Summary:

Part I: Confirmatory Results

w/ Different Exclusion Criteria (5-response min., 2-response min., No min.)

Threshold Model Parameter Estimate SE p.value AIC LogLik nObs nExams nSubs
None PA Outcome 0.417669 0.171179 0.218 13294.44 -6625.222 1704 253 88
None PA PE 3.286408 0.437849 0.004** — — — — —
None NA Outcome -0.648700 0.202300 0.1133 13561.31 -6758.657 1704 253 88
None NA PE -2.780200 0.463400 <0.001*** — — — — —
2 PA Outcome 0.411520 0.178972 0.2366 13261.46 -6608.729 1700 249 88
2 PA PE 3.263114 0.441290 0.00481** — — — — —
2 NA Outcome -0.626000 0.202800 0.117 13527.14 -6741.568 1700 249 88
2 NA PE -2.767500 0.465200 <0.001*** — — — — —
5 PA Outcome 0.438400 0.257700 0.342 11581.12 -5768.561 1487 178 81
5 PA PE 3.470100 0.505300 <0.001*** — — — — —
5 NA Outcome -0.532400 0.286100 0.2966 11853.39 -5904.695 1487 178 81
5 NA PE -2.198700 0.626400 0.1048 — — — — —

Proceeding with No minimum response inclusion criteria…

Part II: Exploratory and Confirmatory Model Fits

Dataset Affect predictor Estimate SE p-value
Exploratory Positive outcome 0.2292979 0.1817715 0.2119148
Exploratory Positive PE 3.3819096 0.5106526 0.0000002
Exploratory Negative outcome -0.5979154 0.3407177 0.1880818
Exploratory Negative PE -2.7743699 0.7936415 0.0664478
Confirmatory Positive outcome 0.4219167 0.1330221 0.0022481
Confirmatory Positive PE 3.2227409 0.4071812 0.0000000
Confirmatory Negative outcome -0.6415713 0.1911985 0.0013328
Confirmatory Negative PE -2.6914964 0.4589421 0.0000000

Part III: CIs for Model Parameters, and PE - Outcome contrasts

  • Outcome terms in Exploratory models are not statistically different from zero
  • PE - Outcome contrasts are significant for all models (PA & NA) and samples (Exploratory & Confirmatory)
Dataset Affect Parameter Estimate SE X2 P Lower Upper
Exploratory Positive Outcome 0.2292979 0.1817715 1.591287 0.2071423 -0.1269677 0.5855635
Exploratory Positive PE 3.3819096 0.5106526 43.860427 0.0000000 2.3810489 4.3827704
Exploratory Positive PE - Outcome 3.1526117 0.5372360 34.435843 0.0000000 2.0996484 4.2055749
Exploratory Negative Outcome -0.5979154 0.3407177 3.079570 0.0792815 -1.2657097 0.0698790
Exploratory Negative PE -2.7743699 0.7936415 12.220248 0.0004727 -4.3298786 -1.2188612
Exploratory Negative PE - Outcome -2.1764545 1.0180621 4.570363 0.0325297 -4.1718195 -0.1810896
Confirmatory Positive Outcome 0.4219167 0.1330221 10.060187 0.0015151 0.1611982 0.6826351
Confirmatory Positive PE 3.2227409 0.4071812 62.643403 0.0000000 2.4246804 4.0208013
Confirmatory Positive PE - Outcome 2.8008242 0.4217458 44.103212 0.0000000 1.9742177 3.6274307
Confirmatory Negative Outcome -0.6415713 0.1911985 11.259545 0.0007921 -1.0163135 -0.2668291
Confirmatory Negative PE -2.6914964 0.4589421 34.393144 0.0000000 -3.5910063 -1.7919865
Confirmatory Negative PE - Outcome -2.0499251 0.5472047 14.033836 0.0001796 -3.1224266 -0.9774237

Part IV: Comparing ‘Outcome-Only’ and ‘PE + Outcome’ Models

  • Including the PE term significantly improves model fit over Outcome alone for PA and NA models in both samples
Dataset Affect Model Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
Exploratory Positive Outcome 12 8442.114 8502.053 -4209.057 8418.114 NA NA NA
Exploratory Positive Outcome + PE 22 8371.188 8481.075 -4163.594 8327.188 90.92624 10 0
Exploratory Negative Outcome 12 8898.657 8958.595 -4437.328 8874.657 NA NA NA
Exploratory Negative Outcome + PE 22 8823.956 8933.843 -4389.978 8779.956 94.70077 10 0
Confirmatory Positive Outcome 12 13420.859 13486.147 -6698.429 13396.859 NA NA NA
Confirmatory Positive Outcome + PE 22 13294.052 13413.748 -6625.026 13250.052 146.80631 10 0
Confirmatory Negative Outcome 12 13686.540 13751.828 -6831.270 13662.540 NA NA NA
Confirmatory Negative Outcome + PE 22 13564.975 13684.671 -6760.487 13520.975 141.56491 10 0
* NOTE: P-v alues are n ot equal to zer o, bu t are very c lose (i.e., 1e-25)

Part V: Interactive Model: modeling PA and NA together

Affect ~ Affect_valence:(outcome + PE) + (1 | cohort / id / exam_num)

  • Results from this model suggest that NA contrast (PE - outcome) is greater than PA contrast
  • Compared to estimates from separate PA and NA linear models, this is surprising
  • Possible collinearity issues?

  • May need to reconsider how we set up this contrast

  • Note: NA estimates are corrected for direction before model is run (NA observations are multiplied by -1 below)

for (i in 1:nrow(long_df)){
  if (long_df$Aff_valence[i] == 2) {
    long_df$Affect[i] <-  -1*(long_df$Affect[i])
  }
} 

long_df.crossed <- lmer(Affect ~ Aff_valence:(outcome + PE) + (1 | cohort / id / exam_num), data = long_df, REML = TRUE)
long_df.crossed.summ <- as.data.frame(coef(summary(long_df.crossed)))

long_df.int.esticon <- esticon(long_df.crossed, L = c(0,-1,1,1,-1), conf.in = NULL) 
long_df.int.esticon.summ <- as.data.frame(long_df.int.esticon)
long_df.int.esticon.summ[,c(1,5)] <- NULL

colnames(long_df.int.esticon.summ) <- c("Estimate", "SE",  "X2", "P", "Lower", "Upper")
long_df.int.esticon.summ$Contrast <- "PA(PE - Outcome) - NA(PE - Outcome)"
long_df.int.esticon.summ <- long_df.int.esticon.summ[,c("Contrast", "Estimate", "SE",  "X2", "P", "Lower", "Upper")]

kable(long_df.crossed.summ)
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -1.8602018 0.8754619 148.5741 -2.124823 0.0352561
Aff_valence1:outcome 0.6119893 0.0912270 3307.0985 6.708422 0.0000000
Aff_valence2:outcome 0.3586038 0.0912270 3307.0985 3.930894 0.0000864
Aff_valence1:PE 2.4912516 0.2486492 2768.9999 10.019140 0.0000000
Aff_valence2:PE 3.1845086 0.2486492 2768.9999 12.807232 0.0000000 
kable(long_df.int.esticon.summ)
Contrast Estimate SE X2 P Lower Upper
PA(PE - Outcome) - NA(PE - Outcome) -0.9466426 0.2192122 18.64845 0.0000157 -1.376291 -0.5169946

Part VI: Model Fits for Sample Subject

  • The plot below depicts the data for a subject in our exploratory sample
  • Note: Figure legends and labels are being edited in Adobe Illustrator before being added to the manuscript