Main Analyses:
Updating Analyses
Updating across exam is not stable. Updating at exam two is greater
than at either of the other two
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 + grade_100_delta + exam_num.f + (1 + PE1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.97 0.78 0.06 2.94 1.00 1025 1462
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.72 0.51 0.03 1.87 1.01 536 1284
## sd(PE1) 0.33 0.04 0.24 0.41 1.00 1087 2001
## cor(Intercept,PE1) 0.31 0.48 -0.78 0.97 1.03 89 266
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.41 0.70 -2.73 0.04 1.00 1984 1646
## PE1 0.53 0.03 0.48 0.59 1.00 4106 3143
## grade_100_delta 0.70 0.02 0.67 0.74 1.00 6858 3136
## exam_num.f2 -0.70 0.64 -1.96 0.55 1.00 5381 3301
## exam_num.f3 2.70 0.66 1.38 4.00 1.00 5389 3294
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.23 0.22 11.80 12.68 1.00 2580 3094
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 + grade_100_delta + exam_num.f + (1 + PE2 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2752)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.91 1.19 0.68 5.03 1.00 1642 2123
##
## ~ID (Number of levels: 1017)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.51 0.37 0.02 1.37 1.00 660 1341
## sd(PE2) 0.24 0.04 0.15 0.30 1.00 1376 1598
## cor(Intercept,PE2) -0.27 0.58 -0.98 0.93 1.06 92 267
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -3.20 1.07 -5.25 -1.05 1.00 2489 2205
## PE2 0.50 0.02 0.45 0.54 1.00 7079 3459
## grade_100_delta 0.67 0.01 0.65 0.70 1.00 8417 3434
## exam_num.f2 0.15 0.56 -0.96 1.26 1.00 6781 3208
## exam_num.f3 1.72 0.57 0.62 2.85 1.00 7562 3048
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.85 0.18 11.50 12.19 1.00 4300 3165
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
Asymmetric Updating
Larger (slope for) updating for positive PE than negative
## Warning: There were 11 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ abs_PE1 * sign_PE1 + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.00 0.79 0.06 3.12 1.00 1078 1593
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.66 0.49 0.04 1.81 1.00 1323 1788
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.86 0.88 -3.59 -0.09 1.00 3190 2162
## abs_PE1 -0.44 0.06 -0.55 -0.33 1.00 4600 3589
## sign_PE11 -1.16 0.88 -2.87 0.60 1.00 4489 3491
## grade_100_delta 0.69 0.02 0.65 0.73 1.00 7680 2726
## exam_num.f2 -0.76 0.67 -2.09 0.54 1.00 6463 2850
## exam_num.f3 2.67 0.71 1.29 4.07 1.00 6381 2862
## abs_PE1:sign_PE11 1.12 0.08 0.96 1.27 1.00 4287 3292
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.76 0.20 12.36 13.15 1.00 6947 2909
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 10 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ abs_PE2 * sign_PE2 + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2752)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.96 1.13 0.73 4.96 1.00 1402 1689
##
## ~ID (Number of levels: 1017)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.47 0.35 0.02 1.29 1.00 1617 1888
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.26 1.19 -4.65 0.11 1.00 1766 1648
## abs_PE2 -0.51 0.05 -0.62 -0.41 1.00 3411 2865
## sign_PE21 -2.55 0.76 -4.06 -1.07 1.00 3521 3407
## grade_100_delta 0.67 0.01 0.64 0.69 1.00 7979 2671
## exam_num.f2 0.05 0.57 -1.06 1.15 1.00 6213 3012
## exam_num.f3 1.63 0.57 0.50 2.75 1.00 6105 3114
## abs_PE2:sign_PE21 1.14 0.07 1.01 1.28 1.00 2965 2732
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.12 0.17 11.80 12.45 1.00 7765 2464
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Accuracy Violins
Accuracy Update, all PE’s trend negative – especially PE0
## `geom_smooth()` using formula = 'y ~ x'
Accuracy models
Accuracy decreases over tie regardless of prediction type
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Accuracy_1 ~ exam_num + (1 | cohort) + (1 | ID)
## Data: predictions
##
## REML criterion at convergence: 26744.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.4586 -0.4158 0.1954 0.6297 2.6923
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 24.76174 4.976
## cohort (Intercept) 0.07894 0.281
## Residual 73.20446 8.556
## Number of obs: 3635, groups: ID, 1150; cohort, 5
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 90.9559 0.3902 25.9486 233.103 < 2e-16 ***
## exam_num -0.8286 0.1302 2709.4776 -6.365 2.29e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## exam_num -0.784
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: Accuracy_2 ~ exam_num + (1 | cohort) + (1 | ID)
## Data: predictions
##
## REML criterion at convergence: 30795.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -8.9443 -0.4139 0.2087 0.6504 2.8370
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 19.2163 4.3836
## cohort (Intercept) 0.3732 0.6109
## Residual 70.0003 8.3666
## Number of obs: 4232, groups: ID, 1172; cohort, 5
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 91.0077 0.4344 12.2632 209.499 < 2e-16 ***
## exam_num -0.6755 0.1168 3168.7134 -5.783 8.03e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## exam_num -0.652
Neuroticism Analyses
PE x NE
- High NE doesn’t update from PE 0
- NE predicts prediction 1 updating, no interaction
- NE predicts prediction 2 updating, no interaction
## Warning: There were 2 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * negative_emotionality + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2072)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.07 0.83 0.08 3.26 1.00 1118 1851
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.64 0.48 0.03 1.78 1.00 1398 1767
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 1.90 1.18 -0.32 4.19 1.00 3781
## PE1 0.55 0.09 0.38 0.72 1.00 5585
## negative_emotionality -0.20 0.05 -0.30 -0.09 1.00 9262
## grade_100_delta 0.70 0.02 0.66 0.73 1.00 8286
## exam_num.f2 -0.70 0.66 -1.99 0.58 1.00 6616
## exam_num.f3 2.82 0.68 1.49 4.14 1.00 6743
## PE1:negative_emotionality -0.00 0.00 -0.01 0.01 1.00 5814
## Tail_ESS
## Intercept 2209
## PE1 2798
## negative_emotionality 2642
## grade_100_delta 2729
## exam_num.f2 3644
## exam_num.f3 3326
## PE1:negative_emotionality 2859
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.76 0.20 12.37 13.17 1.00 8902 2739
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * negative_emotionality + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2737)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.88 1.02 0.68 4.59 1.00 1661 2408
##
## ~ID (Number of levels: 1012)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.46 0.35 0.02 1.31 1.00 1914 2326
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -0.90 1.26 -3.42 1.63 1.00 2683
## PE2 0.42 0.07 0.28 0.55 1.00 6211
## negative_emotionality -0.14 0.04 -0.22 -0.05 1.00 8651
## grade_100_delta 0.67 0.01 0.64 0.70 1.00 9238
## exam_num.f2 0.15 0.57 -0.97 1.29 1.00 7807
## exam_num.f3 1.72 0.57 0.62 2.85 1.00 8193
## PE2:negative_emotionality 0.00 0.00 -0.00 0.01 1.00 6287
## Tail_ESS
## Intercept 2262
## PE2 2774
## negative_emotionality 2856
## grade_100_delta 2544
## exam_num.f2 3223
## exam_num.f3 3318
## PE2:negative_emotionality 3081
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.13 0.17 11.80 12.46 1.00 9001 2578
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
NE x Updating Asymmetric
- PE0 and NE have no bearing on prediction 0 updating
- NE predicts prediction 1 updating (negatively), the interaction of
|PE1| and sign_PE1 predicts prediction 1 updating (+PE -> postive
updating)
- PE2 and NE have no bearing on prediction 2 updating
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ abs_PE1 * sign_PE1 * negative_emotionality + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2074)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 3.22 1.79 1.24 8.11 1.00 1738 2820
##
## ~ID (Number of levels: 913)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.43 0.32 0.02 1.19 1.00 3168 2216
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 1.64 3.24 -4.76 7.84
## abs_PE1 -0.38 0.24 -0.86 0.10
## sign_PE11 -5.01 4.02 -12.86 2.67
## negative_emotionality -0.46 0.16 -0.78 -0.14
## abs_PE1:sign_PE11 1.05 0.37 0.34 1.77
## abs_PE1:negative_emotionality 0.02 0.01 -0.01 0.05
## sign_PE11:negative_emotionality 0.15 0.23 -0.30 0.60
## abs_PE1:sign_PE11:negative_emotionality -0.02 0.02 -0.06 0.02
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 2518 2739
## abs_PE1 1.00 2329 3139
## sign_PE11 1.00 2216 2874
## negative_emotionality 1.00 2398 3121
## abs_PE1:sign_PE11 1.00 2098 3082
## abs_PE1:negative_emotionality 1.00 2304 3063
## sign_PE11:negative_emotionality 1.00 1963 2995
## abs_PE1:sign_PE11:negative_emotionality 1.00 1937 2893
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 16.66 0.25 16.17 17.16 1.00 9694 2906
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ abs_PE2 * sign_PE2 * negative_emotionality + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2740)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 4.04 2.04 1.71 9.39 1.00 1601 2107
##
## ~ID (Number of levels: 1013)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.33 0.25 0.01 0.95 1.00 3513 2346
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.66 3.10 -6.69 5.36
## abs_PE2 -0.33 0.22 -0.76 0.12
## sign_PE21 -3.43 3.46 -10.15 3.05
## negative_emotionality -0.27 0.14 -0.54 0.01
## abs_PE2:sign_PE21 0.68 0.30 0.09 1.27
## abs_PE2:negative_emotionality 0.02 0.01 -0.01 0.04
## sign_PE21:negative_emotionality 0.03 0.20 -0.35 0.42
## abs_PE2:sign_PE21:negative_emotionality -0.01 0.02 -0.04 0.03
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 1935 2385
## abs_PE2 1.00 1980 2779
## sign_PE21 1.00 1806 2496
## negative_emotionality 1.00 2024 2667
## abs_PE2:sign_PE21 1.00 1720 2562
## abs_PE2:negative_emotionality 1.00 2006 2847
## sign_PE21:negative_emotionality 1.00 1793 2435
## abs_PE2:sign_PE21:negative_emotionality 1.00 1756 2558
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 16.21 0.22 15.78 16.66 1.00 8725 2587
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Accruacy x NE
When looking at top and bottom quartile
- Accuracy 0 has no bearing on prediction updating
- Accuracy 1 interacts with high NE. High NE and greater accuracy
predicts prediction 1 updating (negatively)
- Accuracy 2 predicts prediction 2 updating (negatively)
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ Accuracy_1 * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2072)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.61 1.23 0.30 4.52 1.00 1096 1394
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.36 0.28 0.01 1.04 1.00 2264 1871
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -70.22 13.89 -97.71 -42.52 1.00
## Accuracy_1 0.76 0.15 0.46 1.06 1.00
## negative_emotionality 4.39 0.78 2.81 5.93 1.00
## grade_100_delta 0.61 0.02 0.57 0.65 1.00
## exam_num.f2 -0.34 0.72 -1.76 1.05 1.00
## exam_num.f3 3.47 0.75 1.98 4.95 1.00
## Accuracy_1:negative_emotionality -0.05 0.01 -0.07 -0.03 1.00
## Bulk_ESS Tail_ESS
## Intercept 1786 2197
## Accuracy_1 1809 2234
## negative_emotionality 1771 2334
## grade_100_delta 4870 2897
## exam_num.f2 4049 3114
## exam_num.f3 4375 3493
## Accuracy_1:negative_emotionality 1766 2436
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.87 0.21 13.47 14.31 1.00 6161 3083
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ Accuracy_2 * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2737)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.32 1.43 0.87 6.23 1.00 1310 1924
##
## ~ID (Number of levels: 1012)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.29 0.22 0.01 0.79 1.00 3002 2296
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -31.17 11.26 -53.30 -9.32 1.00
## Accuracy_2 0.33 0.12 0.08 0.57 1.00
## negative_emotionality 2.80 0.63 1.60 4.04 1.00
## grade_100_delta 0.58 0.01 0.55 0.61 1.00
## exam_num.f2 0.40 0.62 -0.79 1.58 1.00
## exam_num.f3 1.85 0.62 0.64 3.06 1.00
## Accuracy_2:negative_emotionality -0.03 0.01 -0.04 -0.02 1.00
## Bulk_ESS Tail_ESS
## Intercept 3252 2871
## Accuracy_2 3420 2642
## negative_emotionality 3306 2703
## grade_100_delta 7941 2966
## exam_num.f2 6098 3263
## exam_num.f3 7192 3252
## Accuracy_2:negative_emotionality 3348 2621
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.12 0.18 12.76 13.49 1.00 9081 2665
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Splines PE x NE
## Warning: There were 5 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ t2(PE1, negative_emotionality) + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[predictions$abs_PE1 < 30, ] (Number of observations: 2072)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Smoothing Spline Hyperparameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sds(t2PE1negative_emotionality_1) 7.60 5.28 0.44 20.61 1.00
## sds(t2PE1negative_emotionality_2) 7.28 6.00 0.25 22.23 1.00
## sds(t2PE1negative_emotionality_3) 12.74 7.94 1.03 31.58 1.00
## Bulk_ESS Tail_ESS
## sds(t2PE1negative_emotionality_1) 1932 2133
## sds(t2PE1negative_emotionality_2) 1774 1239
## sds(t2PE1negative_emotionality_3) 1577 1266
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.09 0.94 0.07 3.61 1.00 1061 1346
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.63 0.48 0.02 1.78 1.00 943 1468
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -0.88 0.95 -2.88 0.95 1.00 1564
## grade_100_delta 0.69 0.02 0.66 0.73 1.00 6760
## exam_num.f2 -0.80 0.69 -2.13 0.59 1.00 5718
## exam_num.f3 2.60 0.69 1.21 3.91 1.00 5378
## t2PE1negative_emotionality_1 0.72 0.56 -0.43 1.78 1.00 3259
## t2PE1negative_emotionality_2 -6.56 0.52 -7.55 -5.51 1.00 3741
## t2PE1negative_emotionality_3 -0.64 0.73 -2.13 0.72 1.00 3561
## Tail_ESS
## Intercept 1647
## grade_100_delta 2790
## exam_num.f2 2988
## exam_num.f3 3278
## t2PE1negative_emotionality_1 2205
## t2PE1negative_emotionality_2 2705
## t2PE1negative_emotionality_3 2442
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.72 0.20 12.33 13.12 1.00 5828 3116
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 4 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ t2(PE2, negative_emotionality) + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[predictions$abs_PE2 < 30, ] (Number of observations: 2737)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Smoothing Spline Hyperparameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sds(t2PE2negative_emotionality_1) 5.11 4.70 0.16 17.21 1.00
## sds(t2PE2negative_emotionality_2) 5.87 5.07 0.21 18.50 1.00
## sds(t2PE2negative_emotionality_3) 12.24 7.44 1.15 29.27 1.00
## Bulk_ESS Tail_ESS
## sds(t2PE2negative_emotionality_1) 2124 2289
## sds(t2PE2negative_emotionality_2) 2417 2475
## sds(t2PE2negative_emotionality_3) 1352 852
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.96 1.15 0.71 4.97 1.00 1105 1332
##
## ~ID (Number of levels: 1012)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.46 0.35 0.02 1.30 1.00 1210 1403
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -1.49 1.14 -3.77 0.74 1.00 1082
## grade_100_delta 0.67 0.01 0.64 0.70 1.00 6429
## exam_num.f2 0.11 0.57 -1.01 1.23 1.00 4352
## exam_num.f3 1.64 0.57 0.52 2.74 1.00 4639
## t2PE2negative_emotionality_1 0.37 0.44 -0.51 1.24 1.00 3280
## t2PE2negative_emotionality_2 -6.13 0.40 -6.90 -5.33 1.00 3305
## t2PE2negative_emotionality_3 0.24 0.52 -0.82 1.21 1.00 3570
## Tail_ESS
## Intercept 1011
## grade_100_delta 3086
## exam_num.f2 2882
## exam_num.f3 3294
## t2PE2negative_emotionality_1 3361
## t2PE2negative_emotionality_2 3240
## t2PE2negative_emotionality_3 2772
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.12 0.16 11.80 12.44 1.00 5147 2788
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Conditional Effects plots, NE
EVPE
Distribution
## Warning: Removed 223 rows containing non-finite outside the scale range
## (`stat_density()`).
EVPE Predicts Updating?
- EVPE and PE0 predicts prediction 0 updating
- EVPE and PE1 predicts prediction 1 updating
- EVPE and PE2 predicts prediction 2 updating
## Warning: There were 86 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ EVPE + PE1 + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.27 0.96 0.17 3.92 1.01 765 999
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.94 0.68 0.04 2.51 1.02 180 162
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 0.16 0.84 -1.58 1.78 1.00 1100 891
## EVPE 0.24 0.02 0.19 0.28 1.01 359 263
## PE1 0.64 0.03 0.59 0.70 1.01 292 435
## grade_100_delta 0.66 0.02 0.63 0.70 1.00 3070 2578
## exam_num.f2 -0.42 0.69 -1.81 0.94 1.01 477 412
## exam_num.f3 2.59 0.67 1.33 3.91 1.00 1959 2523
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.41 0.20 12.03 12.79 1.01 456 998
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Warning: There were 24 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ EVPE + PE2 + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2752)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.23 1.59 0.84 6.18 1.01 768 403
##
## ~ID (Number of levels: 1017)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.53 0.41 0.02 1.55 1.00 996 715
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.53 1.11 -4.79 -0.31 1.00 1359 1596
## EVPE 0.14 0.02 0.11 0.18 1.00 5578 2806
## PE2 0.57 0.02 0.52 0.62 1.00 3460 2627
## grade_100_delta 0.64 0.01 0.61 0.67 1.00 6538 2918
## exam_num.f2 0.24 0.55 -0.85 1.31 1.00 6404 3446
## exam_num.f3 1.53 0.55 0.43 2.59 1.00 5984 2564
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.01 0.16 11.69 12.34 1.00 5834 2864
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
EVPE Predicts Updating with Asymmetry
Prediction 1 Updating: - |EVPE| predicts updating negatively - |PE1|
predicts updating negatively - Interaction of: - |EVPE| and sign_EVPE
predicts updating positively - |PE1| and sign_PE1 predicts updating
positively
Prediction21 Updating: - |EVPE| predicts updating negatively - |PE2|
predicts updating negatively - Interaction of: - |EVPE| and sign_EVPE
predicts updating positively - |PE2| and sign_PE2 predicts updating
positively
## Warning: There were 19 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ EVPE_abs * EVPE_sign + abs_PE1 * sign_PE1 + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.11 0.96 0.08 3.62 1.00 976 1233
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.84 0.61 0.04 2.27 1.00 974 1272
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.62 1.08 -2.73 1.54 1.00 2659 2100
## EVPE_abs -0.14 0.04 -0.22 -0.06 1.00 4577 3274
## EVPE_sign1 0.24 1.02 -1.71 2.23 1.00 4882 2993
## abs_PE1 -0.68 0.06 -0.80 -0.57 1.00 5024 3214
## sign_PE11 -0.97 0.90 -2.73 0.75 1.00 4864 3187
## grade_100_delta 0.66 0.02 0.62 0.69 1.00 6276 2738
## exam_num.f2 -0.51 0.65 -1.80 0.73 1.00 5900 2971
## exam_num.f3 2.51 0.67 1.23 3.80 1.00 6256 3234
## EVPE_abs:EVPE_sign1 0.50 0.07 0.36 0.63 1.00 4738 3107
## abs_PE1:sign_PE11 1.33 0.08 1.17 1.49 1.00 4519 2830
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.40 0.20 12.00 12.79 1.00 3502 1492
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ EVPE_abs * EVPE_sign + abs_PE2 * sign_PE2 + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2752)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.97 1.08 0.75 4.92 1.00 1866 2247
##
## ~ID (Number of levels: 1017)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.54 0.41 0.02 1.51 1.01 1025 1645
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.52 1.20 -4.87 -0.11 1.00 1949 2249
## EVPE_abs -0.03 0.04 -0.10 0.04 1.00 4111 3681
## EVPE_sign1 0.89 0.86 -0.79 2.54 1.00 4191 3339
## abs_PE2 -0.70 0.06 -0.80 -0.59 1.00 3535 3061
## sign_PE21 -2.63 0.76 -4.11 -1.17 1.00 4420 3441
## grade_100_delta 0.64 0.01 0.61 0.67 1.00 7997 2749
## exam_num.f2 0.11 0.55 -0.99 1.17 1.00 6965 3552
## exam_num.f3 1.39 0.55 0.33 2.50 1.00 6694 3480
## EVPE_abs:EVPE_sign1 0.26 0.05 0.16 0.37 1.00 3439 3186
## abs_PE2:sign_PE21 1.32 0.07 1.18 1.46 1.00 3364 2696
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.96 0.16 11.64 12.28 1.00 6864 2731
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
EVPE x NE
## Warning: There were 6 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ t2(EVPE, negative_emotionality) + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions (Number of observations: 2164)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Smoothing Spline Hyperparameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sds(t2EVPEnegative_emotionality_1) 7.01 5.89 0.29 21.99 1.00
## sds(t2EVPEnegative_emotionality_2) 6.85 6.22 0.22 23.17 1.00
## sds(t2EVPEnegative_emotionality_3) 10.68 8.82 0.44 33.17 1.00
## Bulk_ESS Tail_ESS
## sds(t2EVPEnegative_emotionality_1) 1883 2434
## sds(t2EVPEnegative_emotionality_2) 3426 2209
## sds(t2EVPEnegative_emotionality_3) 2219 2179
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.23 0.92 0.11 3.70 1.00 1205 1581
##
## ~ID (Number of levels: 925)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.33 0.24 0.01 0.91 1.00 2253 1607
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -2.15 0.96 -4.09 -0.26 1.00
## grade_100_delta 0.58 0.02 0.54 0.62 1.00
## exam_num.f2 0.16 0.76 -1.30 1.69 1.00
## exam_num.f3 3.82 0.79 2.31 5.35 1.00
## t2EVPEnegative_emotionality_1 0.24 0.47 -0.67 1.15 1.00
## t2EVPEnegative_emotionality_2 0.03 0.76 -1.54 1.53 1.00
## t2EVPEnegative_emotionality_3 -0.26 0.97 -2.24 1.58 1.00
## Bulk_ESS Tail_ESS
## Intercept 1915 1625
## grade_100_delta 6784 3087
## exam_num.f2 5026 2648
## exam_num.f3 4797 2243
## t2EVPEnegative_emotionality_1 4732 2889
## t2EVPEnegative_emotionality_2 4072 2605
## t2EVPEnegative_emotionality_3 4168 2645
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 14.71 0.22 14.28 15.16 1.00 6764 2329
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 2 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ t2(EVPE, negative_emotionality) + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions (Number of observations: 2844)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Smoothing Spline Hyperparameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sds(t2EVPEnegative_emotionality_1) 6.94 5.39 0.28 20.53 1.00
## sds(t2EVPEnegative_emotionality_2) 7.07 6.13 0.29 22.00 1.00
## sds(t2EVPEnegative_emotionality_3) 10.11 7.11 0.52 26.70 1.00
## Bulk_ESS Tail_ESS
## sds(t2EVPEnegative_emotionality_1) 1883 1376
## sds(t2EVPEnegative_emotionality_2) 2402 1742
## sds(t2EVPEnegative_emotionality_3) 1859 1574
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.17 1.25 0.76 5.64 1.00 1080 1600
##
## ~ID (Number of levels: 1015)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.25 0.19 0.01 0.72 1.00 3070 1858
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -2.29 1.26 -4.84 0.19 1.00
## grade_100_delta 0.58 0.02 0.55 0.62 1.00
## exam_num.f2 1.14 0.64 -0.06 2.38 1.00
## exam_num.f3 2.77 0.65 1.50 4.06 1.00
## t2EVPEnegative_emotionality_1 0.08 0.42 -0.76 0.89 1.00
## t2EVPEnegative_emotionality_2 1.08 0.68 -0.37 2.34 1.00
## t2EVPEnegative_emotionality_3 0.42 0.83 -1.22 2.06 1.00
## Bulk_ESS Tail_ESS
## Intercept 1293 1594
## grade_100_delta 5962 3057
## exam_num.f2 4121 2875
## exam_num.f3 4076 3085
## t2EVPEnegative_emotionality_1 3227 2787
## t2EVPEnegative_emotionality_2 2932 2458
## t2EVPEnegative_emotionality_3 3169 2864
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.94 0.18 13.59 14.30 1.00 6562 2830
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Follow ups (7/28/26)
Add Delta Goal Grade
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 + grade_100_delta + exam_num.f + (1 | cohort) + (1 + PE1 | ID)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.96 0.83 0.05 3.01 1.01 834 1270
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.74 0.50 0.04 1.87 1.01 449 1008
## sd(PE1) 0.33 0.04 0.24 0.41 1.00 1077 1813
## cor(Intercept,PE1) 0.41 0.45 -0.71 0.97 1.04 99 150
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.42 0.68 -2.72 -0.03 1.00 1560 1701
## PE1 0.53 0.03 0.47 0.59 1.00 2998 3061
## grade_100_delta 0.70 0.02 0.67 0.74 1.00 4740 3037
## exam_num.f2 -0.69 0.66 -1.99 0.59 1.00 3373 2798
## exam_num.f3 2.71 0.68 1.39 4.03 1.00 3538 2971
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.23 0.23 11.78 12.70 1.00 2228 2224
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 + grade_100_delta + exam_num.f + (1 | cohort) + (1 + PE2 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2752)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.86 1.09 0.66 4.68 1.00 1091 1660
##
## ~ID (Number of levels: 1017)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.50 0.37 0.02 1.39 1.00 639 1266
## sd(PE2) 0.24 0.04 0.16 0.31 1.00 1151 1471
## cor(Intercept,PE2) -0.26 0.55 -0.97 0.90 1.04 84 209
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -3.19 1.00 -5.15 -1.14 1.00 1282 1338
## PE2 0.50 0.02 0.45 0.55 1.00 4273 2618
## grade_100_delta 0.67 0.01 0.65 0.70 1.00 5086 2899
## exam_num.f2 0.16 0.54 -0.91 1.23 1.00 4341 3321
## exam_num.f3 1.72 0.55 0.64 2.79 1.00 4363 3070
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.84 0.18 11.50 12.19 1.00 2944 2868
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
Amibigous PEX Analyses
By subsetting to near 0
## Warning: There were 96 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE1) < 5, ] (Number of observations: 734)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.40 1.19 0.08 4.45 1.00 1006 1517
##
## ~ID (Number of levels: 545)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.13 1.45 0.10 5.23 1.02 278 253
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 2.98 1.81 -0.64 6.56 1.00 1915
## PE1 0.36 0.52 -0.66 1.36 1.00 1755
## negative_emotionality -0.30 0.09 -0.47 -0.13 1.00 3496
## grade_100_delta 0.66 0.03 0.61 0.72 1.00 3804
## exam_num.f2 -0.18 1.06 -2.21 1.87 1.00 3222
## exam_num.f3 1.98 1.17 -0.35 4.27 1.00 3215
## PE1:negative_emotionality 0.01 0.03 -0.05 0.07 1.00 2083
## Tail_ESS
## Intercept 1422
## PE1 2093
## negative_emotionality 2726
## grade_100_delta 2137
## exam_num.f2 2290
## exam_num.f3 2523
## PE1:negative_emotionality 2104
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.82 0.42 10.85 12.56 1.01 363 237
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 93 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 5, ] (Number of observations: 936)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.78 1.33 0.23 5.27 1.01 801 832
##
## ~ID (Number of levels: 654)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.49 1.11 0.06 4.02 1.01 381 259
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 0.43 1.65 -2.73 3.72 1.00 2769
## PE2 0.14 0.43 -0.68 0.97 1.00 3347
## negative_emotionality -0.22 0.07 -0.37 -0.08 1.00 4687
## grade_100_delta 0.64 0.02 0.59 0.69 1.01 4443
## exam_num.f2 0.98 0.90 -0.78 2.78 1.00 2894
## exam_num.f3 1.46 0.91 -0.35 3.27 1.00 2282
## PE2:negative_emotionality 0.01 0.02 -0.04 0.05 1.00 3342
## Tail_ESS
## Intercept 1697
## PE2 2292
## negative_emotionality 2080
## grade_100_delta 2348
## exam_num.f2 2185
## exam_num.f3 1054
## PE2:negative_emotionality 2527
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.35 0.32 10.72 11.98 1.00 755 600
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
by splitting (PE as factor)
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1.f * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2072)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.22 0.94 0.12 3.56 1.01 1233 1732
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.43 0.33 0.02 1.21 1.00 2023 1757
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 5.00 1.66 1.69 8.11 1.00
## PE1.fM1 -10.41 2.13 -14.60 -6.20 1.00
## PE1.f0 -1.98 2.58 -6.99 2.95 1.00
## negative_emotionality -0.10 0.08 -0.26 0.07 1.00
## grade_100_delta 0.67 0.02 0.63 0.70 1.00
## exam_num.f2 -0.74 0.73 -2.11 0.70 1.00
## exam_num.f3 2.90 0.71 1.51 4.32 1.00
## PE1.fM1:negative_emotionality 0.00 0.12 -0.24 0.24 1.00
## PE1.f0:negative_emotionality -0.29 0.15 -0.57 0.00 1.00
## Bulk_ESS Tail_ESS
## Intercept 2177 3007
## PE1.fM1 2522 2849
## PE1.f0 2826 2508
## negative_emotionality 2565 2790
## grade_100_delta 8103 2610
## exam_num.f2 6327 2993
## exam_num.f3 5510 3129
## PE1.fM1:negative_emotionality 2441 2789
## PE1.f0:negative_emotionality 2761 2754
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.21 0.21 12.82 13.62 1.00 7053 2365
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2.f * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2616)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.07 1.20 0.76 5.29 1.00 1488 1915
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.33 0.26 0.01 0.97 1.00 2146 2169
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 2.75 1.65 -0.56 6.08 1.00
## PE2.fM1 -8.11 1.79 -11.72 -4.60 1.00
## PE2.f0 -0.30 2.36 -4.95 4.40 1.00
## negative_emotionality -0.01 0.07 -0.15 0.12 1.00
## grade_100_delta 0.63 0.02 0.60 0.66 1.00
## exam_num.f2 0.22 0.59 -0.96 1.39 1.00
## exam_num.f3 1.75 0.59 0.56 2.90 1.00
## PE2.fM1:negative_emotionality -0.09 0.10 -0.29 0.11 1.00
## PE2.f0:negative_emotionality -0.30 0.13 -0.56 -0.04 1.00
## Bulk_ESS Tail_ESS
## Intercept 2131 2337
## PE2.fM1 2754 2631
## PE2.f0 3302 3069
## negative_emotionality 2764 3146
## grade_100_delta 9709 3112
## exam_num.f2 7159 3330
## exam_num.f3 5803 3192
## PE2.fM1:negative_emotionality 2769 2778
## PE2.f0:negative_emotionality 3301 2916
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.52 0.18 12.18 12.86 1.00 9914 2597
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
Simple Slopes for the split PEs
## [1] "Simple Slope for PE1.f * NE"
## PE1.f negative_emotionality.trend lower.HPD upper.HPD
## 1 -0.0968 -0.257 0.0679
## -1 -0.0937 -0.260 0.0904
## 0 -0.3819 -0.639 -0.1554
##
## Results are averaged over the levels of: exam_num.f
## Point estimate displayed: median
## HPD interval probability: 0.95
## [1] "Simple Slope for PE2.f * NE"
## PE2.f negative_emotionality.trend lower.HPD upper.HPD
## 1 -0.0134 -0.153 0.1136
## -1 -0.1010 -0.237 0.0515
## 0 -0.3150 -0.536 -0.0866
##
## Results are averaged over the levels of: exam_num.f
## Point estimate displayed: median
## HPD interval probability: 0.95
Small Positive vs Small Negative
DISCLAIMER:
In the previous ambigious PE analyses we use values between the 40th
and 60th percentiles. But that is a negatively biased sample if I were
to split negative vs. positive. So for this, I’m going to do it as small
positive mean 0 < PE <= X and small negative -X <= PE < 0. X
= the larger magnitude number, either 40/60th of the PE in question
For PE1:
X = 4; |40th percentile of PE1| = 3.746 > 1.960 = |60th percentile
of PE1| (Rounded 3.746 to the nearest integer)
For PE2:
X = 5; |40th percentile of PE1| = 0.690 < 5.000 = |60th percentile
of PE1|
## Warning: There were 33 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ small_PE1sign * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 573)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.01 1.01 0.03 3.79 1.00 1259 1866
##
## ~ID (Number of levels: 457)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.81 1.79 0.12 6.47 1.03 179 262
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 5.86 2.59 0.76 11.03 1.00
## small_PE1signM1 -3.98 3.28 -10.27 2.50 1.00
## negative_emotionality -0.43 0.14 -0.71 -0.15 1.00
## grade_100_delta 0.69 0.03 0.63 0.75 1.00
## exam_num.f2 0.47 1.20 -1.89 2.84 1.00
## exam_num.f3 2.05 1.28 -0.38 4.55 1.00
## small_PE1signM1:negative_emotionality 0.08 0.19 -0.30 0.45 1.00
## Bulk_ESS Tail_ESS
## Intercept 1974 2584
## small_PE1signM1 2058 2622
## negative_emotionality 2048 2808
## grade_100_delta 4417 3072
## exam_num.f2 3941 2811
## exam_num.f3 4200 2576
## small_PE1signM1:negative_emotionality 1883 2461
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.64 0.61 10.22 12.66 1.02 200 256
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## [1] "Simple Slope for small_PE1sign * NE"
## small_PE1sign negative_emotionality.trend lower.HPD upper.HPD
## 1 -0.428 -0.720 -0.1761
## -1 -0.353 -0.634 -0.0922
##
## Results are averaged over the levels of: exam_num.f
## Point estimate displayed: median
## HPD interval probability: 0.95
## Warning: There were 39 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ small_PE2sign * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 927)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.75 1.17 0.22 4.78 1.01 1114 1020
##
## ~ID (Number of levels: 651)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.29 0.97 0.04 3.62 1.03 244 161
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 0.55 2.05 -3.45 4.65 1.00
## small_PE2signM1 -0.55 2.59 -5.56 4.58 1.00
## negative_emotionality -0.21 0.10 -0.41 -0.02 1.00
## grade_100_delta 0.64 0.02 0.59 0.69 1.00
## exam_num.f2 1.07 0.91 -0.68 2.84 1.00
## exam_num.f3 1.51 0.92 -0.35 3.30 1.00
## small_PE2signM1:negative_emotionality -0.01 0.15 -0.29 0.27 1.00
## Bulk_ESS Tail_ESS
## Intercept 2980 2827
## small_PE2signM1 2782 2876
## negative_emotionality 3198 2875
## grade_100_delta 3453 1357
## exam_num.f2 5810 3123
## exam_num.f3 5922 2877
## small_PE2signM1:negative_emotionality 2734 2558
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.39 0.30 10.74 11.96 1.01 526 217
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## [1] "Simple Slope for small_PE2sign * NE"
## small_PE2sign negative_emotionality.trend lower.HPD upper.HPD
## 1 -0.212 -0.41 -0.0175
## -1 -0.220 -0.42 -0.0230
##
## Results are averaged over the levels of: exam_num.f
## Point estimate displayed: median
## HPD interval probability: 0.95
Sx Analysis
GAD_sum
## Warning: There were 8 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * GAD_sum + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2082)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.18 0.85 0.13 3.39 1.00 1096 1589
##
## ~ID (Number of levels: 916)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.62 0.47 0.03 1.72 1.00 1815 2071
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.41 0.84 -2.13 1.29 1.00 4408 2919
## PE1 0.53 0.04 0.45 0.62 1.00 6708 2592
## GAD_sum -0.16 0.06 -0.27 -0.04 1.00 7922 3105
## grade_100_delta 0.70 0.02 0.66 0.73 1.00 8729 3191
## exam_num.f2 -0.69 0.67 -2.01 0.63 1.00 7532 3371
## exam_num.f3 2.85 0.70 1.50 4.19 1.00 6528 3045
## PE1:GAD_sum -0.00 0.00 -0.01 0.01 1.00 6808 2693
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.77 0.20 12.38 13.17 1.00 6799 2137
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 18 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * GAD_sum + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2750)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.03 1.22 0.74 5.68 1.00 1183 964
##
## ~ID (Number of levels: 1016)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.47 0.37 0.02 1.35 1.00 1458 1723
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.58 1.17 -4.74 -0.08 1.00 1146 779
## PE2 0.49 0.04 0.42 0.55 1.00 5266 3260
## GAD_sum -0.09 0.05 -0.19 0.01 1.00 6060 2115
## grade_100_delta 0.67 0.01 0.64 0.70 1.01 7135 2453
## exam_num.f2 0.15 0.56 -0.95 1.26 1.00 6051 2914
## exam_num.f3 1.78 0.56 0.67 2.91 1.00 5687 3116
## PE2:GAD_sum 0.00 0.00 -0.01 0.01 1.00 5178 2997
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.15 0.16 11.83 12.46 1.00 8546 2609
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
PHQ_sum
## Warning: There were 3 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * PHQ_sum + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2082)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.18 0.83 0.13 3.36 1.00 1239 1845
##
## ~ID (Number of levels: 916)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.62 0.46 0.03 1.69 1.00 1505 2135
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.44 0.83 -2.04 1.25 1.00 3518 2441
## PE1 0.55 0.04 0.47 0.63 1.00 7692 2980
## PHQ_sum -0.18 0.06 -0.30 -0.05 1.01 9168 2588
## grade_100_delta 0.70 0.02 0.66 0.73 1.00 7889 2969
## exam_num.f2 -0.73 0.69 -2.05 0.62 1.00 7653 2799
## exam_num.f3 2.84 0.69 1.47 4.19 1.00 6692 2533
## PE1:PHQ_sum -0.01 0.01 -0.02 0.01 1.00 6918 2860
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.76 0.20 12.39 13.16 1.00 7886 2911
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 4 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * PHQ_sum + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2750)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.98 1.20 0.73 5.25 1.00 1307 1393
##
## ~ID (Number of levels: 1016)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.47 0.35 0.02 1.32 1.00 1584 2092
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.86 1.06 -5.07 -0.75 1.00 1721 1893
## PE2 0.48 0.03 0.42 0.54 1.00 6139 3128
## PHQ_sum -0.07 0.05 -0.17 0.03 1.00 7585 2633
## grade_100_delta 0.67 0.01 0.64 0.70 1.00 8740 2653
## exam_num.f2 0.15 0.54 -0.88 1.20 1.00 6275 3426
## exam_num.f3 1.77 0.56 0.68 2.87 1.00 5872 3287
## PE2:PHQ_sum 0.00 0.00 -0.01 0.01 1.00 4537 2211
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.15 0.17 11.82 12.47 1.00 6893 2114
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
