models

knitr::clean_cache()

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# data <- params$data
targets::tar_load(esm_long)
data <- esm_long

library(brms)

## Loading required package: Rcpp

## Loading 'brms' package (version 2.14.4). Useful instructions
## can be found by typing help('brms'). A more detailed introduction
## to the package is available through vignette('brms_overview').

## 
## Attaching package: 'brms'

## The following object is masked from 'package:stats':
## 
##     ar

library(bayesplot)

## This is bayesplot version 1.8.0

## - Online documentation and vignettes at mc-stan.org/bayesplot

## - bayesplot theme set to bayesplot::theme_default()

##    * Does _not_ affect other ggplot2 plots

##    * See ?bayesplot_theme_set for details on theme setting

data$int_val_change <- data$int_val_post - data$int_val_pre

1. What momentary experiences (self-efficacy, frustration, and interest) do students have in CS1?

What are their mean levels?

How variable are they across the grouping factors/random effects of students and situations?

How are they related to each other?

bf_1 <- bf(frustrated ~ 1 +
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             (1|s|number) +
             (1|p|assign))

m1a <- brm(bf_1 + bf_2 + bf_3,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess

m1a

##  Family: MV(gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + (1 | s | number) + (1 | p | assign) 
##    Data: data (Number of observations: 843) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.32      0.06     0.23
## sd(confident_Intercept)                            0.20      0.04     0.14
## sd(interested_Intercept)                           0.16      0.03     0.12
## cor(frustrated_Intercept,confident_Intercept)     -0.88      0.09    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.89      0.10    -0.99
## cor(confident_Intercept,interested_Intercept)      0.94      0.05     0.80
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.45 1.00      562      935
## sd(confident_Intercept)                            0.28 1.00      675      877
## sd(interested_Intercept)                           0.23 1.00      774      804
## cor(frustrated_Intercept,confident_Intercept)     -0.63 1.00      627     1050
## cor(frustrated_Intercept,interested_Intercept)    -0.64 1.00      748      994
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1144     1562
## 
## ~number (Number of levels: 73) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           1.09      0.10     0.91
## sd(confident_Intercept)                            0.86      0.08     0.72
## sd(interested_Intercept)                           0.84      0.07     0.71
## cor(frustrated_Intercept,confident_Intercept)     -0.61      0.08    -0.75
## cor(frustrated_Intercept,interested_Intercept)    -0.37      0.11    -0.57
## cor(confident_Intercept,interested_Intercept)      0.67      0.07     0.51
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.30 1.02      160      325
## sd(confident_Intercept)                            1.02 1.01      205      527
## sd(interested_Intercept)                           0.98 1.00      299      690
## cor(frustrated_Intercept,confident_Intercept)     -0.43 1.01      286      507
## cor(frustrated_Intercept,interested_Intercept)    -0.12 1.03      190      458
## cor(confident_Intercept,interested_Intercept)      0.79 1.01      223      429
## 
## Population-Level Effects: 
##                      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept     2.68      0.14     2.41     2.96 1.01      177
## confident_Intercept      4.08      0.11     3.85     4.30 1.01      139
## interested_Intercept     4.23      0.10     4.04     4.43 1.01      196
##                      Tail_ESS
## frustrated_Intercept      341
## confident_Intercept       343
## interested_Intercept      387
## 
## Family Specific Parameters: 
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated     0.76      0.02     0.72     0.80 1.00     2736     1486
## sigma_confident      0.60      0.02     0.57     0.63 1.00     2473     1645
## sigma_interested     0.48      0.01     0.46     0.51 1.00     2727     1541
## 
## Residual Correlations: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)     -0.25      0.03    -0.32    -0.18 1.00
## rescor(frustrated,interested)    -0.10      0.04    -0.17    -0.03 1.00
## rescor(confident,interested)      0.37      0.03     0.31     0.43 1.00
##                               Bulk_ESS Tail_ESS
## rescor(frustrated,confident)      2376     1607
## rescor(frustrated,interested)     2214     1468
## rescor(confident,interested)      2720     1894
## 
## Samples were drawn 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).

performance::icc(m1a)

## # Random Effect Variances and ICC
## 
## Conditioned on: all random effects
## 
## ## Variance Ratio (comparable to ICC)
## Ratio: 0.80  CI 95%: [0.63 0.96]
## 
## ## Variances of Posterior Predicted Distribution
## Conditioned on fixed effects: 0.10  CI 95%: [-0.14 0.60]
## Conditioned on rand. effects: 0.53  CI 95%: [-0.75 1.80]
## 
## ## Difference in Variances
## Difference: 0.42  CI 95%: [-0.64 1.23]

Just interesting as an initial attempt at modeling variation - how we interpret these really matters

2. What characteristics of students are associated with/related to these momentary experiences?

Are there gender differences in students’ interest, frustration, and self-efficacy?

How does interest at the beginning of the course relate to their momentary experiences?

Do gender differences moderate this effect?

bf_1 <- bf(frustrated ~ 1 +
             course + 
             gender +
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             course + 
             gender +
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             course + 
             gender +
             (1|s|number) +
             (1|p|assign))

m2a <- brm(bf_1 + bf_2 + bf_3,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess

m2a

##  Family: MV(gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + course + gender + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + course + gender + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + course + gender + (1 | s | number) + (1 | p | assign) 
##    Data: data (Number of observations: 828) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.33      0.06     0.23
## sd(confident_Intercept)                            0.20      0.04     0.13
## sd(interested_Intercept)                           0.17      0.03     0.11
## cor(frustrated_Intercept,confident_Intercept)     -0.88      0.09    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.90      0.08    -0.99
## cor(confident_Intercept,interested_Intercept)      0.94      0.06     0.77
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.46 1.01      359      790
## sd(confident_Intercept)                            0.28 1.01      505     1234
## sd(interested_Intercept)                           0.24 1.01      496     1198
## cor(frustrated_Intercept,confident_Intercept)     -0.64 1.01      544      602
## cor(frustrated_Intercept,interested_Intercept)    -0.69 1.00      734     1150
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1271     1315
## 
## ~number (Number of levels: 71) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           1.08      0.10     0.90
## sd(confident_Intercept)                            0.80      0.07     0.67
## sd(interested_Intercept)                           0.82      0.07     0.69
## cor(frustrated_Intercept,confident_Intercept)     -0.60      0.08    -0.74
## cor(frustrated_Intercept,interested_Intercept)    -0.36      0.11    -0.57
## cor(confident_Intercept,interested_Intercept)      0.65      0.07     0.49
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.29 1.00      247      454
## sd(confident_Intercept)                            0.95 1.01      271      448
## sd(interested_Intercept)                           0.98 1.01      305      714
## cor(frustrated_Intercept,confident_Intercept)     -0.41 1.03      242      323
## cor(frustrated_Intercept,interested_Intercept)    -0.14 1.04      203      340
## cor(confident_Intercept,interested_Intercept)      0.76 1.03      233      624
## 
## Population-Level Effects: 
##                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept         3.05      0.26     2.52     3.54 1.02      176
## confident_Intercept          3.66      0.20     3.27     4.06 1.01      138
## interested_Intercept         4.09      0.20     3.69     4.48 1.01      206
## frustrated_courseCOSC111    -0.11      0.46    -1.01     0.81 1.02      354
## frustrated_genderMale       -0.52      0.29    -1.10     0.06 1.01      165
## confident_courseCOSC111     -0.11      0.34    -0.79     0.53 1.01      368
## confident_genderMale         0.60      0.22     0.16     1.04 1.01      140
## interested_courseCOSC111    -0.20      0.33    -0.85     0.44 1.01      385
## interested_genderMale        0.24      0.22    -0.21     0.66 1.01      252
##                          Tail_ESS
## frustrated_Intercept          320
## confident_Intercept           348
## interested_Intercept          558
## frustrated_courseCOSC111      680
## frustrated_genderMale         381
## confident_courseCOSC111       574
## confident_genderMale          406
## interested_courseCOSC111      541
## interested_genderMale         495
## 
## Family Specific Parameters: 
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated     0.74      0.02     0.71     0.78 1.00     1601     1623
## sigma_confident      0.60      0.02     0.57     0.64 1.00     1655     1485
## sigma_interested     0.49      0.01     0.46     0.51 1.00     1512     1404
## 
## Residual Correlations: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)     -0.25      0.03    -0.31    -0.18 1.00
## rescor(frustrated,interested)    -0.09      0.04    -0.16    -0.02 1.00
## rescor(confident,interested)      0.38      0.03     0.31     0.44 1.00
##                               Bulk_ESS Tail_ESS
## rescor(frustrated,confident)      2022     1378
## rescor(frustrated,interested)     2210     1487
## rescor(confident,interested)      1904     1485
## 
## Samples were drawn 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).

How does self-efficacy at the beginning of the course relate to their momentary experiences?

Do gender differences moderate this effect?

bf_1 <- bf(frustrated ~ 1 +
             course + 
             gender +
             self_eff +
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             course + 
             gender +
             self_eff +
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             course + 
             gender +
             self_eff + 
             (1|s|number) +
             (1|p|assign))

#fit the model
m2d <- brm(bf_1 + bf_2 + bf_3,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## recompiling to avoid crashing R session

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

m2d

##  Family: MV(gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + course + gender + self_eff + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + course + gender + self_eff + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + course + gender + self_eff + (1 | s | number) + (1 | p | assign) 
##    Data: data (Number of observations: 828) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.33      0.06     0.23
## sd(confident_Intercept)                            0.20      0.04     0.13
## sd(interested_Intercept)                           0.17      0.03     0.12
## cor(frustrated_Intercept,confident_Intercept)     -0.88      0.10    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.89      0.09    -0.99
## cor(confident_Intercept,interested_Intercept)      0.94      0.06     0.78
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.47 1.01      565     1048
## sd(confident_Intercept)                            0.30 1.00      748      991
## sd(interested_Intercept)                           0.24 1.00      813      992
## cor(frustrated_Intercept,confident_Intercept)     -0.63 1.00      690     1054
## cor(frustrated_Intercept,interested_Intercept)    -0.64 1.01      616      952
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1277     1598
## 
## ~number (Number of levels: 71) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           1.01      0.10     0.85
## sd(confident_Intercept)                            0.71      0.07     0.59
## sd(interested_Intercept)                           0.82      0.07     0.69
## cor(frustrated_Intercept,confident_Intercept)     -0.53      0.10    -0.70
## cor(frustrated_Intercept,interested_Intercept)    -0.33      0.11    -0.53
## cor(confident_Intercept,interested_Intercept)      0.66      0.07     0.51
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.22 1.01      326      622
## sd(confident_Intercept)                            0.86 1.01      411      578
## sd(interested_Intercept)                           0.97 1.01      353      660
## cor(frustrated_Intercept,confident_Intercept)     -0.32 1.01      341      638
## cor(frustrated_Intercept,interested_Intercept)    -0.10 1.01      378      665
## cor(confident_Intercept,interested_Intercept)      0.79 1.00      317      691
## 
## Population-Level Effects: 
##                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept         3.09      0.26     2.59     3.58 1.01      333
## confident_Intercept          3.64      0.18     3.28     3.98 1.01      382
## interested_Intercept         4.08      0.20     3.71     4.47 1.01      452
## frustrated_courseCOSC111     0.11      0.44    -0.76     0.94 1.01      516
## frustrated_genderMale       -0.08      0.32    -0.71     0.55 1.01      269
## frustrated_self_eff         -0.53      0.17    -0.87    -0.22 1.01      353
## confident_courseCOSC111     -0.32      0.32    -0.93     0.32 1.01      422
## confident_genderMale         0.13      0.22    -0.31     0.55 1.00      338
## confident_self_eff           0.52      0.12     0.29     0.78 1.01      402
## interested_courseCOSC111    -0.26      0.36    -0.96     0.45 1.01      506
## interested_genderMale        0.08      0.26    -0.41     0.59 1.00      450
## interested_self_eff          0.18      0.14    -0.07     0.45 1.00      513
##                          Tail_ESS
## frustrated_Intercept          579
## confident_Intercept           646
## interested_Intercept          596
## frustrated_courseCOSC111      652
## frustrated_genderMale         513
## frustrated_self_eff           584
## confident_courseCOSC111       738
## confident_genderMale          590
## confident_self_eff            745
## interested_courseCOSC111      961
## interested_genderMale         700
## interested_self_eff           763
## 
## Family Specific Parameters: 
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated     0.74      0.02     0.70     0.78 1.00     2061     1413
## sigma_confident      0.60      0.02     0.57     0.64 1.00     1841     1492
## sigma_interested     0.49      0.01     0.46     0.51 1.00     1830     1443
## 
## Residual Correlations: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)     -0.25      0.03    -0.31    -0.18 1.00
## rescor(frustrated,interested)    -0.09      0.04    -0.16    -0.02 1.00
## rescor(confident,interested)      0.38      0.03     0.31     0.44 1.00
##                               Bulk_ESS Tail_ESS
## rescor(frustrated,confident)      2037     1547
## rescor(frustrated,interested)     1674     1329
## rescor(confident,interested)      1767     1624
## 
## Samples were drawn 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).

3. How do students’ momentary experiences relate to changes in their interest?

base model

bf_1 <- bf(frustrated ~ 1 +
             course + 
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             course + 
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             course + 
             (1|s|number) +
             (1|p|assign))

bf_int <- bf(int_val_change ~ course)

m3a <- brm(bf_1 + bf_2 + bf_3 +
             bf_int,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess

m3a

##  Family: MV(gaussian, gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          int_val_change ~ course 
##    Data: data (Number of observations: 776) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.34      0.06     0.24
## sd(confident_Intercept)                            0.19      0.04     0.13
## sd(interested_Intercept)                           0.15      0.03     0.10
## cor(frustrated_Intercept,confident_Intercept)     -0.87      0.11    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.88      0.11    -0.99
## cor(confident_Intercept,interested_Intercept)      0.93      0.06     0.75
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.49 1.00      478      875
## sd(confident_Intercept)                            0.28 1.01      489      713
## sd(interested_Intercept)                           0.22 1.00      512      666
## cor(frustrated_Intercept,confident_Intercept)     -0.60 1.01      582      861
## cor(frustrated_Intercept,interested_Intercept)    -0.58 1.01      685     1285
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1223     1227
## 
## ~number (Number of levels: 65) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           1.07      0.10     0.90
## sd(confident_Intercept)                            0.86      0.08     0.71
## sd(interested_Intercept)                           0.75      0.07     0.63
## cor(frustrated_Intercept,confident_Intercept)     -0.62      0.08    -0.76
## cor(frustrated_Intercept,interested_Intercept)    -0.27      0.12    -0.49
## cor(confident_Intercept,interested_Intercept)      0.66      0.08     0.50
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.29 1.01      177      565
## sd(confident_Intercept)                            1.02 1.00      333      509
## sd(interested_Intercept)                           0.91 1.01      380      838
## cor(frustrated_Intercept,confident_Intercept)     -0.46 1.01      243      631
## cor(frustrated_Intercept,interested_Intercept)     0.00 1.02      257      534
## cor(confident_Intercept,interested_Intercept)      0.79 1.01      322      618
## 
## Population-Level Effects: 
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept           2.59      0.17     2.26     2.92 1.04      153
## confident_Intercept            4.12      0.12     3.86     4.34 1.03      228
## interested_Intercept           4.33      0.10     4.12     4.53 1.02      250
## intvalchange_Intercept        -0.16      0.04    -0.24    -0.09 1.00     3323
## frustrated_courseCOSC111       0.39      0.46    -0.47     1.30 1.02      331
## confident_courseCOSC111       -0.57      0.38    -1.32     0.16 1.02      334
## interested_courseCOSC111      -0.62      0.32    -1.27     0.02 1.01      384
## intvalchange_courseCOSC111    -0.23      0.13    -0.50     0.04 1.00     2752
##                            Tail_ESS
## frustrated_Intercept            267
## confident_Intercept             372
## interested_Intercept            371
## intvalchange_Intercept         1418
## frustrated_courseCOSC111        621
## confident_courseCOSC111         446
## interested_courseCOSC111        617
## intvalchange_courseCOSC111     1489
## 
## Family Specific Parameters: 
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated       0.75      0.03     0.71     0.81 1.00      520      659
## sigma_confident        0.61      0.02     0.58     0.66 1.00      842      790
## sigma_interested       0.54      0.04     0.48     0.62 1.01      417      717
## sigma_intvalchange     1.05      0.03     1.00     1.10 1.00     2679     1683
## 
## Residual Correlations: 
##                                 Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)       -0.26      0.04    -0.35    -0.18 1.00
## rescor(frustrated,interested)      -0.15      0.07    -0.30    -0.01 1.01
## rescor(confident,interested)        0.37      0.06     0.25     0.49 1.01
## rescor(frustrated,intvalchange)    -0.14      0.15    -0.42     0.15 1.01
## rescor(confident,intvalchange)      0.09      0.15    -0.22     0.36 1.01
## rescor(interested,intvalchange)     0.40      0.13     0.11     0.62 1.01
##                                 Bulk_ESS Tail_ESS
## rescor(frustrated,confident)         679      671
## rescor(frustrated,interested)        283      543
## rescor(confident,interested)         395      710
## rescor(frustrated,intvalchange)      244      440
## rescor(confident,intvalchange)       336      600
## rescor(interested,intvalchange)      384      622
## 
## Samples were drawn 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).

adding gender and pre self-efficacy

bf_1 <- bf(frustrated ~ 1 +
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_int <- bf(int_val_change ~ course + gender + self_eff)

m3e <- brm(bf_1 + bf_2 + bf_3 +
             bf_int,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## recompiling to avoid crashing R session

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

m3e

##  Family: MV(gaussian, gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          int_val_change ~ course + gender + self_eff 
##    Data: data (Number of observations: 770) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.33      0.06     0.23
## sd(confident_Intercept)                            0.19      0.04     0.12
## sd(interested_Intercept)                           0.15      0.03     0.10
## cor(frustrated_Intercept,confident_Intercept)     -0.87      0.10    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.88      0.10    -0.99
## cor(confident_Intercept,interested_Intercept)      0.93      0.07     0.74
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.47 1.01      644      981
## sd(confident_Intercept)                            0.27 1.00      722      906
## sd(interested_Intercept)                           0.22 1.00      812     1468
## cor(frustrated_Intercept,confident_Intercept)     -0.60 1.00      948     1226
## cor(frustrated_Intercept,interested_Intercept)    -0.65 1.00      981     1053
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1274     1792
## 
## ~number (Number of levels: 64) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.97      0.10     0.80
## sd(confident_Intercept)                            0.69      0.07     0.57
## sd(interested_Intercept)                           0.73      0.07     0.60
## cor(frustrated_Intercept,confident_Intercept)     -0.47      0.10    -0.66
## cor(frustrated_Intercept,interested_Intercept)    -0.15      0.13    -0.38
## cor(confident_Intercept,interested_Intercept)      0.64      0.08     0.47
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.18 1.01      537      712
## sd(confident_Intercept)                            0.85 1.01      573      860
## sd(interested_Intercept)                           0.88 1.02      554      767
## cor(frustrated_Intercept,confident_Intercept)     -0.26 1.01      421      637
## cor(frustrated_Intercept,interested_Intercept)     0.11 1.01      398      866
## cor(confident_Intercept,interested_Intercept)      0.78 1.01      675      982
## 
## Population-Level Effects: 
##                            Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept           3.12      0.26     2.60     3.63 1.00      472
## confident_Intercept            3.57      0.18     3.21     3.92 1.00      663
## interested_Intercept           4.04      0.19     3.69     4.40 1.00      742
## intvalchange_Intercept        -0.10      0.07    -0.24     0.05 1.01     2561
## frustrated_genderMale         -0.19      0.33    -0.83     0.47 1.01      373
## frustrated_courseCOSC111       0.34      0.45    -0.54     1.24 1.00      596
## frustrated_self_eff           -0.55      0.16    -0.87    -0.21 1.01      455
## confident_genderMale           0.24      0.24    -0.23     0.70 1.01      540
## confident_courseCOSC111       -0.47      0.32    -1.10     0.12 1.00      701
## confident_self_eff             0.53      0.12     0.30     0.75 1.02      349
## interested_genderMale          0.21      0.23    -0.24     0.69 1.00      593
## interested_courseCOSC111      -0.43      0.33    -1.08     0.22 1.00      795
## interested_self_eff            0.18      0.12    -0.06     0.42 1.01      544
## intvalchange_courseCOSC111    -0.18      0.15    -0.47     0.12 1.00     2696
## intvalchange_genderMale       -0.10      0.09    -0.28     0.09 1.00     2096
## intvalchange_self_eff          0.01      0.05    -0.08     0.11 1.00     2213
##                            Tail_ESS
## frustrated_Intercept            691
## confident_Intercept             982
## interested_Intercept           1058
## intvalchange_Intercept         1592
## frustrated_genderMale           504
## frustrated_courseCOSC111        873
## frustrated_self_eff             670
## confident_genderMale            841
## confident_courseCOSC111         975
## confident_self_eff              813
## interested_genderMale           821
## interested_courseCOSC111       1033
## interested_self_eff            1082
## intvalchange_courseCOSC111     1404
## intvalchange_genderMale        1567
## intvalchange_self_eff          1577
## 
## Family Specific Parameters: 
##                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated       0.76      0.03     0.71     0.82 1.00      928      913
## sigma_confident        0.61      0.02     0.58     0.66 1.00     1044      985
## sigma_interested       0.54      0.04     0.48     0.62 1.00      670     1164
## sigma_intvalchange     1.06      0.03     1.01     1.11 1.00     2586     1218
## 
## Residual Correlations: 
##                                 Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)       -0.26      0.04    -0.35    -0.17 1.00
## rescor(frustrated,interested)      -0.15      0.07    -0.29    -0.02 1.00
## rescor(confident,interested)        0.37      0.05     0.27     0.48 1.00
## rescor(frustrated,intvalchange)    -0.16      0.14    -0.43     0.13 1.01
## rescor(confident,intvalchange)      0.10      0.13    -0.17     0.35 1.01
## rescor(interested,intvalchange)     0.40      0.13     0.10     0.62 1.00
##                                 Bulk_ESS Tail_ESS
## rescor(frustrated,confident)        1081     1106
## rescor(frustrated,interested)        668     1083
## rescor(confident,interested)         702      883
## rescor(frustrated,intvalchange)      591      855
## rescor(confident,intvalchange)       609      705
## rescor(interested,intvalchange)      608      877
## 
## Samples were drawn 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).

3. Original specification - how do students’ momentary experiences relate to changes in their interest?

base model

bf_1 <- bf(frustrated ~ 1 +
             course + 
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             course + 
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             course + 
             (1|s|number) +
             (1|p|assign))

bf_int <- bf(int_val_post ~ int_val_pre + course)

m3a_pre <- brm(bf_1 + bf_2 + bf_3 +
             bf_int,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess

m3a_pre

##  Family: MV(gaussian, gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          int_val_post ~ int_val_pre + course 
##    Data: data (Number of observations: 776) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.33      0.06     0.22
## sd(confident_Intercept)                            0.19      0.04     0.13
## sd(interested_Intercept)                           0.15      0.03     0.10
## cor(frustrated_Intercept,confident_Intercept)     -0.88      0.09    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.89      0.10    -0.99
## cor(confident_Intercept,interested_Intercept)      0.93      0.07     0.76
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.47 1.00      538      941
## sd(confident_Intercept)                            0.28 1.00      756     1030
## sd(interested_Intercept)                           0.22 1.00      788     1198
## cor(frustrated_Intercept,confident_Intercept)     -0.64 1.00      783     1004
## cor(frustrated_Intercept,interested_Intercept)    -0.64 1.00      857     1079
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1405     1686
## 
## ~number (Number of levels: 65) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           1.04      0.10     0.87
## sd(confident_Intercept)                            0.82      0.08     0.67
## sd(interested_Intercept)                           0.67      0.07     0.55
## cor(frustrated_Intercept,confident_Intercept)     -0.60      0.09    -0.75
## cor(frustrated_Intercept,interested_Intercept)    -0.20      0.13    -0.44
## cor(confident_Intercept,interested_Intercept)      0.61      0.09     0.42
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.24 1.01      288      776
## sd(confident_Intercept)                            1.00 1.01      285      610
## sd(interested_Intercept)                           0.82 1.02      337      705
## cor(frustrated_Intercept,confident_Intercept)     -0.39 1.01      282      579
## cor(frustrated_Intercept,interested_Intercept)     0.09 1.01      288      435
## cor(confident_Intercept,interested_Intercept)      0.76 1.01      353      686
## 
## Population-Level Effects: 
##                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept         2.59      0.16     2.26     2.90 1.01      252
## confident_Intercept          4.13      0.12     3.87     4.36 1.00      251
## interested_Intercept         4.33      0.10     4.13     4.52 1.02      278
## intvalpost_Intercept         0.45      0.06     0.33     0.58 1.00     1876
## frustrated_courseCOSC111     0.38      0.44    -0.48     1.26 1.01      342
## confident_courseCOSC111     -0.54      0.35    -1.28     0.09 1.01      346
## interested_courseCOSC111    -0.56      0.30    -1.16     0.01 1.01      331
## intvalpost_int_val_pre       0.55      0.04     0.46     0.62 1.00     1754
## intvalpost_courseCOSC111    -0.45      0.13    -0.70    -0.21 1.00     2549
##                          Tail_ESS
## frustrated_Intercept          482
## confident_Intercept           446
## interested_Intercept          522
## intvalpost_Intercept         1680
## frustrated_courseCOSC111      626
## confident_courseCOSC111       655
## interested_courseCOSC111      482
## intvalpost_int_val_pre       1619
## intvalpost_courseCOSC111     1465
## 
## Family Specific Parameters: 
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated     0.78      0.04     0.71     0.87 1.02      242      384
## sigma_confident      0.65      0.04     0.59     0.73 1.04      201      614
## sigma_interested     0.61      0.05     0.52     0.71 1.02      378      631
## sigma_intvalpost     0.98      0.02     0.94     1.03 1.00     2892     1286
## 
## Residual Correlations: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)     -0.32      0.06    -0.46    -0.20 1.03
## rescor(frustrated,interested)    -0.23      0.09    -0.41    -0.06 1.03
## rescor(confident,interested)      0.47      0.07     0.32     0.60 1.05
## rescor(frustrated,intvalpost)    -0.27      0.14    -0.52     0.03 1.02
## rescor(confident,intvalpost)      0.33      0.13     0.02     0.56 1.05
## rescor(interested,intvalpost)     0.59      0.09     0.38     0.73 1.02
##                               Bulk_ESS Tail_ESS
## rescor(frustrated,confident)       199      384
## rescor(frustrated,interested)      177      391
## rescor(confident,interested)       160      488
## rescor(frustrated,intvalpost)      172      365
## rescor(confident,intvalpost)       233      532
## rescor(interested,intvalpost)      378      569
## 
## Samples were drawn 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).

adding gender and pre self-efficacy

bf_1 <- bf(frustrated ~ 1 +
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_int <- bf(int_val_post ~ int_val_pre + course + gender + self_eff)

m3e_pre <- brm(bf_1 + bf_2 + bf_3 +
             bf_int,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## recompiling to avoid crashing R session

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

m3e_pre

##  Family: MV(gaussian, gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          int_val_post ~ int_val_pre + course + gender + self_eff 
##    Data: data (Number of observations: 770) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.33      0.06     0.22
## sd(confident_Intercept)                            0.19      0.04     0.13
## sd(interested_Intercept)                           0.15      0.03     0.10
## cor(frustrated_Intercept,confident_Intercept)     -0.87      0.10    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.89      0.10    -0.99
## cor(confident_Intercept,interested_Intercept)      0.93      0.07     0.74
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.46 1.00      486      670
## sd(confident_Intercept)                            0.28 1.00      621      906
## sd(interested_Intercept)                           0.22 1.00      737     1000
## cor(frustrated_Intercept,confident_Intercept)     -0.63 1.01      589     1010
## cor(frustrated_Intercept,interested_Intercept)    -0.63 1.01      801     1434
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1242     1443
## 
## ~number (Number of levels: 64) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.96      0.09     0.80
## sd(confident_Intercept)                            0.67      0.06     0.55
## sd(interested_Intercept)                           0.64      0.06     0.52
## cor(frustrated_Intercept,confident_Intercept)     -0.46      0.11    -0.65
## cor(frustrated_Intercept,interested_Intercept)    -0.11      0.14    -0.35
## cor(confident_Intercept,interested_Intercept)      0.59      0.09     0.40
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.16 1.01      452      820
## sd(confident_Intercept)                            0.81 1.01      495      867
## sd(interested_Intercept)                           0.78 1.01      440      839
## cor(frustrated_Intercept,confident_Intercept)     -0.21 1.01      338      649
## cor(frustrated_Intercept,interested_Intercept)     0.15 1.01      293      622
## cor(confident_Intercept,interested_Intercept)      0.76 1.01      403      771
## 
## Population-Level Effects: 
##                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept         3.12      0.24     2.61     3.57 1.01      383
## confident_Intercept          3.57      0.17     3.22     3.90 1.00      519
## interested_Intercept         4.04      0.16     3.72     4.35 1.00      430
## intvalpost_Intercept         0.43      0.08     0.28     0.57 1.00     2425
## frustrated_genderMale       -0.17      0.31    -0.75     0.47 1.01      402
## frustrated_courseCOSC111     0.35      0.45    -0.55     1.22 1.01      423
## frustrated_self_eff         -0.56      0.16    -0.87    -0.22 1.01      366
## confident_genderMale         0.25      0.22    -0.17     0.67 1.00      378
## confident_courseCOSC111     -0.48      0.32    -1.08     0.14 1.01      474
## confident_self_eff           0.53      0.11     0.32     0.76 1.02      421
## interested_genderMale        0.24      0.22    -0.19     0.67 1.01      386
## interested_courseCOSC111    -0.42      0.30    -1.01     0.19 1.00      465
## interested_self_eff          0.17      0.11    -0.04     0.37 1.02      373
## intvalpost_int_val_pre       0.40      0.04     0.32     0.49 1.00     1589
## intvalpost_courseCOSC111    -0.36      0.14    -0.62    -0.10 1.00     2280
## intvalpost_genderMale        0.02      0.09    -0.15     0.19 1.00     1678
## intvalpost_self_eff          0.26      0.05     0.17     0.36 1.00     1858
##                          Tail_ESS
## frustrated_Intercept          551
## confident_Intercept           844
## interested_Intercept          642
## intvalpost_Intercept         1699
## frustrated_genderMale         707
## frustrated_courseCOSC111      691
## frustrated_self_eff           653
## confident_genderMale          553
## confident_courseCOSC111       780
## confident_self_eff            756
## interested_genderMale         636
## interested_courseCOSC111      898
## interested_self_eff           592
## intvalpost_int_val_pre       1462
## intvalpost_courseCOSC111     1481
## intvalpost_genderMale        1396
## intvalpost_self_eff          1545
## 
## Family Specific Parameters: 
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated     0.76      0.03     0.71     0.84 1.00      462      574
## sigma_confident      0.64      0.03     0.59     0.70 1.00      575      617
## sigma_interested     0.61      0.05     0.53     0.71 1.00      494      834
## sigma_intvalpost     0.96      0.02     0.91     1.01 1.00     2133     1376
## 
## Residual Correlations: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)     -0.28      0.05    -0.40    -0.18 1.00
## rescor(frustrated,interested)    -0.19      0.09    -0.35    -0.01 1.01
## rescor(confident,interested)      0.44      0.06     0.32     0.57 1.00
## rescor(frustrated,intvalpost)    -0.19      0.14    -0.45     0.08 1.01
## rescor(confident,intvalpost)      0.28      0.11     0.04     0.48 1.01
## rescor(interested,intvalpost)     0.60      0.08     0.41     0.73 1.01
##                               Bulk_ESS Tail_ESS
## rescor(frustrated,confident)       385      522
## rescor(frustrated,interested)      293      462
## rescor(confident,interested)       504      695
## rescor(frustrated,intvalpost)      319      476
## rescor(confident,intvalpost)       475      629
## rescor(interested,intvalpost)      491      833
## 
## Samples were drawn 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).

4. How do students’ momentary experiences relate to changes in their achievement?

initial model with only course

bf_1 <- bf(frustrated ~ 1 +
             course + 
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             course + 
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             course + 
             (1|s|number) +
             (1|p|assign))

bf_int <- bf(final_score ~ course)

m4a <- brm(bf_1 + bf_2 + bf_3 +
             bf_int,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## Start sampling

## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess

## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess

m4a

##  Family: MV(gaussian, gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + course + (1 | s | number) + (1 | p | assign) 
##          final_score ~ course 
##    Data: data (Number of observations: 831) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.33      0.06     0.22
## sd(confident_Intercept)                            0.19      0.04     0.13
## sd(interested_Intercept)                           0.16      0.03     0.11
## cor(frustrated_Intercept,confident_Intercept)     -0.89      0.09    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.90      0.08    -0.99
## cor(confident_Intercept,interested_Intercept)      0.95      0.05     0.80
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.47 1.00      407      599
## sd(confident_Intercept)                            0.27 1.00      532      703
## sd(interested_Intercept)                           0.23 1.00      554      916
## cor(frustrated_Intercept,confident_Intercept)     -0.67 1.00      613      862
## cor(frustrated_Intercept,interested_Intercept)    -0.67 1.00      630     1022
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1157     1317
## 
## ~number (Number of levels: 71) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.97      0.09     0.82
## sd(confident_Intercept)                            0.82      0.08     0.68
## sd(interested_Intercept)                           0.84      0.07     0.70
## cor(frustrated_Intercept,confident_Intercept)     -0.57      0.09    -0.72
## cor(frustrated_Intercept,interested_Intercept)    -0.33      0.11    -0.54
## cor(confident_Intercept,interested_Intercept)      0.65      0.08     0.48
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.17 1.01      307      523
## sd(confident_Intercept)                            0.99 1.01      200      520
## sd(interested_Intercept)                           1.00 1.02      280      616
## cor(frustrated_Intercept,confident_Intercept)     -0.38 1.02      226      570
## cor(frustrated_Intercept,interested_Intercept)    -0.11 1.01      215      424
## cor(confident_Intercept,interested_Intercept)      0.78 1.02      250      339
## 
## Population-Level Effects: 
##                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept         2.63      0.15     2.33     2.90 1.03      177
## confident_Intercept          4.15      0.11     3.94     4.38 1.03      162
## interested_Intercept         4.29      0.11     4.08     4.52 1.04      160
## finalscore_Intercept        93.76      0.39    93.01    94.54 1.00     2307
## frustrated_courseCOSC111     0.05      0.41    -0.75     0.86 1.01      319
## confident_courseCOSC111     -0.38      0.32    -0.99     0.26 1.01      413
## interested_courseCOSC111    -0.40      0.32    -1.02     0.21 1.01      394
## finalscore_courseCOSC111     2.96      1.52    -0.10     5.82 1.01     2916
##                          Tail_ESS
## frustrated_Intercept          392
## confident_Intercept           321
## interested_Intercept          335
## finalscore_Intercept         1649
## frustrated_courseCOSC111      769
## confident_courseCOSC111       740
## interested_courseCOSC111      607
## finalscore_courseCOSC111     1304
## 
## Family Specific Parameters: 
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated     0.89      0.06     0.78     1.02 1.01      258      494
## sigma_confident      0.63      0.03     0.58     0.72 1.01      301      391
## sigma_interested     0.50      0.02     0.46     0.56 1.01      325      369
## sigma_finalscore    11.28      0.28    10.73    11.84 1.00     2697     1334
## 
## Residual Correlations: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)     -0.38      0.07    -0.52    -0.24 1.01
## rescor(frustrated,interested)    -0.19      0.10    -0.38     0.02 1.02
## rescor(confident,interested)      0.43      0.06     0.32     0.56 1.01
## rescor(frustrated,finalscore)    -0.52      0.09    -0.67    -0.31 1.01
## rescor(confident,finalscore)      0.32      0.13     0.05     0.56 1.01
## rescor(interested,finalscore)     0.17      0.18    -0.21     0.48 1.02
##                               Bulk_ESS Tail_ESS
## rescor(frustrated,confident)       266      466
## rescor(frustrated,interested)      222      363
## rescor(confident,interested)       270      392
## rescor(frustrated,finalscore)      246      473
## rescor(confident,finalscore)       247      345
## rescor(interested,finalscore)      226      322
## 
## Samples were drawn 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).

adding gender and pre self-efficacy

bf_1 <- bf(frustrated ~ 1 +
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_2 <- bf(confident ~ 1 + 
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_3 <- bf(interested ~ 1 + 
             gender + 
             course + 
             self_eff + 
             (1|s|number) +
             (1|p|assign))

bf_int <- bf(final_score~ course + gender + self_eff)

m4c <- brm(bf_1 + bf_2 + bf_3 +
             bf_int,
           data = data, 
           chains = 4, cores = 4, iter = 1000, 
           control = list(max_treedepth = 20))

## Setting 'rescor' to TRUE by default for this model

## Warning: In the future, 'rescor' will be set to FALSE by default for all models.
## It is thus recommended to explicitely set 'rescor' via 'set_recor' instead of
## using the default.

## Warning: Rows containing NAs were excluded from the model.

## Compiling Stan program...

## recompiling to avoid crashing R session

## Start sampling

m4c

##  Family: MV(gaussian, gaussian, gaussian, gaussian) 
##   Links: mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity
##          mu = identity; sigma = identity 
## Formula: frustrated ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          confident ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          interested ~ 1 + gender + course + self_eff + (1 | s | number) + (1 | p | assign) 
##          final_score ~ course + gender + self_eff 
##    Data: data (Number of observations: 816) 
## Samples: 4 chains, each with iter = 1000; warmup = 500; thin = 1;
##          total post-warmup samples = 2000
## 
## Group-Level Effects: 
## ~assign (Number of levels: 25) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.34      0.06     0.23
## sd(confident_Intercept)                            0.19      0.04     0.13
## sd(interested_Intercept)                           0.17      0.03     0.11
## cor(frustrated_Intercept,confident_Intercept)     -0.89      0.09    -0.99
## cor(frustrated_Intercept,interested_Intercept)    -0.90      0.09    -0.99
## cor(confident_Intercept,interested_Intercept)      0.94      0.06     0.79
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           0.47 1.00      818      951
## sd(confident_Intercept)                            0.27 1.00      974     1117
## sd(interested_Intercept)                           0.23 1.00     1044     1404
## cor(frustrated_Intercept,confident_Intercept)     -0.65 1.00     1129     1567
## cor(frustrated_Intercept,interested_Intercept)    -0.66 1.00     1163     1372
## cor(confident_Intercept,interested_Intercept)      1.00 1.00     1544     1482
## 
## ~number (Number of levels: 69) 
##                                                Estimate Est.Error l-95% CI
## sd(frustrated_Intercept)                           0.91      0.09     0.76
## sd(confident_Intercept)                            0.71      0.07     0.59
## sd(interested_Intercept)                           0.83      0.08     0.70
## cor(frustrated_Intercept,confident_Intercept)     -0.50      0.10    -0.68
## cor(frustrated_Intercept,interested_Intercept)    -0.32      0.12    -0.54
## cor(confident_Intercept,interested_Intercept)      0.66      0.08     0.49
##                                                u-95% CI Rhat Bulk_ESS Tail_ESS
## sd(frustrated_Intercept)                           1.12 1.01      569      857
## sd(confident_Intercept)                            0.85 1.00      806     1197
## sd(interested_Intercept)                           0.99 1.00      565      609
## cor(frustrated_Intercept,confident_Intercept)     -0.28 1.00      519      829
## cor(frustrated_Intercept,interested_Intercept)    -0.08 1.00      616      868
## cor(confident_Intercept,interested_Intercept)      0.79 1.01      597      774
## 
## Population-Level Effects: 
##                          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## frustrated_Intercept         3.10      0.24     2.65     3.58 1.00      738
## confident_Intercept          3.64      0.17     3.31     3.98 1.01      869
## interested_Intercept         4.09      0.20     3.69     4.47 1.00      945
## finalscore_Intercept        91.75      0.70    90.46    93.14 1.00     3089
## frustrated_genderMale       -0.05      0.30    -0.64     0.54 1.02      645
## frustrated_courseCOSC111     0.06      0.40    -0.74     0.82 1.00      943
## frustrated_self_eff         -0.59      0.15    -0.88    -0.27 1.01      601
## confident_genderMale         0.11      0.22    -0.31     0.54 1.01      781
## confident_courseCOSC111     -0.32      0.30    -0.93     0.25 1.01      867
## confident_self_eff           0.56      0.12     0.33     0.79 1.01      643
## interested_genderMale        0.05      0.26    -0.42     0.58 1.01      730
## interested_courseCOSC111    -0.26      0.36    -0.94     0.46 1.01      902
## interested_self_eff          0.20      0.13    -0.07     0.47 1.00      798
## finalscore_courseCOSC111     3.32      1.47     0.47     6.07 1.00     2710
## finalscore_genderMale       -2.64      0.96    -4.47    -0.75 1.00     2887
## finalscore_self_eff          5.09      0.51     4.07     6.06 1.00     2658
##                          Tail_ESS
## frustrated_Intercept          949
## confident_Intercept          1143
## interested_Intercept         1095
## finalscore_Intercept         1538
## frustrated_genderMale         656
## frustrated_courseCOSC111     1384
## frustrated_self_eff           744
## confident_genderMale          938
## confident_courseCOSC111      1006
## confident_self_eff            845
## interested_genderMale        1014
## interested_courseCOSC111     1076
## interested_self_eff          1076
## finalscore_courseCOSC111     1695
## finalscore_genderMale        1758
## finalscore_self_eff          1531
## 
## Family Specific Parameters: 
##                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma_frustrated     0.83      0.05     0.75     0.95 1.00      643     1136
## sigma_confident      0.60      0.02     0.57     0.65 1.00      990      597
## sigma_interested     0.49      0.02     0.46     0.54 1.00     1039      947
## sigma_finalscore    10.58      0.26    10.07    11.11 1.00     2232     1448
## 
## Residual Correlations: 
##                               Estimate Est.Error l-95% CI u-95% CI Rhat
## rescor(frustrated,confident)     -0.29      0.06    -0.42    -0.16 1.00
## rescor(frustrated,interested)    -0.13      0.09    -0.30     0.03 1.00
## rescor(confident,interested)      0.41      0.04     0.33     0.49 1.00
## rescor(frustrated,finalscore)    -0.43      0.11    -0.62    -0.20 1.01
## rescor(confident,finalscore)      0.11      0.13    -0.15     0.37 1.00
## rescor(interested,finalscore)     0.08      0.18    -0.28     0.42 1.01
##                               Bulk_ESS Tail_ESS
## rescor(frustrated,confident)       678      731
## rescor(frustrated,interested)      714      874
## rescor(confident,interested)      1237     1209
## rescor(frustrated,finalscore)      632      825
## rescor(confident,finalscore)       662      682
## rescor(interested,finalscore)      670      752
## 
## Samples were drawn 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).