Outcomes, Prediction Errors, and Daily Affect
Part I: Confirmatory Analyses
Mixed-effects models using baseline-corrected positive and negative affect
The models diplayed in the following blocks constitute our main exploratory vs. confirmatory test. Parameter estimates are derived from a computational model in which affect is construed as an integration of a subject’s most-recent exam grade outcomes and prediction errors, which are decayed by a term called gamma.
Separate gamma values were fit to our PA and NA models using our exploratory dataset. These gammas (PA: 0.94, NA: 0.98) are also used for our confirmatory tests.
PA mixed-effects model using exploratory dataset
PA_exp.lmer <- lmer(bc_pa ~ outcome + PE + ( 1 + outcome + PE | id), data = PA_exp, REML = TRUE)
summary(PA_exp.lmer)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bc_pa ~ outcome + PE + (1 + outcome + PE | id)
## Data: PA_exp
##
## REML criterion at convergence: 7268
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.1545 -0.5106 0.0437 0.5353 3.2685
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 427.319 20.672
## outcome 5.704 2.388 -0.90
## PE 165.706 12.873 0.45 -0.57
## Residual 112.639 10.613
## Number of obs: 926, groups: id, 56
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -1.2511 3.1306 48.0036 -0.400 0.691
## outcome -0.1063 0.3961 50.2942 -0.268 0.790
## PE 9.3928 2.1718 40.8635 4.325 9.57e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) outcom
## outcome -0.889
## PE 0.395 -0.523NA mixed-effects model using exploratory dataset
NA_exp.lmer <- lmer(bc_na ~ outcome + PE + ( 1 + outcome + PE | id), data = NA_exp, REML = TRUE)
summary(NA_exp.lmer)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bc_na ~ outcome + PE + (1 + outcome + PE | id)
## Data: NA_exp
##
## REML criterion at convergence: 7588.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.8759 -0.5264 -0.0717 0.5448 4.5116
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 917.851 30.296
## outcome 9.692 3.113 -0.95
## PE 263.342 16.228 0.43 -0.59
## Residual 165.671 12.871
## Number of obs: 926, groups: id, 56
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 19.8010 5.4945 38.3637 3.604 0.00089 ***
## outcome -1.8893 0.6192 37.3363 -3.051 0.00418 **
## PE -2.0575 2.6894 36.7953 -0.765 0.44913
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) outcom
## outcome -0.957
## PE 0.445 -0.567PA mixed-effects model using confirmatory dataset
PA_confrm.lmer <- lmer(bc_pa ~ outcome + PE + ( 1 + outcome + PE | id), data = PA_confrm, REML = TRUE)
summary(PA_confrm.lmer)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bc_pa ~ outcome + PE + (1 + outcome + PE | id)
## Data: PA_confrm
##
## REML criterion at convergence: 10742.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.6023 -0.5259 0.0218 0.5549 4.5331
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 123.301 11.104
## outcome 2.053 1.433 -0.50
## PE 33.292 5.770 0.12 0.22
## Residual 154.990 12.449
## Number of obs: 1325, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.8074 1.9552 50.6470 1.436 0.1572
## outcome -0.1670 0.2676 44.3735 -0.624 0.5357
## PE 1.8323 0.8695 38.4966 2.107 0.0417 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) outcom
## outcome -0.699
## PE 0.216 0.018NA mixed-effects model using confirmatory dataset
NA_confrm.lmer <- lmer(bc_na ~ outcome + PE + ( 1 + outcome + PE | id), data = NA_confrm, REML = TRUE)
summary(NA_confrm.lmer)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: bc_na ~ outcome + PE + (1 + outcome + PE | id)
## Data: NA_confrm
##
## REML criterion at convergence: 10968.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5850 -0.5364 -0.0024 0.4486 4.2201
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 1512.67 38.893
## outcome 15.35 3.917 -0.97
## PE 42.15 6.492 0.76 -0.72
## Residual 186.77 13.667
## Number of obs: 1325, groups: id, 69
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.1274 6.3278 64.8564 0.178 0.859
## outcome 0.0906 0.6552 65.3254 0.138 0.890
## PE -1.0607 1.0060 52.1507 -1.054 0.297
##
## Correlation of Fixed Effects:
## (Intr) outcom
## outcome -0.973
## PE 0.755 -0.711Parameter estimates for exploratory and confirmatory datasets
Exploratory PA model:
## Estimate SE df t_stat p_Val
## outcome -0.1063078 0.3961097 50.29423 -0.2683798 7.895048e-01
## PE 9.3927900 2.1718084 40.86354 4.3248705 9.571879e-05Prediction Error (PE) term is significant at a<0.0001
Confirmatory PA model:
## Estimate SE df t_stat p_Val
## outcome -0.1670308 0.2675987 44.37348 -0.624184 0.53570285
## PE 1.8322969 0.8694858 38.49658 2.107334 0.04165618Prediction Error (PE) term is significant at a<0.05
Exploratory NA model:
## Estimate SE df t_stat p_Val
## outcome -1.889332 0.619186 37.33632 -3.0513157 0.004179788
## PE -2.057517 2.689429 36.79527 -0.7650385 0.449127877Outcome term is significant at a<0.5
Confirmatory NA model:
## Estimate SE df t_stat p_Val
## outcome 0.09060443 0.6551913 65.32542 0.138287 0.8904390
## PE -1.06071695 1.0059797 52.15070 -1.054412 0.2965551No significant estimates for confirmatory NA model
Distribution of subject-fit gamma values (exploratory vs confirmatory)
Part II
Mean parameter estimates from subject-level models with individually-fit gamma values.
The following two plots depict parameter estimates for outcome and prediction error. Estimates are derived from single-subject fixed effects models, for which gammas are individually fit to each subject’s PA or NA measures.
Subjects with negative parameter estimates for Prediction Error term have been removed
Subjects with negative parameter estimates for Prediction Error term have been removed
The following two plots depict parameter estimates for prediction and prediction error (PE), as suggested by Robb. Estimates are derived from single-subject fixed effects models, for which gammas are individually fit to each subject’s PA or NA measures.
Subjects with negative parameter estimates for Prediction Error term have been removed
Subjects with negative parameter estimates for Prediction Error term have been removed
Part III
Comparing parameter estimates from Robb Rutledge’s decision task with estimates from post-grade experience sampling
Prediction (EV) and Prediction Error (RPE) parameter estimates from a model predicting the timecourse of positive affect are used in the scatter plots below. All parameter estimates are derived from models using gamma values that are fit to individual subjects.
Spearman’s rho: 0.206087 p-value: 0.3323898
Spearman’s rho: -0.3648619 p-value: 0.0795946