Main Analyses:
Updating Analyses
Updating across exam is not stable. Updating at exam two is greater
than at either of the other two
## 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.
## 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$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.98 0.80 0.06 3.09 1.00 1093 1532
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.69 0.51 0.03 1.91 1.02 342 1210
## sd(PE1) 0.33 0.04 0.24 0.41 1.00 910 2129
## cor(Intercept,PE1) 0.25 0.56 -0.92 0.97 1.10 54 88
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.44 0.71 -2.91 -0.06 1.00 1813 1605
## PE1 0.53 0.03 0.47 0.59 1.00 3775 3103
## grade_100_delta 0.70 0.02 0.67 0.74 1.00 5246 3160
## exam_num.f2 -0.70 0.65 -1.97 0.58 1.00 4063 3142
## exam_num.f3 2.70 0.67 1.41 4.05 1.00 3888 3136
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.25 0.22 11.80 12.69 1.00 2154 3030
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Warning: There were 3 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 + grade_100_delta + exam_num.f + (1 + PE2 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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) 2.05 1.16 0.76 5.30 1.00 1141 2013
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.37 0.28 0.01 1.06 1.00 1857 1567
## sd(PE2) 0.15 0.06 0.02 0.25 1.01 438 635
## cor(Intercept,PE2) -0.19 0.57 -0.97 0.90 1.01 258 533
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -3.16 1.14 -5.40 -0.78 1.00 1282 1643
## PE2 0.44 0.02 0.40 0.49 1.00 4562 2458
## grade_100_delta 0.66 0.01 0.63 0.68 1.00 5949 2808
## exam_num.f2 0.64 0.58 -0.51 1.75 1.00 4356 2606
## exam_num.f3 1.71 0.59 0.54 2.86 1.00 4820 3016
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.40 0.19 12.03 12.78 1.00 1708 2503
##
## 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 16 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$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.04 0.87 0.06 3.47 1.01 553 301
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.63 0.48 0.03 1.79 1.00 1246 2181
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.79 1.05 -3.65 0.18 1.00 754 251
## abs_PE1 -0.44 0.06 -0.55 -0.33 1.00 4013 3014
## sign_PE11 -1.15 0.91 -2.93 0.63 1.00 4103 3106
## grade_100_delta 0.69 0.02 0.65 0.73 1.00 5881 2958
## exam_num.f2 -0.80 0.72 -2.23 0.56 1.01 1264 481
## exam_num.f3 2.65 0.70 1.25 4.04 1.00 6579 2449
## abs_PE1:sign_PE11 1.11 0.08 0.96 1.28 1.00 3467 2912
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.76 0.20 12.38 13.15 1.00 5221 2532
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 7 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ abs_PE2 * sign_PE2 + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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) 2.18 1.23 0.82 5.72 1.00 1375 1477
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.34 0.26 0.01 0.96 1.00 2085 1554
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.90 1.27 -4.36 0.73 1.00 1660 1204
## abs_PE2 -0.50 0.06 -0.61 -0.39 1.00 4168 3574
## sign_PE21 -2.59 0.79 -4.16 -1.03 1.00 3923 3332
## grade_100_delta 0.65 0.01 0.62 0.68 1.00 8171 2958
## exam_num.f2 0.54 0.58 -0.61 1.70 1.00 7603 3161
## exam_num.f3 1.64 0.58 0.50 2.82 1.00 6477 3109
## abs_PE2:sign_PE21 1.05 0.07 0.91 1.19 1.00 3641 3057
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.51 0.17 12.18 12.84 1.00 10375 2765
##
## 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: 30072.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -9.6077 -0.3805 0.1547 0.5760 3.8369
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 24.584 4.958
## cohort (Intercept) 1.959 1.400
## Residual 57.872 7.607
## Number of obs: 4204, groups: ID, 1161; cohort, 5
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 91.2640 0.7030 5.3060 129.820 1.69e-10 ***
## exam_num -0.6372 0.1067 3137.8685 -5.969 2.65e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## exam_num -0.367
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 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 ~ PE1 * negative_emotionality + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2072)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.11 0.88 0.07 3.51 1.01 845 1652
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.63 0.48 0.03 1.74 1.01 1092 1592
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 1.89 1.18 -0.53 4.16 1.00 4076
## PE1 0.55 0.08 0.39 0.72 1.00 5555
## negative_emotionality -0.20 0.05 -0.31 -0.09 1.00 9541
## grade_100_delta 0.70 0.02 0.66 0.73 1.00 7950
## exam_num.f2 -0.68 0.67 -1.94 0.61 1.00 6742
## exam_num.f3 2.83 0.68 1.51 4.17 1.00 7254
## PE1:negative_emotionality -0.00 0.00 -0.01 0.01 1.00 5321
## Tail_ESS
## Intercept 2235
## PE1 2755
## negative_emotionality 3011
## grade_100_delta 2568
## exam_num.f2 3261
## exam_num.f3 3168
## PE1:negative_emotionality 2686
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.76 0.20 12.37 13.16 1.00 7126 2648
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 2 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * negative_emotionality + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2730)
## 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) 2.08 1.16 0.79 5.20 1.01 1583 2064
##
## ~ID (Number of levels: 1000)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.33 0.25 0.01 0.94 1.00 2417 1835
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -1.13 1.38 -3.89 1.59 1.00 2619
## PE2 0.36 0.07 0.22 0.49 1.00 5190
## negative_emotionality -0.12 0.05 -0.21 -0.03 1.00 8917
## grade_100_delta 0.66 0.01 0.63 0.68 1.00 10018
## exam_num.f2 0.60 0.60 -0.55 1.79 1.00 6981
## exam_num.f3 1.67 0.59 0.49 2.82 1.00 6980
## PE2:negative_emotionality 0.01 0.00 -0.00 0.01 1.00 4918
## Tail_ESS
## Intercept 2130
## PE2 2823
## negative_emotionality 2766
## grade_100_delta 2416
## exam_num.f2 3236
## exam_num.f3 2850
## PE2:negative_emotionality 3084
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.51 0.18 12.18 12.86 1.00 10115 2861
##
## 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) 3.20 1.87 1.23 8.05 1.00 1323 2264
##
## ~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 1.20 1.00 2500 1747
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept 1.64 3.22 -4.87 7.97
## abs_PE1 -0.37 0.24 -0.84 0.11
## sign_PE11 -4.85 3.97 -12.66 2.82
## negative_emotionality -0.46 0.16 -0.78 -0.13
## abs_PE1:sign_PE11 1.03 0.37 0.29 1.77
## abs_PE1:negative_emotionality 0.02 0.01 -0.01 0.05
## sign_PE11:negative_emotionality 0.14 0.23 -0.30 0.58
## abs_PE1:sign_PE11:negative_emotionality -0.02 0.02 -0.06 0.02
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 2172 3148
## abs_PE1 1.00 2180 3010
## sign_PE11 1.00 1975 2717
## negative_emotionality 1.00 2335 2986
## abs_PE1:sign_PE11 1.00 2008 2807
## abs_PE1:negative_emotionality 1.00 2168 2942
## sign_PE11:negative_emotionality 1.00 1940 2521
## abs_PE1:sign_PE11:negative_emotionality 1.00 1882 2625
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 16.66 0.26 16.15 17.16 1.00 9317 2932
##
## 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 ~ abs_PE2 * sign_PE2 * negative_emotionality + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2733)
## 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) 4.39 2.42 1.86 10.75 1.00 1528 1905
##
## ~ID (Number of levels: 1001)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.32 0.24 0.01 0.87 1.00 2659 1943
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI
## Intercept -0.43 3.24 -6.83 6.02
## abs_PE2 -0.32 0.22 -0.76 0.13
## sign_PE21 -3.53 3.41 -10.19 3.18
## negative_emotionality -0.25 0.15 -0.53 0.04
## abs_PE2:sign_PE21 0.62 0.30 -0.00 1.20
## abs_PE2:negative_emotionality 0.02 0.01 -0.01 0.04
## sign_PE21:negative_emotionality 0.03 0.20 -0.35 0.41
## abs_PE2:sign_PE21:negative_emotionality -0.01 0.02 -0.04 0.03
## Rhat Bulk_ESS Tail_ESS
## Intercept 1.00 2162 2476
## abs_PE2 1.00 2238 2490
## sign_PE21 1.00 2145 2760
## negative_emotionality 1.00 2352 2795
## abs_PE2:sign_PE21 1.00 1966 2460
## abs_PE2:negative_emotionality 1.00 2281 2721
## sign_PE21:negative_emotionality 1.00 2183 3032
## abs_PE2:sign_PE21:negative_emotionality 1.00 1977 2693
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 16.40 0.22 15.97 16.84 1.00 10030 2343
##
## 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$PE1) < 30, ] (Number of observations: 2072)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.61 1.10 0.37 4.49 1.01 1049 1642
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.36 0.28 0.01 1.05 1.00 1828 1563
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -70.74 13.77 -97.45 -43.30 1.00
## Accuracy_1 0.77 0.15 0.47 1.06 1.00
## negative_emotionality 4.42 0.77 2.92 5.91 1.00
## grade_100_delta 0.61 0.02 0.57 0.65 1.00
## exam_num.f2 -0.34 0.74 -1.79 1.11 1.00
## exam_num.f3 3.44 0.76 1.95 4.93 1.00
## Accuracy_1:negative_emotionality -0.05 0.01 -0.07 -0.03 1.00
## Bulk_ESS Tail_ESS
## Intercept 2100 2435
## Accuracy_1 2118 2516
## negative_emotionality 2077 2284
## grade_100_delta 5600 3074
## exam_num.f2 4344 2831
## exam_num.f3 4720 3201
## Accuracy_1:negative_emotionality 2080 2317
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.87 0.21 13.46 14.29 1.00 5785 3099
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ Accuracy_2 * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2730)
## 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) 2.42 1.46 0.90 6.07 1.00 1232 1965
##
## ~ID (Number of levels: 1000)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.27 0.20 0.01 0.74 1.00 2254 1803
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -35.03 11.06 -56.82 -13.21 1.00
## Accuracy_2 0.36 0.12 0.13 0.60 1.00
## negative_emotionality 2.74 0.62 1.52 3.96 1.00
## grade_100_delta 0.58 0.01 0.55 0.61 1.00
## exam_num.f2 0.73 0.61 -0.45 1.95 1.00
## exam_num.f3 2.07 0.64 0.82 3.34 1.00
## Accuracy_2:negative_emotionality -0.03 0.01 -0.04 -0.02 1.00
## Bulk_ESS Tail_ESS
## Intercept 1781 2435
## Accuracy_2 1839 2103
## negative_emotionality 1844 2025
## grade_100_delta 5677 2813
## exam_num.f2 4559 3102
## exam_num.f3 4672 2754
## Accuracy_2:negative_emotionality 1864 2027
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.29 0.18 12.94 13.64 1.00 5435 2657
##
## 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
## 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) 7.67 5.35 0.43 20.04 1.00
## sds(t2PE1negative_emotionality_2) 7.33 6.35 0.26 23.34 1.00
## sds(t2PE1negative_emotionality_3) 13.13 8.02 1.00 31.53 1.00
## Bulk_ESS Tail_ESS
## sds(t2PE1negative_emotionality_1) 1539 1506
## sds(t2PE1negative_emotionality_2) 1818 2051
## sds(t2PE1negative_emotionality_3) 1414 1353
##
## 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 0.85 0.07 3.27 1.00 1141 1312
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.65 0.51 0.02 1.90 1.01 693 1276
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -0.84 0.92 -2.66 1.03 1.00 1893
## grade_100_delta 0.69 0.02 0.66 0.73 1.00 5045
## exam_num.f2 -0.80 0.68 -2.13 0.50 1.00 4307
## exam_num.f3 2.60 0.70 1.25 3.97 1.00 4001
## t2PE1negative_emotionality_1 0.70 0.56 -0.45 1.76 1.00 2929
## t2PE1negative_emotionality_2 -6.55 0.52 -7.56 -5.49 1.00 3118
## t2PE1negative_emotionality_3 -0.64 0.71 -2.07 0.73 1.00 3023
## Tail_ESS
## Intercept 2052
## grade_100_delta 3002
## exam_num.f2 3077
## exam_num.f3 3190
## t2PE1negative_emotionality_1 3102
## t2PE1negative_emotionality_2 2661
## t2PE1negative_emotionality_3 2888
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.71 0.21 12.33 13.12 1.00 5193 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).
## 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 ~ t2(PE2, negative_emotionality) + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[predictions$abs_PE2 < 30, ] (Number of observations: 2730)
## 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) 5.50 5.03 0.19 18.44 1.00
## sds(t2PE2negative_emotionality_2) 5.67 5.45 0.18 18.71 1.00
## sds(t2PE2negative_emotionality_3) 13.63 8.97 1.01 34.57 1.00
## Bulk_ESS Tail_ESS
## sds(t2PE2negative_emotionality_1) 2364 2509
## sds(t2PE2negative_emotionality_2) 2364 2229
## sds(t2PE2negative_emotionality_3) 1471 1475
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.15 1.20 0.79 5.33 1.00 1097 1481
##
## ~ID (Number of levels: 1000)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.34 0.26 0.01 0.94 1.00 1828 1515
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -1.67 1.23 -4.24 0.85 1.00 1191
## grade_100_delta 0.66 0.01 0.63 0.68 1.00 6520
## exam_num.f2 0.57 0.58 -0.58 1.70 1.00 4960
## exam_num.f3 1.61 0.58 0.52 2.77 1.00 4845
## t2PE2negative_emotionality_1 0.35 0.45 -0.53 1.23 1.00 2693
## t2PE2negative_emotionality_2 -5.66 0.43 -6.55 -4.82 1.00 3004
## t2PE2negative_emotionality_3 0.22 0.55 -0.87 1.26 1.00 3791
## Tail_ESS
## Intercept 1500
## grade_100_delta 2967
## exam_num.f2 3229
## exam_num.f3 3292
## t2PE2negative_emotionality_1 2730
## t2PE2negative_emotionality_2 2760
## t2PE2negative_emotionality_3 3188
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.50 0.17 12.17 12.85 1.00 6917 2656
##
## 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 50 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) 1.45 1.30 0.17 6.48 1.02 143 31
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.84 0.63 0.03 2.34 1.00 734 1119
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.00 1.06 -3.67 1.71 1.03 180 30
## EVPE 0.23 0.02 0.19 0.28 1.00 4489 2961
## PE1 0.64 0.03 0.59 0.70 1.00 2114 2642
## grade_100_delta 0.66 0.02 0.63 0.70 1.01 439 1425
## exam_num.f2 -0.47 0.66 -1.72 0.85 1.01 768 2104
## exam_num.f3 2.58 0.66 1.28 3.86 1.00 5114 3087
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.42 0.19 12.04 12.79 1.00 3192 2439
##
## 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: 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 193 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: 2745)
## 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) 2.98 2.90 0.89 13.47 1.05 53 26
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.36 0.26 0.02 1.00 1.01 2130 2067
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.37 1.33 -4.79 0.44 1.03 92 37
## EVPE 0.12 0.02 0.08 0.16 1.03 100 57
## PE2 0.50 0.02 0.45 0.55 1.01 4977 2692
## grade_100_delta 0.63 0.02 0.60 0.66 1.03 103 143
## exam_num.f2 0.75 0.60 -0.45 1.85 1.02 157 366
## exam_num.f3 1.51 0.58 0.34 2.64 1.00 4656 2915
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.45 0.17 12.12 12.78 1.01 466 2852
##
## 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 25 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$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.01 0.78 0.06 2.93 1.00 1033 1248
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.83 0.62 0.03 2.32 1.01 719 771
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.62 1.04 -2.67 1.39 1.00 3278 2571
## EVPE_abs -0.14 0.04 -0.22 -0.06 1.00 4419 2842
## EVPE_sign1 0.20 1.02 -1.74 2.24 1.00 5033 3132
## abs_PE1 -0.68 0.06 -0.80 -0.57 1.00 4905 2995
## sign_PE11 -0.94 0.90 -2.72 0.78 1.00 4719 3293
## grade_100_delta 0.66 0.02 0.62 0.69 1.00 6633 2892
## exam_num.f2 -0.53 0.66 -1.84 0.77 1.00 5516 2523
## exam_num.f3 2.51 0.67 1.25 3.81 1.00 6319 2824
## EVPE_abs:EVPE_sign1 0.50 0.07 0.36 0.64 1.00 3913 3272
## abs_PE1:sign_PE11 1.33 0.08 1.17 1.49 1.00 3943 3039
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.40 0.20 12.02 12.78 1.00 3807 2204
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 7 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ EVPE_abs * EVPE_sign + abs_PE2 * sign_PE2 + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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) 2.06 1.20 0.77 5.30 1.00 1488 1581
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.34 0.26 0.02 0.96 1.00 2060 2011
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -2.67 1.25 -5.14 -0.23 1.00 2343 2097
## EVPE_abs 0.01 0.04 -0.06 0.08 1.00 4653 3386
## EVPE_sign1 1.00 0.89 -0.74 2.72 1.00 4072 2857
## abs_PE2 -0.65 0.06 -0.76 -0.54 1.00 4225 3392
## sign_PE21 -2.68 0.80 -4.24 -1.10 1.00 4293 2733
## grade_100_delta 0.63 0.02 0.60 0.66 1.00 8323 2709
## exam_num.f2 0.58 0.58 -0.56 1.70 1.00 6701 3208
## exam_num.f3 1.38 0.58 0.25 2.50 1.00 6465 3153
## EVPE_abs:EVPE_sign1 0.20 0.06 0.09 0.31 1.00 3692 2909
## abs_PE2:sign_PE21 1.20 0.07 1.04 1.34 1.00 3679 2791
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.39 0.17 12.07 12.72 1.00 9666 3117
##
## 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 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 ~ 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) 6.86 5.82 0.23 21.29 1.00
## sds(t2EVPEnegative_emotionality_2) 6.63 5.91 0.20 21.62 1.00
## sds(t2EVPEnegative_emotionality_3) 10.55 8.96 0.37 33.37 1.00
## Bulk_ESS Tail_ESS
## sds(t2EVPEnegative_emotionality_1) 2825 2332
## sds(t2EVPEnegative_emotionality_2) 2960 2358
## sds(t2EVPEnegative_emotionality_3) 2276 2083
##
## 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 0.93 0.09 3.71 1.00 1149 1545
##
## ~ID (Number of levels: 925)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.33 0.26 0.01 0.95 1.00 2629 1877
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -2.15 0.95 -4.04 -0.23 1.00
## grade_100_delta 0.58 0.02 0.54 0.62 1.00
## exam_num.f2 0.18 0.75 -1.26 1.66 1.00
## exam_num.f3 3.82 0.78 2.26 5.32 1.00
## t2EVPEnegative_emotionality_1 0.24 0.45 -0.66 1.15 1.00
## t2EVPEnegative_emotionality_2 0.05 0.77 -1.45 1.60 1.00
## t2EVPEnegative_emotionality_3 -0.23 0.97 -2.21 1.62 1.00
## Bulk_ESS Tail_ESS
## Intercept 2531 2479
## grade_100_delta 7614 3182
## exam_num.f2 6214 3060
## exam_num.f3 5896 3127
## t2EVPEnegative_emotionality_1 4455 3048
## t2EVPEnegative_emotionality_2 4397 3302
## t2EVPEnegative_emotionality_3 4585 2691
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 14.71 0.23 14.28 15.16 1.00 7785 2727
##
## 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 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_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) 6.90 5.32 0.31 20.27 1.00
## sds(t2EVPEnegative_emotionality_2) 6.87 5.93 0.26 22.50 1.00
## sds(t2EVPEnegative_emotionality_3) 10.42 7.53 0.45 28.91 1.00
## Bulk_ESS Tail_ESS
## sds(t2EVPEnegative_emotionality_1) 1873 1298
## sds(t2EVPEnegative_emotionality_2) 2903 2137
## sds(t2EVPEnegative_emotionality_3) 2566 2265
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.15 1.29 0.74 5.44 1.00 1265 1862
##
## ~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 2519 1479
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept -2.26 1.25 -4.74 0.23 1.00
## grade_100_delta 0.58 0.02 0.55 0.62 1.00
## exam_num.f2 1.14 0.64 -0.12 2.38 1.00
## exam_num.f3 2.78 0.65 1.51 4.05 1.00
## t2EVPEnegative_emotionality_1 0.08 0.42 -0.73 0.91 1.00
## t2EVPEnegative_emotionality_2 1.11 0.66 -0.24 2.41 1.00
## t2EVPEnegative_emotionality_3 0.41 0.84 -1.21 2.15 1.00
## Bulk_ESS Tail_ESS
## Intercept 1722 2075
## grade_100_delta 6459 3065
## exam_num.f2 5769 3305
## exam_num.f3 5898 3013
## t2EVPEnegative_emotionality_1 3912 2903
## t2EVPEnegative_emotionality_2 3394 3117
## t2EVPEnegative_emotionality_3 3919 2843
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.93 0.18 13.59 14.29 1.00 8204 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).
Follow ups (7/28/26)
Add Delta Goal Grade
## 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_1_delta ~ PE1 + grade_100_delta + exam_num.f + (1 | cohort) + (1 + PE1 | ID)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.97 0.84 0.04 3.15 1.00 726 1132
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.73 0.50 0.04 1.87 1.01 385 1352
## sd(PE1) 0.32 0.04 0.24 0.40 1.00 999 1491
## cor(Intercept,PE1) 0.35 0.48 -0.83 0.97 1.06 59 126
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -1.48 0.71 -3.02 -0.16 1.00 1192 1174
## PE1 0.53 0.03 0.48 0.59 1.00 3131 3144
## grade_100_delta 0.70 0.02 0.67 0.74 1.00 3835 2666
## exam_num.f2 -0.72 0.65 -1.99 0.52 1.00 3747 3130
## exam_num.f3 2.69 0.68 1.38 4.03 1.00 3613 2887
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.24 0.22 11.81 12.69 1.00 2123 2727
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Ignoring unknown labels:
## • fill : "NA"
## • colour : "NA"
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 + grade_100_delta + exam_num.f + (1 | cohort) + (1 + PE2 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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 1.21 0.75 5.32 1.00 1264 1360
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.36 0.27 0.02 1.00 1.01 1450 1969
## sd(PE2) 0.15 0.06 0.02 0.24 1.01 583 479
## cor(Intercept,PE2) -0.18 0.55 -0.95 0.91 1.00 247 853
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -3.13 1.10 -5.34 -0.83 1.00 1453 1528
## PE2 0.44 0.02 0.40 0.49 1.00 4271 2896
## grade_100_delta 0.66 0.01 0.63 0.69 1.00 5613 3260
## exam_num.f2 0.62 0.59 -0.51 1.78 1.00 4821 3182
## exam_num.f3 1.69 0.59 0.55 2.87 1.00 4282 3244
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.41 0.19 12.03 12.80 1.00 2615 2255
##
## 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 103 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$PE1) < 5, ] (Number of observations: 734)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.45 1.26 0.07 4.79 1.00 848 1467
##
## ~ID (Number of levels: 545)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 2.14 1.46 0.08 5.26 1.02 227 275
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 2.94 1.79 -0.52 6.63 1.00 2190
## PE1 0.38 0.50 -0.62 1.35 1.00 1536
## negative_emotionality -0.30 0.09 -0.47 -0.12 1.00 4168
## grade_100_delta 0.66 0.03 0.60 0.72 1.00 1242
## exam_num.f2 -0.22 1.04 -2.24 1.79 1.00 3402
## exam_num.f3 1.94 1.16 -0.30 4.15 1.00 2237
## PE1:negative_emotionality 0.01 0.03 -0.05 0.07 1.00 1696
## Tail_ESS
## Intercept 2018
## PE1 999
## negative_emotionality 2420
## grade_100_delta 444
## exam_num.f2 3102
## exam_num.f3 2085
## PE1:negative_emotionality 1325
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 11.81 0.43 10.86 12.59 1.01 346 236
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.8 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 5, ] (Number of observations: 969)
## 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) 1.95 1.29 0.35 5.28 1.00 1027 1667
##
## ~ID (Number of levels: 600)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.60 0.45 0.03 1.69 1.00 2145 1921
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 0.61 1.67 -2.62 3.95 1.00 4970
## PE2 0.04 0.48 -0.87 1.00 1.00 6638
## negative_emotionality -0.24 0.07 -0.38 -0.10 1.00 11665
## grade_100_delta 0.64 0.02 0.59 0.68 1.00 10444
## exam_num.f2 2.11 0.94 0.27 3.99 1.00 7528
## exam_num.f3 1.85 0.97 -0.04 3.75 1.00 7666
## PE2:negative_emotionality 0.01 0.03 -0.05 0.06 1.00 6382
## Tail_ESS
## Intercept 2828
## PE2 2912
## negative_emotionality 2994
## grade_100_delta 2589
## exam_num.f2 2968
## exam_num.f3 3309
## PE2:negative_emotionality 2850
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.15 0.28 11.63 12.71 1.00 9674 3018
##
## 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) 1.17 0.87 0.10 3.46 1.00 1321 1767
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.42 0.33 0.02 1.22 1.00 2157 2008
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 4.99 1.69 1.66 8.37 1.00
## PE1.fM1 -10.36 2.17 -14.70 -6.13 1.00
## PE1.f0 -1.91 2.58 -7.01 3.21 1.00
## negative_emotionality -0.09 0.08 -0.26 0.07 1.00
## grade_100_delta 0.67 0.02 0.63 0.70 1.00
## exam_num.f2 -0.76 0.69 -2.08 0.62 1.00
## exam_num.f3 2.89 0.72 1.48 4.31 1.00
## PE1.fM1:negative_emotionality -0.00 0.12 -0.24 0.24 1.00
## PE1.f0:negative_emotionality -0.29 0.15 -0.58 -0.00 1.00
## Bulk_ESS Tail_ESS
## Intercept 3042 2834
## PE1.fM1 3415 3245
## PE1.f0 3623 3137
## negative_emotionality 3131 3270
## grade_100_delta 7461 2817
## exam_num.f2 7751 2924
## exam_num.f3 6983 3127
## PE1.fM1:negative_emotionality 3401 3482
## PE1.f0:negative_emotionality 3962 2913
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.22 0.20 12.83 13.62 1.00 11376 2908
##
## 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 ~ PE2.f * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2588)
## 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) 2.09 1.27 0.73 5.52 1.00 1159 1476
##
## ~ID (Number of levels: 995)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.32 0.24 0.01 0.91 1.00 2283 1593
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## Intercept 1.21 1.68 -2.19 4.64 1.00
## PE2.fM1 -5.61 1.78 -9.17 -2.12 1.00
## PE2.f0 1.74 2.53 -3.29 6.49 1.00
## negative_emotionality 0.03 0.07 -0.11 0.17 1.00
## grade_100_delta 0.63 0.02 0.60 0.66 1.00
## exam_num.f2 0.27 0.60 -0.89 1.45 1.00
## exam_num.f3 1.74 0.61 0.53 2.93 1.00
## PE2.fM1:negative_emotionality -0.15 0.10 -0.35 0.06 1.00
## PE2.f0:negative_emotionality -0.37 0.14 -0.64 -0.09 1.00
## Bulk_ESS Tail_ESS
## Intercept 2113 1703
## PE2.fM1 2982 1836
## PE2.f0 3357 2009
## negative_emotionality 2793 3014
## grade_100_delta 8645 2578
## exam_num.f2 6551 3422
## exam_num.f3 7962 3315
## PE2.fM1:negative_emotionality 2900 1955
## PE2.f0:negative_emotionality 3259 1970
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.81 0.18 12.46 13.17 1.00 9016 2426
##
## 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).
0 + PE as factor
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ 0 + 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) 1.20 0.94 0.13 3.60 1.00 1249 1491
##
## ~ID (Number of levels: 912)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.45 0.34 0.02 1.26 1.00 1638 1776
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## PE1.f1 5.95 1.96 2.08 9.74 1.00
## PE1.fM1 -6.08 1.79 -9.71 -2.62 1.00
## PE1.f0 3.17 1.75 -0.18 6.53 1.00
## negative_emotionality -0.09 0.10 -0.28 0.11 1.00
## grade_100_delta 0.67 0.02 0.64 0.71 1.00
## exam_num.f2 -0.67 0.69 -2.02 0.71 1.00
## exam_num.f3 2.98 0.71 1.60 4.36 1.00
## PE1.fM1:negative_emotionality -0.02 0.13 -0.28 0.24 1.00
## PE1.f0:negative_emotionality -0.22 0.13 -0.48 0.03 1.00
## Bulk_ESS Tail_ESS
## PE1.f1 1385 1966
## PE1.fM1 3266 2781
## PE1.f0 3025 2844
## negative_emotionality 1710 2430
## grade_100_delta 6572 3378
## exam_num.f2 4111 3019
## exam_num.f3 3718 2805
## PE1.fM1:negative_emotionality 2157 2759
## PE1.f0:negative_emotionality 2084 2622
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 13.14 0.20 12.76 13.55 1.00 5552 3091
##
## 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 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_2_delta ~ 0 + PE2.f * negative_emotionality + grade_100_delta + exam_num.f + (1 | cohort) + (1 | ID)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2730)
## 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) 2.04 1.22 0.77 5.21 1.00 972 1141
##
## ~ID (Number of levels: 1000)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.30 0.22 0.01 0.84 1.00 1955 1730
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat
## PE2.f1 1.34 1.72 -2.09 4.79 1.00
## PE2.fM1 -7.56 2.01 -11.54 -3.67 1.00
## PE2.f0 0.84 1.72 -2.52 4.24 1.00
## negative_emotionality 0.02 0.07 -0.11 0.17 1.00
## grade_100_delta 0.64 0.01 0.61 0.67 1.00
## exam_num.f2 0.73 0.60 -0.45 1.89 1.00
## exam_num.f3 1.95 0.61 0.76 3.16 1.00
## PE2.fM1:negative_emotionality -0.09 0.12 -0.32 0.16 1.00
## PE2.f0:negative_emotionality -0.24 0.10 -0.44 -0.04 1.00
## Bulk_ESS Tail_ESS
## PE2.f1 991 1238
## PE2.fM1 1543 1420
## PE2.f0 1301 1150
## negative_emotionality 2097 2171
## grade_100_delta 5081 2812
## exam_num.f2 3674 3206
## exam_num.f3 3531 2468
## PE2.fM1:negative_emotionality 2682 2752
## PE2.f0:negative_emotionality 2302 2703
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.79 0.17 12.46 13.12 1.00 5499 2908
##
## 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).
Sx Analysis
###GAD_sum_mean
## 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.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * GAD_sum_mean + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.65 0.73 0.01 2.80 1.40 9 27
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.78 0.53 0.05 2.03 1.95 6 13
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 2336.34 13107.15 -23252.12 41967.65 2.01 6 12
## PE1 93.27 186.24 -237.31 439.17 2.25 5 13
## GAD_sum_mean -206.25 1156.51 -3703.12 2051.64 2.01 6 12
## grade_100_delta 0.70 0.02 0.67 0.73 1.17 16 104
## exam_num.f2 -0.79 0.68 -2.10 0.58 1.27 13 30
## exam_num.f3 2.68 0.71 1.38 4.24 1.41 8 33
## PE1:GAD_sum_mean -8.18 16.43 -38.71 20.99 2.25 5 13
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.83 0.18 12.46 13.15 1.35 11 67
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * GAD_sum_mean + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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) 1.85 1.19 0.81 4.69 1.90 6 31
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.50 0.27 0.01 1.05 1.39 9 13
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -5349.08 15106.37 -40274.33 21178.50 2.31 5 16
## PE2 109.58 295.72 -604.67 393.78 2.31 5 11
## GAD_sum_mean 471.70 1332.92 -1868.92 3553.35 2.31 5 16
## grade_100_delta 0.65 0.02 0.62 0.68 1.56 7 15
## exam_num.f2 0.40 0.58 -0.71 1.49 1.42 9 43
## exam_num.f3 1.57 0.60 0.39 2.67 1.23 13 25
## PE2:GAD_sum_mean -9.63 26.09 -34.71 53.39 2.31 5 11
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.62 0.18 12.25 12.96 1.42 8 16
##
## 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).
###GAD_sum_std
## 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.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * GAD_sum_std + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 1.27 0.94 0.09 3.40 1.21 16 85
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.90 0.61 0.10 2.15 1.75 6 18
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 414.21 8678.44 -22209.70 17214.42 1.83 10 14
## PE1 122.87 291.23 -315.13 644.96 2.63 5 12
## GAD_sum_std -109.71 2292.26 -4547.25 5866.13 1.83 10 14
## grade_100_delta 0.70 0.02 0.67 0.73 1.13 23 78
## exam_num.f2 -0.91 0.65 -2.28 0.24 1.48 8 16
## exam_num.f3 2.57 0.75 1.33 4.02 1.23 13 33
## PE1:GAD_sum_std -32.32 76.92 -170.22 83.38 2.63 5 12
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.79 0.18 12.44 13.11 1.06 49 131
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * GAD_sum_std + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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) 2.39 1.48 0.93 6.14 1.73 6 16
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.45 0.28 0.05 1.12 1.56 7 18
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -8011.42 12969.72 -29901.10 11521.30 2.54 5 12
## PE2 32.21 253.51 -311.28 546.36 3.30 4 18
## GAD_sum_std 2115.16 3425.62 -3043.63 7897.02 2.54 5 12
## grade_100_delta 0.65 0.01 0.63 0.68 1.17 17 47
## exam_num.f2 0.30 0.57 -0.75 1.39 1.16 18 80
## exam_num.f3 1.53 0.52 0.50 2.46 1.23 13 26
## PE2:GAD_sum_std -8.39 66.96 -144.20 82.33 3.30 4 18
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.56 0.15 12.25 12.82 1.16 20 78
##
## 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_mean
## 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.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * PHQ_sum_mean + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.84 0.63 0.07 2.49 1.27 14 20
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.78 0.53 0.13 2.11 1.65 7 28
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3020.50 16186.67 -26930.27 27094.64 2.33 5 16
## PE1 -68.42 151.15 -344.34 192.84 2.28 5 12
## PHQ_sum_mean -232.46 1245.13 -2084.30 2071.46 2.33 5 16
## grade_100_delta 0.70 0.02 0.66 0.73 1.17 17 40
## exam_num.f2 -0.61 0.75 -1.86 1.05 1.38 9 24
## exam_num.f3 2.94 0.73 1.61 4.29 1.22 17 65
## PE1:PHQ_sum_mean 5.30 11.63 -14.79 26.53 2.28 5 12
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.84 0.25 12.34 13.28 1.43 9 54
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * PHQ_sum_mean + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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) 1.85 0.79 0.54 3.74 1.63 7 22
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.47 0.31 0.09 1.22 1.46 8 37
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -17698.43 32344.00 -88368.72 18275.12 2.85 5 14
## PE2 -55.60 106.46 -230.13 131.55 1.78 6 18
## PHQ_sum_mean 1361.17 2487.99 -1406.22 6797.27 2.85 5 14
## grade_100_delta 0.65 0.01 0.63 0.68 1.37 9 39
## exam_num.f2 0.42 0.59 -0.76 1.51 1.27 11 41
## exam_num.f3 1.63 0.64 0.38 2.88 1.28 12 40
## PE2:PHQ_sum_mean 4.31 8.19 -10.09 17.73 1.78 6 18
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.53 0.15 12.21 12.82 1.10 49 48
##
## 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_std
## 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.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_1_delta ~ PE1 * PHQ_sum_std + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE1) < 30, ] (Number of observations: 2084)
## Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup draws = 4000
##
## Multilevel Hyperparameters:
## ~cohort (Number of levels: 5)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.93 0.63 0.10 2.41 1.29 12 15
##
## ~ID (Number of levels: 917)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.67 0.46 0.04 1.71 2.00 6 21
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 3868.06 7785.78 -3307.35 23297.72 2.37 6 16
## PE1 -72.25 189.34 -369.61 267.46 2.77 5 13
## PHQ_sum_std -1073.24 2159.44 -6462.25 916.87 2.37 6 16
## grade_100_delta 0.70 0.02 0.67 0.74 1.27 11 39
## exam_num.f2 -0.61 0.69 -2.31 0.51 1.31 11 19
## exam_num.f3 2.97 0.67 1.75 4.64 1.19 16 25
## PE1:PHQ_sum_std 20.18 52.51 -74.04 102.66 2.77 5 13
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.83 0.20 12.44 13.22 1.16 24 82
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).
## Warning: Parts of the model have not converged (some Rhats are > 1.05). Be
## careful when analysing the results! We recommend running more iterations and/or
## setting stronger priors.
## Family: gaussian
## Links: mu = identity
## Formula: Prediction_2_delta ~ PE2 * PHQ_sum_std + grade_100_delta + exam_num.f + (1 | ID) + (1 | cohort)
## Data: predictions[abs(predictions$PE2) < 30, ] (Number of observations: 2745)
## 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) 2.00 1.18 0.94 4.70 1.23 18 33
##
## ~ID (Number of levels: 1005)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(Intercept) 0.49 0.28 0.04 1.02 1.30 11 74
##
## Regression Coefficients:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept 1631.40 2778.69 -892.65 9057.75 2.02 6 29
## PE2 -141.42 475.16 -1038.08 434.29 2.81 5 12
## PHQ_sum_std -453.31 770.61 -2512.92 246.67 2.02 6 29
## grade_100_delta 0.66 0.01 0.63 0.69 1.18 21 94
## exam_num.f2 0.62 0.55 -0.38 1.67 1.20 16 85
## exam_num.f3 1.91 0.52 0.80 2.88 1.14 21 74
## PE2:PHQ_sum_std 39.35 131.79 -120.33 288.04 2.81 5 12
##
## Further Distributional Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 12.51 0.14 12.19 12.79 1.13 60 69
##
## 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).
