IQWST Motivation Models

For use later on.

calculate_pooled_sd <- function(sd_group1, n_group1, sd_group2, n_group2) {
  sqrt(((n_group1 - 1) * (sd_group1 ^ 2) + (n_group2 - 1) * (sd_group2 ^ 2)) / (n_group1 + n_group2 - 2))
}

# test
calculate_pooled_sd(sd_group1 = 17.85, n_group1 = 6, sd_group2 = 8.16, n_group2 = 8)

## [1] 13.09966

Mixed effects models

library(lme4)

## Loading required package: Matrix

m_utility_val <- lmer(PostUV_ave ~ Int + PreUV_ave*PreEff_Ave + (1|ClassTeacher), data = df)
sjPlot::sjt.lmer(m_utility_val)

## Warning in checkMatrixPackageVersion(): Package version inconsistency detected.
## TMB was built with Matrix version 1.2.10
## Current Matrix version is 1.2.11
## Please re-install 'TMB' from source or restore original 'Matrix' package

## Computing p-values via Kenward-Roger approximation. Use `p.kr = FALSE` if computation takes too long.

		PostUV_ave
		B	CI	p
Fixed Parts
(Intercept)		5.36	2.15 – 8.57	.001
Int		0.44	0.04 – 0.85	.034
PreUV_ave		-0.07	-0.69 – 0.56	.831
PreEff_Ave		-0.53	-1.17 – 0.12	.111
PreUV_ave:PreEff_Ave		0.11	-0.01 – 0.22	.080
Random Parts
σ2		1.773
τ00, ClassTeacher		0.075
NClassTeacher		8
ICCClassTeacher		0.040
Observations		170
R2 / Ω02		.268 / .267

m_val <- lmer(PostVal_Ave ~ Int + PreVal_Ave*PreEff_Ave + (1|ClassTeacher), data = df)
sjPlot::sjt.lmer(m_val)

## Computing p-values via Kenward-Roger approximation. Use `p.kr = FALSE` if computation takes too long.

		PostVal_Ave
		B	CI	p
Fixed Parts
(Intercept)		3.71	0.38 – 7.05	.030
Int		0.32	-0.02 – 0.65	.065
PreVal_Ave		0.30	-0.33 – 0.93	.358
PreEff_Ave		-0.30	-0.98 – 0.37	.376
PreVal_Ave:PreEff_Ave		0.05	-0.06 – 0.17	.373
Random Parts
σ2		1.252
τ00, ClassTeacher		0.095
NClassTeacher		8
ICCClassTeacher		0.071
Observations		177
R2 / Ω02		.322 / .321

m_interest <- lmer(PostInt_Ave ~ Int + PreInt_Ave*PreEff_Ave + (1|ClassTeacher), data = df)
sjPlot::sjt.lmer(m_interest)

## Computing p-values via Kenward-Roger approximation. Use `p.kr = FALSE` if computation takes too long.

		PostInt_Ave
		B	CI	p
Fixed Parts
(Intercept)		-1.15	-5.48 – 3.18	.603
Int		0.02	-0.38 – 0.41	.934
PreInt_Ave		1.14	0.33 – 1.94	.006
PreEff_Ave		0.63	-0.19 – 1.45	.134
PreInt_Ave:PreEff_Ave		-0.11	-0.26 – 0.04	.147
Random Parts
σ2		1.733
τ00, ClassTeacher		0.213
NClassTeacher		8
ICCClassTeacher		0.109
Observations		177
R2 / Ω02		.340 / .338

Models with gender added.

m_utility_val_g <- lmer(PostUV_ave ~ Int + PreUV_ave*PreEff_Ave + Gender + (1|ClassTeacher), data = df)
sjPlot::sjt.lmer(m_utility_val_g)

## Computing p-values via Kenward-Roger approximation. Use `p.kr = FALSE` if computation takes too long.

		PostUV_ave
		B	CI	p
Fixed Parts
(Intercept)		5.52	2.31 – 8.72	<.001
Int		0.44	0.04 – 0.85	.034
PreUV_ave		-0.08	-0.70 – 0.55	.809
PreEff_Ave		-0.53	-1.17 – 0.11	.108
Gender		-0.29	-0.69 – 0.11	.156
PreUV_ave:PreEff_Ave		0.11	-0.01 – 0.22	.074
Random Parts
σ2		1.758
τ00, ClassTeacher		0.083
NClassTeacher		8
ICCClassTeacher		0.045
Observations		170
R2 / Ω02		.280 / .279

m_val_g <- lmer(PostVal_Ave ~ Int + PreVal_Ave*PreEff_Ave + Gender + (1|ClassTeacher), data = df)
sjPlot::sjt.lmer(m_val_g)

## Computing p-values via Kenward-Roger approximation. Use `p.kr = FALSE` if computation takes too long.

		PostVal_Ave
		B	CI	p
Fixed Parts
(Intercept)		3.77	0.41 – 7.12	.029
Int		0.32	-0.02 – 0.65	.066
PreVal_Ave		0.29	-0.34 – 0.92	.369
PreEff_Ave		-0.31	-0.98 – 0.37	.373
Gender		-0.07	-0.40 – 0.27	.695
PreVal_Ave:PreEff_Ave		0.05	-0.06 – 0.17	.366
Random Parts
σ2		1.258
τ00, ClassTeacher		0.097
NClassTeacher		8
ICCClassTeacher		0.071
Observations		177
R2 / Ω02		.323 / .322

m_interest_g <- lmer(PostInt_Ave ~ Int + PreInt_Ave*PreEff_Ave + Gender + (1|ClassTeacher), data = df)
sjPlot::sjt.lmer(m_interest_g)

## Computing p-values via Kenward-Roger approximation. Use `p.kr = FALSE` if computation takes too long.

		PostInt_Ave
		B	CI	p
Fixed Parts
(Intercept)		-0.80	-5.15 – 3.54	.718
Int		0.02	-0.38 – 0.41	.933
PreInt_Ave		1.08	0.28 – 1.88	.009
PreEff_Ave		0.60	-0.22 – 1.43	.151
Gender		-0.26	-0.66 – 0.13	.193
PreInt_Ave:PreEff_Ave		-0.10	-0.25 – 0.05	.178
Random Parts
σ2		1.724
τ00, ClassTeacher		0.223
NClassTeacher		8
ICCClassTeacher		0.115
Observations		177
R2 / Ω02		.347 / .346

Participant flow

df <- tbl_df(df)

# UTILITY VALUE

df %>%
  filter(is.na(PreUV_ave)) # 3 students missing pre UV

## # A tibble: 3 x 13
##   Gender   Age PreUV_all_ave PostUV_all_ave PreInt_Ave PreEff_Ave   Int
##    <int> <int>         <dbl>          <dbl>      <dbl>      <dbl> <int>
## 1      1    10            NA            6.2        4.0        6.2     1
## 2      0    11            NA            2.4        4.6        4.2     1
## 3      0    11            NA            4.8        7.0        5.4     0
## # ... with 6 more variables: PreUV_ave <dbl>, PostUV_ave <dbl>,
## #   PostInt_Ave <dbl>, PreVal_Ave <dbl>, PostVal_Ave <dbl>,
## #   ClassTeacher <fctr>

df %>%
  filter(is.na(PostUV_ave)) # 20 students missing pre UV

## # A tibble: 20 x 13
##    Gender   Age PreUV_all_ave PostUV_all_ave PreInt_Ave PreEff_Ave   Int
##     <int> <int>         <dbl>          <dbl>      <dbl>      <dbl> <int>
##  1      0    11           7.0             NA       7.00        7.0     1
##  2      0    10           3.6             NA       5.60        3.2    NA
##  3      0    11           3.6             NA       4.40        6.2     1
##  4      0    11           6.8             NA       6.80        5.4     1
##  5      0    11           6.8             NA       6.40        6.4     1
##  6      1    11           7.0             NA       7.00        6.8     1
##  7      0    10           5.6             NA       6.00        5.4     0
##  8      1    11           6.4             NA       6.80        3.0    NA
##  9      1    11           5.2             NA       7.00        5.6     0
## 10      1    10            NA             NA       6.75        6.6    NA
## 11      0    10           7.0             NA       7.00        7.0     1
## 12      1    10           6.4             NA       6.60        5.8     1
## 13      0    10           7.0             NA       7.00        6.4     1
## 14      0    11           4.8             NA       6.60        5.8     0
## 15      1    10           5.4             NA       6.80        5.6     0
## 16      0    10           5.8             NA       6.40        3.6     1
## 17      1    11           6.4             NA       6.60        5.8     0
## 18      0    10           5.2             NA       5.00        2.8    NA
## 19      0    11           4.2             NA       2.25        6.2     0
## 20      0    10           2.8             NA       1.00        3.4    NA
## # ... with 6 more variables: PreUV_ave <dbl>, PostUV_ave <dbl>,
## #   PostInt_Ave <dbl>, PreVal_Ave <dbl>, PostVal_Ave <dbl>,
## #   ClassTeacher <fctr>

df %>%
  filter(is.na(PreUV_ave) | is.na(PostUV_ave)) # 23 students missing either pre or post UV

## # A tibble: 23 x 13
##    Gender   Age PreUV_all_ave PostUV_all_ave PreInt_Ave PreEff_Ave   Int
##     <int> <int>         <dbl>          <dbl>      <dbl>      <dbl> <int>
##  1      1    10            NA            6.2        4.0        6.2     1
##  2      0    11           7.0             NA        7.0        7.0     1
##  3      0    10           3.6             NA        5.6        3.2    NA
##  4      0    11           3.6             NA        4.4        6.2     1
##  5      0    11            NA            2.4        4.6        4.2     1
##  6      0    11           6.8             NA        6.8        5.4     1
##  7      0    11           6.8             NA        6.4        6.4     1
##  8      1    11           7.0             NA        7.0        6.8     1
##  9      0    10           5.6             NA        6.0        5.4     0
## 10      1    11           6.4             NA        6.8        3.0    NA
## # ... with 13 more rows, and 6 more variables: PreUV_ave <dbl>,
## #   PostUV_ave <dbl>, PostInt_Ave <dbl>, PreVal_Ave <dbl>,
## #   PostVal_Ave <dbl>, ClassTeacher <fctr>

# VALUE

df %>%
  filter(is.na(PreVal_Ave)) # 0 students missing pre val

## # A tibble: 0 x 13
## # ... with 13 variables: Gender <int>, Age <int>, PreUV_all_ave <dbl>,
## #   PostUV_all_ave <dbl>, PreInt_Ave <dbl>, PreEff_Ave <dbl>, Int <int>,
## #   PreUV_ave <dbl>, PostUV_ave <dbl>, PostInt_Ave <dbl>,
## #   PreVal_Ave <dbl>, PostVal_Ave <dbl>, ClassTeacher <fctr>

df %>%
  filter(is.na(PostVal_Ave)) # 16 students missing pre val

## # A tibble: 16 x 13
##    Gender   Age PreUV_all_ave PostUV_all_ave PreInt_Ave PreEff_Ave   Int
##     <int> <int>         <dbl>          <dbl>      <dbl>      <dbl> <int>
##  1      0    11           7.0             NA       7.00        7.0     1
##  2      0    10           3.6             NA       5.60        3.2    NA
##  3      0    11           3.6             NA       4.40        6.2     1
##  4      0    11           6.8             NA       6.40        6.4     1
##  5      1    11           7.0             NA       7.00        6.8     1
##  6      1    11           6.4             NA       6.80        3.0    NA
##  7      1    11           5.2             NA       7.00        5.6     0
##  8      1    10            NA             NA       6.75        6.6    NA
##  9      0    10           7.0             NA       7.00        7.0     1
## 10      1    10           6.4             NA       6.60        5.8     1
## 11      0    11           4.8             NA       6.60        5.8     0
## 12      1    10           5.4             NA       6.80        5.6     0
## 13      0    10           5.8             NA       6.40        3.6     1
## 14      1    11           6.4             NA       6.60        5.8     0
## 15      0    10           5.2             NA       5.00        2.8    NA
## 16      0    10           2.8             NA       1.00        3.4    NA
## # ... with 6 more variables: PreUV_ave <dbl>, PostUV_ave <dbl>,
## #   PostInt_Ave <dbl>, PreVal_Ave <dbl>, PostVal_Ave <dbl>,
## #   ClassTeacher <fctr>

df %>%
  filter(is.na(PreVal_Ave) | is.na(PostVal_Ave)) # 16 students missing either pre or post val

## # A tibble: 16 x 13
##    Gender   Age PreUV_all_ave PostUV_all_ave PreInt_Ave PreEff_Ave   Int
##     <int> <int>         <dbl>          <dbl>      <dbl>      <dbl> <int>
##  1      0    11           7.0             NA       7.00        7.0     1
##  2      0    10           3.6             NA       5.60        3.2    NA
##  3      0    11           3.6             NA       4.40        6.2     1
##  4      0    11           6.8             NA       6.40        6.4     1
##  5      1    11           7.0             NA       7.00        6.8     1
##  6      1    11           6.4             NA       6.80        3.0    NA
##  7      1    11           5.2             NA       7.00        5.6     0
##  8      1    10            NA             NA       6.75        6.6    NA
##  9      0    10           7.0             NA       7.00        7.0     1
## 10      1    10           6.4             NA       6.60        5.8     1
## 11      0    11           4.8             NA       6.60        5.8     0
## 12      1    10           5.4             NA       6.80        5.6     0
## 13      0    10           5.8             NA       6.40        3.6     1
## 14      1    11           6.4             NA       6.60        5.8     0
## 15      0    10           5.2             NA       5.00        2.8    NA
## 16      0    10           2.8             NA       1.00        3.4    NA
## # ... with 6 more variables: PreUV_ave <dbl>, PostUV_ave <dbl>,
## #   PostInt_Ave <dbl>, PreVal_Ave <dbl>, PostVal_Ave <dbl>,
## #   ClassTeacher <fctr>

# INTEREST

df %>%
  filter(is.na(PreInt_Ave)) # 0 students missing pre interest

## # A tibble: 0 x 13
## # ... with 13 variables: Gender <int>, Age <int>, PreUV_all_ave <dbl>,
## #   PostUV_all_ave <dbl>, PreInt_Ave <dbl>, PreEff_Ave <dbl>, Int <int>,
## #   PreUV_ave <dbl>, PostUV_ave <dbl>, PostInt_Ave <dbl>,
## #   PreVal_Ave <dbl>, PostVal_Ave <dbl>, ClassTeacher <fctr>

df %>%
  filter(is.na(PostInt_Ave)) # 16 students missing pre int

## # A tibble: 16 x 13
##    Gender   Age PreUV_all_ave PostUV_all_ave PreInt_Ave PreEff_Ave   Int
##     <int> <int>         <dbl>          <dbl>      <dbl>      <dbl> <int>
##  1      0    11           7.0             NA       7.00        7.0     1
##  2      0    10           3.6             NA       5.60        3.2    NA
##  3      0    11           3.6             NA       4.40        6.2     1
##  4      0    11           6.8             NA       6.40        6.4     1
##  5      1    11           7.0             NA       7.00        6.8     1
##  6      1    11           6.4             NA       6.80        3.0    NA
##  7      1    11           5.2             NA       7.00        5.6     0
##  8      1    10            NA             NA       6.75        6.6    NA
##  9      0    10           7.0             NA       7.00        7.0     1
## 10      1    10           6.4             NA       6.60        5.8     1
## 11      0    11           4.8             NA       6.60        5.8     0
## 12      1    10           5.4             NA       6.80        5.6     0
## 13      0    10           5.8             NA       6.40        3.6     1
## 14      1    11           6.4             NA       6.60        5.8     0
## 15      0    10           5.2             NA       5.00        2.8    NA
## 16      0    10           2.8             NA       1.00        3.4    NA
## # ... with 6 more variables: PreUV_ave <dbl>, PostUV_ave <dbl>,
## #   PostInt_Ave <dbl>, PreVal_Ave <dbl>, PostVal_Ave <dbl>,
## #   ClassTeacher <fctr>

df %>%
  filter(is.na(PreInt_Ave) | is.na(PostInt_Ave)) # 16 students missing either pre or post int

## # A tibble: 16 x 13
##    Gender   Age PreUV_all_ave PostUV_all_ave PreInt_Ave PreEff_Ave   Int
##     <int> <int>         <dbl>          <dbl>      <dbl>      <dbl> <int>
##  1      0    11           7.0             NA       7.00        7.0     1
##  2      0    10           3.6             NA       5.60        3.2    NA
##  3      0    11           3.6             NA       4.40        6.2     1
##  4      0    11           6.8             NA       6.40        6.4     1
##  5      1    11           7.0             NA       7.00        6.8     1
##  6      1    11           6.4             NA       6.80        3.0    NA
##  7      1    11           5.2             NA       7.00        5.6     0
##  8      1    10            NA             NA       6.75        6.6    NA
##  9      0    10           7.0             NA       7.00        7.0     1
## 10      1    10           6.4             NA       6.60        5.8     1
## 11      0    11           4.8             NA       6.60        5.8     0
## 12      1    10           5.4             NA       6.80        5.6     0
## 13      0    10           5.8             NA       6.40        3.6     1
## 14      1    11           6.4             NA       6.60        5.8     0
## 15      0    10           5.2             NA       5.00        2.8    NA
## 16      0    10           2.8             NA       1.00        3.4    NA
## # ... with 6 more variables: PreUV_ave <dbl>, PostUV_ave <dbl>,
## #   PostInt_Ave <dbl>, PreVal_Ave <dbl>, PostVal_Ave <dbl>,
## #   ClassTeacher <fctr>

# SELF-EFFICACY

df %>% 
  filter(is.na(PreEff_Ave)) # 0 students missing pre eff ave

## # A tibble: 0 x 13
## # ... with 13 variables: Gender <int>, Age <int>, PreUV_all_ave <dbl>,
## #   PostUV_all_ave <dbl>, PreInt_Ave <dbl>, PreEff_Ave <dbl>, Int <int>,
## #   PreUV_ave <dbl>, PostUV_ave <dbl>, PostInt_Ave <dbl>,
## #   PreVal_Ave <dbl>, PostVal_Ave <dbl>, ClassTeacher <fctr>

# GENDER

df %>% 
  filter(is.na(Gender)) # 0 missing

## # A tibble: 0 x 13
## # ... with 13 variables: Gender <int>, Age <int>, PreUV_all_ave <dbl>,
## #   PostUV_all_ave <dbl>, PreInt_Ave <dbl>, PreEff_Ave <dbl>, Int <int>,
## #   PreUV_ave <dbl>, PostUV_ave <dbl>, PostInt_Ave <dbl>,
## #   PreVal_Ave <dbl>, PostVal_Ave <dbl>, ClassTeacher <fctr>

df %>% 
  filter(is.na(ClassTeacher)) # 0 missing

## # A tibble: 0 x 13
## # ... with 13 variables: Gender <int>, Age <int>, PreUV_all_ave <dbl>,
## #   PostUV_all_ave <dbl>, PreInt_Ave <dbl>, PreEff_Ave <dbl>, Int <int>,
## #   PreUV_ave <dbl>, PostUV_ave <dbl>, PostInt_Ave <dbl>,
## #   PreVal_Ave <dbl>, PostVal_Ave <dbl>, ClassTeacher <fctr>