
x1_complex_background ~~ x2_complex_background
x1_complex_dissimilar_deviant ~~ x2_complex_dissimilar_deviant
x1_simple_background ~~ x2_simple_background
x1_simple_dissimilar_deviant ~~ x2_simple_dissimilar_deviant
# Latent Variable Means
first_half_rt ~ 0*1
second_half_rt ~ 1
# Latent Variable Variances and Covariance
first_half_rt ~~ 1*first_half_rt
second_half_rt ~~ second_half_rt
first_half_rt ~~ second_half_rt
'fit_weak <- cfa(weak, data = d_processed, mimic = "mplus")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some observed variances are larger than 1000000
## lavaan NOTE: use varTable(fit) to investigate## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= -6.770970e-11) is smaller than zero. This may be a symptom that
## the model is not identified.summary(fit_weak, fit.measures = TRUE)## lavaan 0.6-8 ended normally after 31 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 31
## Number of equality constraints 5
##
## Number of observations 158
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 93.780
## Degrees of freedom 18
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 711.134
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.889
## Tucker-Lewis Index (TLI) 0.827
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11521.295
## Loglikelihood unrestricted model (H1) -11474.406
##
## Akaike (AIC) 23094.591
## Bayesian (BIC) 23174.218
## Sample-size adjusted Bayesian (BIC) 23091.916
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.163
## 90 Percent confidence interval - lower 0.131
## 90 Percent confidence interval - upper 0.197
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.056
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## first_half_rt =~
## x1_cmp_ (lmb1) 2191.860 175.484 12.490 0.000
## x1_cm__ (lmb2) 2853.480 225.189 12.671 0.000
## x1_smp_ (lmb3) 2280.489 178.274 12.792 0.000
## x1_sm__ (lmb4) 2797.092 231.685 12.073 0.000
## second_half_rt =~
## x2_cmp_ (lmb1) 2191.860 175.484 12.490 0.000
## x2_cm__ (lmb2) 2853.480 225.189 12.671 0.000
## x2_smp_ (lmb3) 2280.489 178.274 12.792 0.000
## x2_sm__ (lmb4) 2797.092 231.685 12.073 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .x1_complex_background ~~
## .x2_cmplx_bckgr 0.000 0.110 0.000 1.000
## .x1_complex_dissimilar_deviant ~~
## .x2_cmplx_dssm_ 0.000 0.015 0.000 1.000
## .x1_simple_background ~~
## .x2_smpl_bckgrn 0.000 0.049 0.000 1.000
## .x1_simple_dissimilar_deviant ~~
## .x2_smpl_dssml_ 0.000 0.016 0.000 1.000
## first_half_rt ~~
## second_half_rt 0.589 0.050 11.737 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_ (i1) 4347.569 233.383 18.628 0.000
## .x1_cmpl__ 5001.803 288.016 17.366 0.000
## .x1_smpl_b 3916.266 232.485 16.845 0.000
## .x1_smpl__ 4321.519 307.377 14.059 0.000
## .x2_cmplx_ (i1) 4347.569 233.383 18.628 0.000
## .x2_cmpl__ 5370.133 390.979 13.735 0.000
## .x2_smpl_b 4140.199 300.491 13.778 0.000
## .x2_smpl__ 4673.448 370.220 12.623 0.000
## frst_hlf_ 0.000
## scnd_hlf_ -0.662 0.108 -6.141 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_bckgr 3801626.022 0.046 81976603.613 0.000
## .x1_cmplx_dssm_ 4964244.268 0.016 307933812.958 0.000
## .x1_smpl_bckgrn 3339170.037 0.028 119991598.255 0.000
## .x1_smpl_dssml_ 7104218.106 0.023 312969401.846 0.000
## .x2_cmplx_bckgr 1259291.459 0.133 9491942.062 0.000
## .x2_cmplx_dssm_ 4514948.153 0.021 215759411.407 0.000
## .x2_smpl_bckgrn 1846639.054 0.058 31747630.347 0.000
## .x2_smpl_dssml_ 2758114.442 0.045 61794196.088 0.000
## first_half_rt 1.000
## second_half_rt 0.518 0.071 7.337 0.000semPaths(fit_weak, what="est",
sizeLat = 7, sizeMan = 7, edge.label.cex = .75)
strong variance
strong <- '
# Define the latent factors.
first_half_rt =~ NA*x1_complex_background + lambda1*x1_complex_background + lambda2*x1_complex_dissimilar_deviant + lambda3*x1_simple_background + lambda4*x1_simple_dissimilar_deviant
second_half_rt =~NA*x2_complex_background + lambda1*x2_complex_background + lambda2*x2_complex_dissimilar_deviant + lambda3*x2_simple_background + lambda4*x2_simple_dissimilar_deviant
# Intercepts
x1_complex_background ~ i1*1
x1_complex_dissimilar_deviant ~ i2*1
x1_simple_background ~ i3*1
x1_simple_dissimilar_deviant ~ i4*1
x2_complex_background ~ i1*1
x2_complex_dissimilar_deviant ~ i2*1
x2_simple_background ~ i3*1
x2_simple_dissimilar_deviant ~ i4*1
# Unique Variances and Covariances
x1_complex_background ~~ x1_complex_background
x1_complex_dissimilar_deviant ~~ x1_complex_dissimilar_deviant
x1_simple_background ~~ x1_simple_background
x1_simple_dissimilar_deviant ~~ x1_simple_dissimilar_deviant
x2_complex_background ~~ x2_complex_background
x2_complex_dissimilar_deviant ~~ x2_complex_dissimilar_deviant
x2_simple_background ~~ x2_simple_background
x2_simple_dissimilar_deviant ~~ x2_simple_dissimilar_deviant
x1_complex_background ~~ x2_complex_background
x1_complex_dissimilar_deviant ~~ x2_complex_dissimilar_deviant
x1_simple_background ~~ x2_simple_background
x1_simple_dissimilar_deviant ~~ x2_simple_dissimilar_deviant
# Latent Variable Means
first_half_rt ~ 0*1
second_half_rt ~ 1
# Latent Variable Variances and Covariance
first_half_rt ~~ 1*first_half_rt
second_half_rt ~~ second_half_rt
first_half_rt ~~ second_half_rt
'fit_strong <- cfa(strong, data = d_processed, mimic = "mplus")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some observed variances are larger than 1000000
## lavaan NOTE: use varTable(fit) to investigate## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## The variance-covariance matrix of the estimated parameters (vcov)
## does not appear to be positive definite! The smallest eigenvalue
## (= -4.010192e-09) is smaller than zero. This may be a symptom that
## the model is not identified.summary(fit_strong, fit.measures = TRUE)## lavaan 0.6-8 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 31
## Number of equality constraints 8
##
## Number of observations 158
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 95.173
## Degrees of freedom 21
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 711.134
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.891
## Tucker-Lewis Index (TLI) 0.855
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11521.992
## Loglikelihood unrestricted model (H1) -11474.406
##
## Akaike (AIC) 23089.985
## Bayesian (BIC) 23160.424
## Sample-size adjusted Bayesian (BIC) 23087.618
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.150
## 90 Percent confidence interval - lower 0.120
## 90 Percent confidence interval - upper 0.181
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.056
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## first_half_rt =~
## x1_cmp_ (lmb1) 2234.616 174.391 12.814 0.000
## x1_cm__ (lmb2) 2835.276 220.742 12.844 0.000
## x1_smp_ (lmb3) 2272.715 175.388 12.958 0.000
## x1_sm__ (lmb4) 2774.226 226.615 12.242 0.000
## second_half_rt =~
## x2_cmp_ (lmb1) 2234.616 174.391 12.814 0.000
## x2_cm__ (lmb2) 2835.276 220.742 12.844 0.000
## x2_smp_ (lmb3) 2272.715 175.388 12.958 0.000
## x2_sm__ (lmb4) 2774.226 226.615 12.242 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .x1_complex_background ~~
## .x2_cmplx_bckgr 0.000 0.044 0.000 1.000
## .x1_complex_dissimilar_deviant ~~
## .x2_cmplx_dssm_ 0.000 0.015 0.000 1.000
## .x1_simple_background ~~
## .x2_smpl_bckgrn 0.000 0.047 0.000 1.000
## .x1_simple_dissimilar_deviant ~~
## .x2_smpl_dssml_ 0.000 0.012 0.000 1.000
## first_half_rt ~~
## second_half_rt 0.589 0.050 11.804 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_ (i1) 4225.003 209.805 20.138 0.000
## .x1_cmpl__ (i2) 5061.377 266.661 18.981 0.000
## .x1_smpl_b (i3) 3932.023 212.420 18.511 0.000
## .x1_smpl__ (i4) 4393.141 266.617 16.477 0.000
## .x2_cmplx_ (i1) 4225.003 209.805 20.138 0.000
## .x2_cmpl__ (i2) 5061.377 266.661 18.981 0.000
## .x2_smpl_b (i3) 3932.023 212.420 18.511 0.000
## .x2_smpl__ (i4) 4393.141 266.617 16.477 0.000
## frst_hlf_ 0.000
## scnd_hlf_ -0.577 0.073 -7.879 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_bckgr 3777232.734 0.029 131296967.610 0.000
## .x1_cmplx_dssm_ 4959119.210 0.015 323399053.989 0.000
## .x1_smpl_bckgrn 3357774.695 0.022 150245449.239 0.000
## .x1_smpl_dssml_ 7151058.946 0.019 369639978.960 0.000
## .x2_cmplx_bckgr 1235842.415 0.039 31545587.782 0.000
## .x2_cmplx_dssm_ 4526121.642 0.014 315955068.447 0.000
## .x2_smpl_bckgrn 1871555.554 0.022 85216907.660 0.000
## .x2_smpl_dssml_ 2800902.304 0.021 130646344.425 0.000
## first_half_rt 1.000
## second_half_rt 0.515 0.070 7.363 0.000semPaths(fit_strong, what="est",
sizeLat = 7, sizeMan = 7, edge.label.cex = .75)
strict invariance model
strict <- '
# Define the latent factors.
first_half_rt =~ NA*x1_complex_background + lambda1*x1_complex_background + lambda2*x1_complex_dissimilar_deviant + lambda3*x1_simple_background + lambda4*x1_simple_dissimilar_deviant
second_half_rt =~NA*x2_complex_background + lambda1*x2_complex_background + lambda2*x2_complex_dissimilar_deviant + lambda3*x2_simple_background + lambda4*x2_simple_dissimilar_deviant
# Intercepts
x1_complex_background ~ i1*1
x1_complex_dissimilar_deviant ~ i2*1
x1_simple_background ~ i3*1
x1_simple_dissimilar_deviant ~ i4*1
x2_complex_background ~ i1*1
x2_complex_dissimilar_deviant ~ i2*1
x2_simple_background ~ i3*1
x2_simple_dissimilar_deviant ~ i4*1
# Unique Variances
x1_complex_background ~~ u1 * x1_complex_background
x1_complex_dissimilar_deviant ~~ u2 * x1_complex_dissimilar_deviant
x1_simple_background ~~ u3 * x1_simple_background
x1_simple_dissimilar_deviant ~~ u4 * x1_simple_dissimilar_deviant
x2_complex_background ~~ u1 * x2_complex_background
x2_complex_dissimilar_deviant ~~ u2 * x2_complex_dissimilar_deviant
x2_simple_background ~~ u3 * x2_simple_background
x2_simple_dissimilar_deviant ~~ u4 * x2_simple_dissimilar_deviant
# Latent Variable Means
first_half_rt ~ 0*1
second_half_rt ~ 1
# Latent Variable Variances and Covariance
first_half_rt ~~ 1*first_half_rt
second_half_rt ~~ second_half_rt
first_half_rt ~~ second_half_rt
'fit_strict <- cfa(strict, data = d_processed, mimic = "mplus")## Warning in lav_data_full(data = data, group = group, cluster = cluster, : lavaan WARNING: some observed variances are larger than 1000000
## lavaan NOTE: use varTable(fit) to investigatesummary(fit_strict, fit.measures = TRUE)## lavaan 0.6-8 ended normally after 59 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 27
## Number of equality constraints 12
##
## Number of observations 158
## Number of missing patterns 1
##
## Model Test User Model:
##
## Test statistic 164.863
## Degrees of freedom 29
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 711.134
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.801
## Tucker-Lewis Index (TLI) 0.808
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -11556.837
## Loglikelihood unrestricted model (H1) -11474.406
##
## Akaike (AIC) 23143.675
## Bayesian (BIC) 23189.614
## Sample-size adjusted Bayesian (BIC) 23142.132
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.172
## 90 Percent confidence interval - lower 0.147
## 90 Percent confidence interval - upper 0.198
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.117
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## first_half_rt =~
## x1_cmp_ (lmb1) 2346.054 172.741 13.581 0.000
## x1_cm__ (lmb2) 2863.754 222.488 12.871 0.000
## x1_smp_ (lmb3) 2287.220 173.739 13.165 0.000
## x1_sm__ (lmb4) 2903.528 226.224 12.835 0.000
## second_half_rt =~
## x2_cmp_ (lmb1) 2346.054 172.741 13.581 0.000
## x2_cm__ (lmb2) 2863.754 222.488 12.871 0.000
## x2_smp_ (lmb3) 2287.220 173.739 13.165 0.000
## x2_sm__ (lmb4) 2903.528 226.224 12.835 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## first_half_rt ~~
## second_half_rt 0.553 0.048 11.564 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_ (i1) 4281.346 212.626 20.136 0.000
## .x1_cmpl__ (i2) 5046.197 268.338 18.805 0.000
## .x1_smpl_b (i3) 3916.112 211.192 18.543 0.000
## .x1_smpl__ (i4) 4387.573 270.731 16.206 0.000
## .x2_cmplx_ (i1) 4281.346 212.626 20.136 0.000
## .x2_cmpl__ (i2) 5046.197 268.338 18.805 0.000
## .x2_smpl_b (i3) 3916.112 211.192 18.543 0.000
## .x2_smpl__ (i4) 4387.573 270.731 16.206 0.000
## frst_hlf_ 0.000
## scnd_hlf_ -0.562 0.071 -7.869 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1_cmplx_ (u1) 2358948.001 0.021 111719564.755 0.000
## .x1_cmpl__ (u2) 4873494.077 0.011 424127932.360 0.000
## .x1_smpl_b (u3) 2724189.120 0.016 172367976.605 0.000
## .x1_smpl__ (u4) 4807334.931 0.019 259342110.492 0.000
## .x2_cmplx_ (u1) 2358948.001 0.021 111719564.755 0.000
## .x2_cmpl__ (u2) 4873494.077 0.011 424127932.364 0.000
## .x2_smpl_b (u3) 2724189.120 0.016 172367976.605 0.000
## .x2_smpl__ (u4) 4807334.931 0.019 259342110.492 0.000
## frst_hlf_ 1.000
## scnd_hlf_ 0.452 0.064 7.063 0.000semPaths(fit_strict, what="est",
sizeLat = 7, sizeMan = 7, edge.label.cex = .75)
model comparison
round(cbind(configural=inspect(fit_configural, 'fit.measures'),
weak=inspect(fit_weak, 'fit.measures'),
strong=inspect(fit_strong, 'fit.measures'),
strict=inspect(fit_strict, 'fit.measures')),3) ## configural weak strong strict
## npar 25.000 26.000 23.000 15.000
## fmin 0.291 0.297 0.301 0.522
## chisq 92.043 93.780 95.173 164.863
## df 19.000 18.000 21.000 29.000
## pvalue 0.000 0.000 0.000 0.000
## baseline.chisq 711.134 711.134 711.134 711.134
## baseline.df 28.000 28.000 28.000 28.000
## baseline.pvalue 0.000 0.000 0.000 0.000
## cfi 0.893 0.889 0.891 0.801
## tli 0.842 0.827 0.855 0.808
## nnfi 0.842 0.827 0.855 0.808
## rfi 0.809 0.795 0.822 NA
## nfi 0.871 0.868 0.866 NA
## pnfi 0.591 0.558 0.650 0.796
## ifi 0.894 0.891 0.893 0.801
## rni 0.893 0.889 0.891 0.801
## logl -11520.427 -11521.295 -11521.992 -11556.837
## unrestricted.logl -11474.406 -11474.406 -11474.406 -11474.406
## aic 23090.855 23094.591 23089.985 23143.675
## bic 23167.420 23174.218 23160.424 23189.614
## ntotal 158.000 158.000 158.000 158.000
## bic2 23088.283 23091.916 23087.618 23142.132
## rmsea 0.156 0.163 0.150 0.172
## rmsea.ci.lower 0.125 0.131 0.120 0.147
## rmsea.ci.upper 0.189 0.197 0.181 0.198
## rmsea.pvalue 0.000 0.000 0.000 0.000
## rmr 426676.394 467410.557 463334.998 709779.734
## rmr_nomean 471708.502 516741.813 512236.112 784691.020
## srmr 0.054 0.056 0.056 0.117
## srmr_bentler 0.054 0.057 0.057 0.096
## srmr_bentler_nomean 0.059 0.063 0.062 0.106
## crmr 0.059 0.060 0.060 0.099
## crmr_nomean 0.067 0.067 0.067 0.099
## srmr_mplus 0.054 0.056 0.056 0.117
## srmr_mplus_nomean 0.059 0.062 0.061 0.121
## cn_05 52.744 49.639 55.237 41.785
## cn_01 63.125 59.640 65.632 48.524
## gfi 0.927 0.925 0.924 0.882
## agfi 0.830 0.817 0.840 0.821
## pgfi 0.400 0.378 0.441 0.581
## mfi 0.794 0.787 0.791 0.651
## ecvi 0.899 0.923 0.894 1.233anova(fit_configural, fit_weak)## Warning in lavTestLRT(object = new("lavaan", version = "0.6.8", call = lavaan::lavaan(model = configural, : lavaan WARNING: some restricted models fit better than less
## restricted models; either these models are not nested, or
## the less restricted model failed to reach a global optimum.## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_weak 18 23095 23174 93.779
## fit_configural 19 23091 23167 92.043 -1.7361 1 1anova(fit_weak, fit_strong)## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_weak 18 23095 23174 93.779
## fit_strong 21 23090 23160 95.173 1.3937 3 0.707anova(fit_strong, fit_strict)## Chi-Squared Difference Test
##
## Df AIC BIC Chisq Chisq diff Df diff Pr(>Chisq)
## fit_strong 21 23090 23160 95.173
## fit_strict 29 23144 23190 164.863 69.69 8 5.664e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1