Expectation updating, PEs, and information content
William Villano
2/24/2021
Does PE direction matter for updating?
95% Confidence intervals for positive and negative PE parameters do not overlap. Effects of positive and negative PEs on latter updating are significantly different.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## delta_pred_2 ~ 0 + isPosPE_lag1:unsigned_lag_pe_2 + isNegPE_lag1:unsigned_lag_pe_2 +
## (1 | id)
## Data: df.new
##
## REML criterion at convergence: 12596.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9181 -0.5717 -0.0298 0.4869 3.6850
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 224.1 14.97
## Number of obs: 1526, groups: id, 696
##
## Fixed effects:
## Estimate Std. Error df t value
## isPosPE_lag10:unsigned_lag_pe_2 -0.17702 0.04964 1524.00000 -3.566
## isPosPE_lag11:unsigned_lag_pe_2 0.35671 0.03992 1524.00000 8.936
## Pr(>|t|)
## isPosPE_lag10:unsigned_lag_pe_2 0.000374 ***
## isPosPE_lag11:unsigned_lag_pe_2 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## iPPE_10
## iPPE_11:___ 0.000
## fit warnings:
## fixed-effect model matrix is rank deficient so dropping 1 column / coefficient
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
## 2.5 % 97.5 %
## isPosPE_lag10:unsigned_lag_pe_2 -0.2743219 -0.07972609
## isPosPE_lag11:unsigned_lag_pe_2 0.2784738 0.43493884distribution of prediction adjustment
| n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Prediction Adjustment | 2565 | -2.47 | 7.02 | 0 | -2.23 | 2.97 | -40 | 45 | 85 | -0.3 | 6.34 | 0.14 |
distribution of confidence in Prediction 1 and Prediction 2
How does confidence relate to prediction adjustment?
Confidence is associated with lower prediction adjustment.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: unsigned_pred_adj ~ conf_1 + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 16413.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.8502 -0.6401 -0.3008 0.2802 6.5953
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 5.058 2.249
## Residual 31.213 5.587
## Number of obs: 2560, groups: id, 873
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.458e+00 3.447e-01 1.622e+03 15.834 < 2e-16 ***
## conf_1 -1.589e-02 5.214e-03 1.911e+03 -3.047 0.00234 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## conf_1 -0.918
Does direction of prediction adjustment matter for confidence?
Low confidence is more strongly associated with negative prediction adjustments than positive.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: conf_1 ~ unsigned_pred_adj:pred_adj_sign + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 12794.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.77686 -0.52454 0.05481 0.59979 2.91508
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 251.3 15.85
## Residual 307.7 17.54
## Number of obs: 1415, groups: id, 755
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 62.4294 1.0944 1210.9308 57.046
## unsigned_pred_adj:pred_adj_sign-1 -0.3921 0.1039 1377.4743 -3.774
## unsigned_pred_adj:pred_adj_sign1 0.1220 0.1377 1285.7425 0.886
## Pr(>|t|)
## (Intercept) < 2e-16 ***
## unsigned_pred_adj:pred_adj_sign-1 0.000168 ***
## unsigned_pred_adj:pred_adj_sign1 0.375758
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) u__:__-
## unsg__:__-1 -0.689
## unsgn__:__1 -0.465 0.406
Negative, but not positive prediction adjustments are associated with confidence in prediction 1. Effect of confidence on positive prediction adjustment does not differ significantly from zero.
Does prediction adjustment track cumulative error in prediction (SSE) at the final exam?
SSE at the final exam is unrelated to confidence. This is true for confidence in both first and second prediction.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: conf_2 ~ pred_2_sse + (1 | cohort/class)
## Data: df.new[which(df.new$is_final == 1), ]
##
## REML criterion at convergence: 3347.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.30678 -0.58688 -0.01982 0.76697 1.89781
##
## Random effects:
## Groups Name Variance Std.Dev.
## class:cohort (Intercept) 2.516 1.586
## cohort (Intercept) 0.000 0.000
## Residual 598.170 24.458
## Number of obs: 362, groups: class:cohort, 3; cohort, 2
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 57.615490 2.262717 7.595607 25.46 1.25e-08 ***
## pred_2_sse -0.002527 0.003280 302.286651 -0.77 0.442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## pred_2_sse -0.708
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularIf prediction adjustment is a proxy for uncertainty, is it related to updating?
Greater prediction adjustment is associated with larger updates on subsequent exams.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: delta_pred_2 ~ unsigned_pred_adj_lag1 + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 12605.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9167 -0.5559 0.1090 0.5413 4.3644
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 226.2 15.04
## Number of obs: 1526, groups: id, 696
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -1.63929 0.47157 1524.00000 -3.476 0.000523 ***
## unsigned_pred_adj_lag1 0.55853 0.06476 1524.00000 8.624 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## unsgnd_p__1 -0.577
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
Does direction of prediciton adustment matter for latter updating?
Learning rate is apparently steeper following negative prediction adjustments.
##
## Call:
## lm(formula = delta_pred_2 ~ pred_adj_sign_lag1:unsigned_pred_adj_lag1,
## data = df.new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -74.316 -7.807 0.684 8.438 53.333
##
## Coefficients:
## Estimate Std. Error t value
## (Intercept) -4.98189 0.83067 -5.997
## pred_adj_sign_lag1-1:unsigned_pred_adj_lag1 0.92975 0.09116 10.199
## pred_adj_sign_lag11:unsigned_pred_adj_lag1 0.50396 0.11981 4.206
## Pr(>|t|)
## (Intercept) 2.99e-09 ***
## pred_adj_sign_lag1-1:unsigned_pred_adj_lag1 < 2e-16 ***
## pred_adj_sign_lag11:unsigned_pred_adj_lag1 2.88e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14.86 on 828 degrees of freedom
## (3534 observations deleted due to missingness)
## Multiple R-squared: 0.1119, Adjusted R-squared: 0.1097
## F-statistic: 52.15 on 2 and 828 DF, p-value: < 2.2e-16
Does uncertainty modulate affective reactivity to PEs?
Prediction adjustment as a proxy for uncertainty
Here, mean PA and NA following grade reveal are the criterion variables. Affective reactivity to PEs is greater when uncertainty is low (i.e., less prediction adjustment).
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PA_Mean_DSP_bc ~ unsigned_pred_adj * pe_2 + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 20312.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.6118 -0.5486 0.0328 0.5781 4.4511
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 14.01 3.743
## Residual 147.26 12.135
## Number of obs: 2565, groups: id, 873
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -1.862e+00 3.358e-01 1.073e+03 -5.543 3.73e-08 ***
## unsigned_pred_adj -2.236e-01 4.501e-02 2.558e+03 -4.968 7.19e-07 ***
## pe_2 4.816e-01 2.577e-02 2.530e+03 18.690 < 2e-16 ***
## unsigned_pred_adj:pe_2 -1.342e-02 2.977e-03 2.554e+03 -4.508 6.85e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) unsg__ pe_2
## unsgnd_prd_ -0.555
## pe_2 -0.127 0.107
## unsgnd__:_2 0.138 -0.354 -0.582
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: NA_Mean_DSP_bc ~ unsigned_pred_adj * pe_2 + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 21432.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7337 -0.6020 -0.0831 0.5653 4.3735
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 27.06 5.202
## Residual 223.71 14.957
## Number of obs: 2565, groups: id, 873
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.831e+00 4.245e-01 1.092e+03 6.668 4.10e-11 ***
## unsigned_pred_adj 3.099e-01 5.602e-02 2.561e+03 5.532 3.50e-08 ***
## pe_2 -5.878e-01 3.210e-02 2.544e+03 -18.311 < 2e-16 ***
## unsigned_pred_adj:pe_2 1.539e-02 3.701e-03 2.548e+03 4.158 3.32e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) unsg__ pe_2
## unsgnd_prd_ -0.548
## pe_2 -0.124 0.105
## unsgnd__:_2 0.135 -0.353 -0.580
Prediction adjustment (unsigned; uncertainty in prediction) differentiates reactivity to positive, but not negative PEs. People who make large prediction adjustments are less reactive to positive PEs. People who maintain the same prediction, and presumably have greater certainty in their predictions, display the greatest reactivity to positive PEs.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PA_overall_BC ~ unsigned_pred_adj * pe_2 * bindex + exam + (1 |
## id)
## Data: df
##
## REML criterion at convergence: 168029.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4801 -0.5727 0.0105 0.5865 4.7087
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 77.74 8.817
## Residual 212.70 14.584
## Number of obs: 20269, groups: id, 873
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -8.490e+00 4.659e-01 3.138e+03 -18.220 < 2e-16
## unsigned_pred_adj -3.592e-01 3.951e-02 2.026e+04 -9.092 < 2e-16
## pe_2 9.366e-01 2.216e-02 2.026e+04 42.272 < 2e-16
## bindex 1.886e-01 2.361e-02 1.957e+04 7.987 1.46e-15
## exam 1.645e+00 9.511e-02 2.022e+04 17.301 < 2e-16
## unsigned_pred_adj:pe_2 -2.470e-02 2.637e-03 2.025e+04 -9.367 < 2e-16
## unsigned_pred_adj:bindex 1.963e-02 3.466e-03 1.964e+04 5.662 1.52e-08
## pe_2:bindex -3.672e-02 1.941e-03 1.958e+04 -18.912 < 2e-16
## unsigned_pred_adj:pe_2:bindex 9.364e-04 2.304e-04 1.969e+04 4.065 4.82e-05
##
## (Intercept) ***
## unsigned_pred_adj ***
## pe_2 ***
## bindex ***
## exam ***
## unsigned_pred_adj:pe_2 ***
## unsigned_pred_adj:bindex ***
## pe_2:bindex ***
## unsigned_pred_adj:pe_2:bindex ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) unsg__ pe_2 bindex exam un__:_2 uns__: p_2:bn
## unsgnd_prd_ -0.378
## pe_2 -0.079 0.114
## bindex -0.440 0.458 0.136
## exam -0.504 0.054 -0.015 -0.015
## unsgnd__:_2 0.101 -0.383 -0.578 -0.142 -0.018
## unsgnd_pr_: 0.264 -0.787 -0.110 -0.581 0.002 0.322
## pe_2:bindex 0.077 -0.113 -0.785 -0.180 0.007 0.462 0.141
## unsgn__:_2: -0.085 0.326 0.462 0.182 0.003 -0.790 -0.411 -0.586
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
A similar pattern emerges for NA reactivity as a function of unsigned prediction adjustment.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: NA_overall_BC ~ unsigned_pred_adj * pe_2 * bindex + exam + (1 |
## id)
## Data: df
##
## REML criterion at convergence: 174960
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.3515 -0.6091 -0.0419 0.5833 4.7733
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 126.4 11.24
## Residual 297.8 17.26
## Number of obs: 20269, groups: id, 873
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.292e+01 5.701e-01 2.784e+03 22.671 < 2e-16
## unsigned_pred_adj 3.997e-01 4.687e-02 2.025e+04 8.528 < 2e-16
## pe_2 -1.064e+00 2.628e-02 2.025e+04 -40.493 < 2e-16
## bindex -3.522e-01 2.795e-02 1.954e+04 -12.600 < 2e-16
## exam -2.274e+00 1.128e-01 2.017e+04 -20.168 < 2e-16
## unsigned_pred_adj:pe_2 2.672e-02 3.129e-03 2.026e+04 8.538 < 2e-16
## unsigned_pred_adj:bindex -1.196e-02 4.103e-03 1.961e+04 -2.914 0.003574
## pe_2:bindex 3.838e-02 2.298e-03 1.955e+04 16.701 < 2e-16
## unsigned_pred_adj:pe_2:bindex -1.030e-03 2.727e-04 1.965e+04 -3.778 0.000158
##
## (Intercept) ***
## unsigned_pred_adj ***
## pe_2 ***
## bindex ***
## exam ***
## unsigned_pred_adj:pe_2 ***
## unsigned_pred_adj:bindex **
## pe_2:bindex ***
## unsigned_pred_adj:pe_2:bindex ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) unsg__ pe_2 bindex exam un__:_2 uns__: p_2:bn
## unsgnd_prd_ -0.367
## pe_2 -0.076 0.113
## bindex -0.426 0.457 0.136
## exam -0.488 0.054 -0.014 -0.015
## unsgnd__:_2 0.097 -0.382 -0.577 -0.142 -0.018
## unsgnd_pr_: 0.256 -0.785 -0.110 -0.581 0.002 0.321
## pe_2:bindex 0.074 -0.113 -0.784 -0.180 0.007 0.461 0.141
## unsgn__:_2: -0.082 0.326 0.461 0.182 0.003 -0.788 -0.411 -0.586
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
SSE as a proxy for uncertainty
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PA_Mean_DSP_bc ~ pred_2_sse * pe_2 + exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 14331.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5542 -0.5156 0.0408 0.5694 4.3053
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 12.13 3.482
## Residual 135.22 11.628
## Number of obs: 1828, groups: id, 611
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -5.943e+00 6.075e-01 1.823e+03 -9.784 < 2e-16 ***
## pred_2_sse -3.390e-03 1.020e-03 7.495e+02 -3.323 0.000934 ***
## pe_2 5.229e-01 4.413e-02 1.822e+03 11.849 < 2e-16 ***
## exam 1.930e+00 2.565e-01 1.820e+03 7.524 8.33e-14 ***
## pred_2_sse:pe_2 -2.078e-04 6.579e-05 1.822e+03 -3.159 0.001608 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) prd_2_ pe_2 exam
## pred_2_sse -0.129
## pe_2 -0.038 0.059
## exam -0.691 -0.463 -0.036
## prd_2_ss:_2 0.040 -0.082 -0.840 0.022
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: NA_Mean_DSP_bc ~ pred_2_sse * pe_2 + exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 15174.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8567 -0.6246 -0.0760 0.5435 4.2394
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 23.33 4.83
## Residual 211.46 14.54
## Number of obs: 1828, groups: id, 611
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.936e+00 7.654e-01 1.823e+03 11.675 < 2e-16 ***
## pred_2_sse 4.670e-03 1.303e-03 7.901e+02 3.584 0.000359 ***
## pe_2 -6.679e-01 5.559e-02 1.819e+03 -12.016 < 2e-16 ***
## exam -2.657e+00 3.233e-01 1.822e+03 -8.218 3.89e-16 ***
## pred_2_sse:pe_2 2.800e-04 8.291e-05 1.823e+03 3.377 0.000749 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) prd_2_ pe_2 exam
## pred_2_sse -0.130
## pe_2 -0.038 0.058
## exam -0.681 -0.469 -0.035
## prd_2_ss:_2 0.040 -0.081 -0.839 0.022
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PA_overall_BC ~ SSE_2 * pe_2 * bindex + exam + (1 | id)
## Data: df
##
## REML criterion at convergence: 156063.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.7192 -0.5694 0.0118 0.5822 4.7026
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 91.71 9.576
## Residual 207.47 14.404
## Number of obs: 18856, groups: id, 873
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -1.070e+01 4.911e-01 2.883e+03 -21.780 < 2e-16 ***
## SSE_2 -2.141e-03 9.122e-04 1.195e+04 -2.347 0.0189 *
## pe_2 1.069e+00 3.470e-02 1.882e+04 30.815 < 2e-16 ***
## bindex 3.086e-01 2.821e-02 1.817e+04 10.938 < 2e-16 ***
## exam 2.047e+00 1.370e-01 1.396e+04 14.940 < 2e-16 ***
## SSE_2:pe_2 -4.982e-04 5.331e-05 1.875e+04 -9.344 < 2e-16 ***
## SSE_2:bindex -6.623e-05 6.088e-05 1.812e+04 -1.088 0.2767
## pe_2:bindex -4.604e-02 3.067e-03 1.816e+04 -15.012 < 2e-16 ***
## SSE_2:pe_2:bindex 2.614e-05 4.732e-06 1.810e+04 5.524 3.35e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) SSE_2 pe_2 bindex exam SSE_2:p_2 SSE_2:b p_2:bn
## SSE_2 -0.266
## pe_2 -0.108 0.113
## bindex -0.503 0.422 0.141
## exam -0.327 -0.509 -0.017 0.002
## SSE_2:pe_2 0.104 -0.197 -0.844 -0.140 0.033
## SSE_2:bindx 0.370 -0.589 -0.108 -0.717 -0.014 0.185
## pe_2:bindex 0.085 -0.078 -0.787 -0.186 0.006 0.673 0.143
## SSE_2:p_2:b -0.089 0.134 0.671 0.184 0.001 -0.793 -0.242 -0.851
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: NA_overall_BC ~ SSE_2 * pe_2 * bindex + exam + (1 | id)
## Data: df
##
## REML criterion at convergence: 162624.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4625 -0.6088 -0.0386 0.5744 5.0505
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 145.1 12.05
## Residual 292.5 17.10
## Number of obs: 18856, groups: id, 873
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.556e+01 5.988e-01 2.626e+03 25.980 < 2e-16 ***
## SSE_2 3.494e-03 1.094e-03 1.260e+04 3.195 0.0014 **
## pe_2 -1.210e+00 4.127e-02 1.880e+04 -29.310 < 2e-16 ***
## bindex -4.625e-01 3.351e-02 1.815e+04 -13.803 < 2e-16 ***
## exam -2.927e+00 1.640e-01 1.455e+04 -17.851 < 2e-16 ***
## SSE_2:pe_2 5.446e-04 6.340e-05 1.871e+04 8.590 < 2e-16 ***
## SSE_2:bindex 1.222e-04 7.231e-05 1.810e+04 1.690 0.0911 .
## pe_2:bindex 4.667e-02 3.643e-03 1.813e+04 12.810 < 2e-16 ***
## SSE_2:pe_2:bindex -2.534e-05 5.620e-06 1.808e+04 -4.509 6.56e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) SSE_2 pe_2 bindex exam SSE_2:p_2 SSE_2:b p_2:bn
## SSE_2 -0.258
## pe_2 -0.105 0.112
## bindex -0.489 0.418 0.140
## exam -0.316 -0.516 -0.016 0.002
## SSE_2:pe_2 0.101 -0.197 -0.844 -0.140 0.033
## SSE_2:bindx 0.361 -0.583 -0.108 -0.717 -0.014 0.185
## pe_2:bindex 0.083 -0.078 -0.786 -0.186 0.006 0.672 0.143
## SSE_2:p_2:b -0.086 0.133 0.670 0.184 0.001 -0.792 -0.242 -0.851
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
Info Content as a proxy for uncertainty
Check with Aaron + Ross: including main effects makes this interaction N.S.
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PA_Mean_DSP_bc ~ info_content:pe_2 + exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 6610.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7774 -0.5511 0.0472 0.5160 4.0353
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 30.16 5.492
## Residual 119.64 10.938
## Number of obs: 846, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -6.147022 1.327836 786.670257 -4.629 4.29e-06 ***
## exam 1.877197 0.379741 640.813838 4.943 9.82e-07 ***
## info_content:pe_2 0.007356 0.001104 842.198079 6.662 4.86e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.922
## inf_cntn:_2 0.001 -0.019
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: NA_Mean_DSP_bc ~ info_content:pe_2 + exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 6987.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1126 -0.5821 -0.0598 0.5499 3.7299
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 50.79 7.127
## Residual 185.08 13.605
## Number of obs: 846, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.339140 1.657195 791.262140 4.429 1.08e-05 ***
## exam -1.927382 0.472635 642.496678 -4.078 5.11e-05 ***
## info_content:pe_2 -0.009287 0.001381 842.868177 -6.722 3.29e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.919
## inf_cntn:_2 0.001 -0.020
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PA_overall_BC ~ log_info_content:pe_2:bindex + exam + (1 | id)
## Data: df
##
## REML criterion at convergence: 60172.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5039 -0.5372 0.0307 0.5691 4.6301
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 68.11 8.253
## Residual 205.58 14.338
## Number of obs: 7299, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -7.709e+00 7.871e-01 9.567e+02 -9.794 <2e-16
## exam 2.276e+00 1.767e-01 7.156e+03 12.879 <2e-16
## log_info_content:pe_2:bindex 1.037e-02 7.414e-04 7.291e+03 13.989 <2e-16
##
## (Intercept) ***
## exam ***
## log_info_content:pe_2:bindex ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.709
## lg_nf_c:_2: -0.007 -0.039
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: NA_overall_BC ~ log_info_content * pe_2 * bindex + exam + (1 |
## id)
## Data: df
##
## REML criterion at convergence: 61939.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5595 -0.6207 -0.0560 0.5591 4.8761
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 103.1 10.16
## Residual 259.7 16.12
## Number of obs: 7299, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.540e+01 1.481e+00 3.304e+03 10.396 < 2e-16
## log_info_content -1.269e+00 5.760e-01 7.262e+03 -2.203 0.02765
## pe_2 -9.245e-01 1.021e-01 7.285e+03 -9.052 < 2e-16
## bindex -6.459e-01 1.007e-01 7.073e+03 -6.414 1.51e-10
## exam -2.024e+00 1.993e-01 7.145e+03 -10.154 < 2e-16
## log_info_content:pe_2 -1.209e-02 4.154e-02 7.281e+03 -0.291 0.77093
## log_info_content:bindex 1.302e-01 4.751e-02 7.068e+03 2.740 0.00616
## pe_2:bindex 4.488e-02 8.745e-03 7.066e+03 5.131 2.95e-07
## log_info_content:pe_2:bindex -4.357e-03 3.559e-03 7.063e+03 -1.224 0.22083
##
## (Intercept) ***
## log_info_content *
## pe_2 ***
## bindex ***
## exam ***
## log_info_content:pe_2
## log_info_content:bindex **
## pe_2:bindex ***
## log_info_content:pe_2:bindex
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) lg_nf_ pe_2 bindex exam lg__:_2 lg_n_: p_2:bn
## lg_nf_cntnt -0.753
## pe_2 -0.085 0.052
## bindex -0.619 0.708 0.147
## exam -0.395 -0.033 0.016 -0.004
## lg_nf_cn:_2 0.073 -0.055 -0.921 -0.133 -0.031
## lg_nf_cntn: 0.585 -0.757 -0.117 -0.936 -0.004 0.123
## pe_2:bindex 0.111 -0.106 -0.789 -0.188 0.004 0.727 0.149
## lg_nf_c:_2: -0.101 0.112 0.728 0.171 0.000 -0.791 -0.158 -0.921
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: NA_overall_BC ~ log_info_content:pe_2:bindex + exam + (1 | id)
## Data: df
##
## REML criterion at convergence: 62536.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.6159 -0.6055 -0.0659 0.5518 5.1934
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 107.9 10.39
## Residual 283.0 16.82
## Number of obs: 7299, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 9.049e+00 9.540e-01 8.499e+02 9.485 <2e-16
## exam -2.180e+00 2.075e-01 7.144e+03 -10.508 <2e-16
## log_info_content:pe_2:bindex -1.257e-02 8.719e-04 7.296e+03 -14.421 <2e-16
##
## (Intercept) ***
## exam ***
## log_info_content:pe_2:bindex ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.687
## lg_nf_c:_2: -0.007 -0.039
Relative effects of SSE, prediction adjustment, and information content
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: PA_overall_BC ~ SSE_2:(pe_2:bindex) + pred_adj:(pe_2:bindex) +
## log_info_content:(pe_2:bindex) + exam + (1 | id)
## Data: df
##
## REML criterion at convergence: 60208.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.4995 -0.5380 0.0297 0.5709 4.6347
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 67.97 8.245
## Residual 205.60 14.339
## Number of obs: 7299, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -7.671e+00 7.879e-01 9.625e+02 -9.735 <2e-16
## exam 2.271e+00 1.770e-01 7.152e+03 12.835 <2e-16
## SSE_2:pe_2:bindex -9.515e-07 3.942e-06 7.293e+03 -0.241 0.809
## pe_2:bindex:pred_adj 2.959e-04 2.565e-04 7.281e+03 1.154 0.249
## pe_2:bindex:log_info_content 1.088e-02 1.181e-03 7.293e+03 9.210 <2e-16
##
## (Intercept) ***
## exam ***
## SSE_2:pe_2:bindex
## pe_2:bindex:pred_adj
## pe_2:bindex:log_info_content ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam SSE_2: p_2:b:_
## exam -0.710
## SSE_2:p_2:b 0.031 -0.041
## p_2:bndx:p_ 0.051 -0.037 0.215
## p_2:bndx:__ -0.019 0.001 -0.753 0.032
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
3-way Interactions: uncertainty, PE, and affect on prediction updating
Metric of uncertainty: unsigned prediction adjustment
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: delta_pred_2 ~ unsigned_pred_adj_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 +
## exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 12675.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5227 -0.5218 -0.0209 0.5557 4.1509
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 235.4 15.34
## Number of obs: 1526, groups: id, 696
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 2.744e+00 1.335e+00
## exam -6.060e-01 4.094e-01
## unsigned_pred_adj_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 -9.378e-04 2.781e-04
## df t value
## (Intercept) 1.523e+03 2.055
## exam 1.523e+03 -1.480
## unsigned_pred_adj_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 1.523e+03 -3.372
## Pr(>|t|)
## (Intercept) 0.040061 *
## exam 0.139074
## unsigned_pred_adj_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 0.000765 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.955
## u___1:_2_1: -0.072 0.040
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: delta_pred_2 ~ unsigned_pred_adj_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 +
## exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 12676.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5749 -0.5391 -0.0186 0.5585 4.1529
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 235.4 15.34
## Number of obs: 1526, groups: id, 696
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) 2.681e+00 1.334e+00
## exam -5.988e-01 4.094e-01
## unsigned_pred_adj_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 6.469e-04 1.934e-04
## df t value
## (Intercept) 1.523e+03 2.009
## exam 1.523e+03 -1.463
## unsigned_pred_adj_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 1.523e+03 3.344
## Pr(>|t|)
## (Intercept) 0.044663 *
## exam 0.143732
## unsigned_pred_adj_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 0.000844 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.955
## u___1:_2_1: 0.058 -0.035
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
Metric of uncertainty: SSE
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: delta_pred_2 ~ pred_2_sse:pe_2_lag1:PA_Mean_DSP_bc_lag1 + exam +
## (1 | id)
## Data: df.new
##
## REML criterion at convergence: 9969.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.0270 -0.5038 -0.0783 0.5358 4.2288
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0 0.00
## Residual 208 14.42
## Number of obs: 1217, groups: id, 486
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 5.168e+00 1.336e+00 1.214e+03
## exam -9.972e-01 4.244e-01 1.214e+03
## pred_2_sse:pe_2_lag1:PA_Mean_DSP_bc_lag1 -9.709e-06 3.184e-06 1.214e+03
## t value Pr(>|t|)
## (Intercept) 3.869 0.000115 ***
## exam -2.350 0.018957 *
## pred_2_sse:pe_2_lag1:PA_Mean_DSP_bc_lag1 -3.049 0.002344 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.947
## p_2_:_2_1:P -0.076 -0.006
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: delta_pred_2 ~ pred_2_sse:pe_2_lag1:NA_Mean_DSP_bc_lag1 + exam +
## (1 | id)
## Data: df.new
##
## REML criterion at convergence: 9966.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.0487 -0.5089 -0.0793 0.5284 4.2856
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.0
## Residual 207.3 14.4
## Number of obs: 1217, groups: id, 486
##
## Fixed effects:
## Estimate Std. Error df
## (Intercept) 5.205e+00 1.333e+00 1.214e+03
## exam -9.983e-01 4.237e-01 1.214e+03
## pred_2_sse:pe_2_lag1:NA_Mean_DSP_bc_lag1 8.562e-06 2.338e-06 1.214e+03
## t value Pr(>|t|)
## (Intercept) 3.905 9.94e-05 ***
## exam -2.356 0.018629 *
## pred_2_sse:pe_2_lag1:NA_Mean_DSP_bc_lag1 3.662 0.000261 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.948
## p_2_:_2_1:N 0.071 0.004
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
Alternative operationalization of uncertainty: Information Content
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: delta_pred_2 ~ log_info_content_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 +
## exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 4827.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5909 -0.5706 -0.0593 0.5547 3.8477
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 185.8 13.63
## Number of obs: 598, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) -6.963e+00 2.942e+00
## exam 1.949e+00 7.690e-01
## log_info_content_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 8.758e-04 1.431e-03
## df t value Pr(>|t|)
## (Intercept) 5.950e+02 -2.367 0.0183
## exam 5.950e+02 2.534 0.0115
## log_info_content_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 5.950e+02 0.612 0.5408
##
## (Intercept) *
## exam *
## log_info_content_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.980
## l___1:_2_1: -0.030 -0.024
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: delta_pred_2 ~ log_info_content_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 +
## exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 4826.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5909 -0.5614 -0.0506 0.5547 3.9437
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 185.3 13.61
## Number of obs: 598, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) -7.098402 2.939758
## exam 1.951152 0.767737
## log_info_content_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 -0.001542 0.001100
## df t value Pr(>|t|)
## (Intercept) 595.000000 -2.415 0.0161
## exam 595.000000 2.541 0.0113
## log_info_content_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 595.000000 -1.402 0.1613
##
## (Intercept) *
## exam *
## log_info_content_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam
## exam -0.980
## l___1:_2_1: 0.046 0.008
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
Relative magnitude of uncertainty parameter estimates in 3-way interactions
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## delta_pred_2 ~ log_info_content_lag1:(pe_2_lag1:PA_Mean_DSP_bc_lag1) +
## pred_2_sse:(pe_2_lag1:PA_Mean_DSP_bc_lag1) + unsigned_pred_adj_lag1:(pe_2_lag1:PA_Mean_DSP_bc_lag1) +
## exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 4846.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6340 -0.5529 -0.0389 0.5358 3.9266
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 181.7 13.48
## Number of obs: 598, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) -7.611e+00 2.923e+00
## exam 2.130e+00 7.643e-01
## log_info_content_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 8.749e-03 2.674e-03
## pe_2_lag1:PA_Mean_DSP_bc_lag1:pred_2_sse -3.631e-05 9.321e-06
## pe_2_lag1:PA_Mean_DSP_bc_lag1:unsigned_pred_adj_lag1 1.025e-03 7.295e-04
## df t value
## (Intercept) 5.930e+02 -2.604
## exam 5.930e+02 2.787
## log_info_content_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 5.930e+02 3.272
## pe_2_lag1:PA_Mean_DSP_bc_lag1:pred_2_sse 5.930e+02 -3.896
## pe_2_lag1:PA_Mean_DSP_bc_lag1:unsigned_pred_adj_lag1 5.930e+02 1.405
## Pr(>|t|)
## (Intercept) 0.009447 **
## exam 0.005485 **
## log_info_content_lag1:pe_2_lag1:PA_Mean_DSP_bc_lag1 0.001130 **
## pe_2_lag1:PA_Mean_DSP_bc_lag1:pred_2_sse 0.000109 ***
## pe_2_lag1:PA_Mean_DSP_bc_lag1:unsigned_pred_adj_lag1 0.160398
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam l___1: p_2_1:PA_M_DSP__1:_2
## exam -0.981
## l___1:_2_1: -0.030 0.003
## p_2_1:PA_M_DSP__1:_2 0.053 -0.057 -0.774
## p_2_1:PA_M_DSP__1:__ -0.091 0.094 -0.090 -0.310
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula:
## delta_pred_2 ~ log_info_content_lag1:(pe_2_lag1:NA_Mean_DSP_bc_lag1) +
## pred_2_sse:(pe_2_lag1:NA_Mean_DSP_bc_lag1) + unsigned_pred_adj_lag1:(pe_2_lag1:NA_Mean_DSP_bc_lag1) +
## exam + (1 | id)
## Data: df.new
##
## REML criterion at convergence: 4853.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.6108 -0.5577 -0.0471 0.5285 4.0524
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 0.0 0.00
## Residual 183.2 13.54
## Number of obs: 598, groups: id, 248
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) -7.759e+00 2.939e+00
## exam 2.125e+00 7.682e-01
## log_info_content_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 -5.541e-03 2.114e-03
## pe_2_lag1:NA_Mean_DSP_bc_lag1:pred_2_sse 1.854e-05 6.663e-06
## pe_2_lag1:NA_Mean_DSP_bc_lag1:unsigned_pred_adj_lag1 -7.439e-04 5.101e-04
## df t value
## (Intercept) 5.930e+02 -2.640
## exam 5.930e+02 2.767
## log_info_content_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 5.930e+02 -2.621
## pe_2_lag1:NA_Mean_DSP_bc_lag1:pred_2_sse 5.930e+02 2.783
## pe_2_lag1:NA_Mean_DSP_bc_lag1:unsigned_pred_adj_lag1 5.930e+02 -1.459
## Pr(>|t|)
## (Intercept) 0.00851 **
## exam 0.00584 **
## log_info_content_lag1:pe_2_lag1:NA_Mean_DSP_bc_lag1 0.00899 **
## pe_2_lag1:NA_Mean_DSP_bc_lag1:pred_2_sse 0.00555 **
## pe_2_lag1:NA_Mean_DSP_bc_lag1:unsigned_pred_adj_lag1 0.14522
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) exam l___1: p_2_1:NA_M_DSP__1:_2
## exam -0.981
## l___1:_2_1: 0.034 -0.001
## p_2_1:NA_M_DSP__1:_2 -0.050 0.048 -0.791
## p_2_1:NA_M_DSP__1:__ 0.098 -0.106 -0.170 -0.190
## fit warnings:
## Some predictor variables are on very different scales: consider rescaling
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingular