Validation
Erhebungsinstrument „Überzeugungen zum Verhältnis von Theorie und Praxis von Lehramtsstudierenden“
Jürgen Schneider
University of TübingenRuben Kulcsar
University of Linz// Further Cooperation
Thomas Fischer
University of FlensburgKathrin Rheinländer
University of Vechta2024-04-19
Link to OSF-Project
Questionnaire realized with formr
see the questionnaire here
Preregistration
Available here: https://osf.io/2jw7m
Preregistration dates after the data collection, last modification was -
however - before data collection. I simply clicked on “save” and not on
“register” at the time.
Data import & cleaning
Import
library(tidyverse)
library(psych)
library(rio)
library(lavaanPlot)
library(BayesFactor)
library(lavaan)
library(knitr)
valid <- rio::import("https://raw.githubusercontent.com/j-5chneider/uzvvtp-las/master/data/pilot2.csv")Delete empty rows/ rows of test run
valid <- valid %>%
dplyr::filter(!is.na(lehramt)) # only include students that completed the questionnaireSample description
and editing/deleting unreasonable values (e.g. out of range data)
Semester
# semester: no unreasonable values
ggplot(valid, aes(x = as.factor(semester))) +
geom_bar() +
labs(title = "Count of participants by semester",
caption = "Note: There were no participants from 11th, 13th, 14th, 15th semester.") +
xlab("Semester") +
geom_text(aes(label = ..count..), stat = "count", vjust = -0.3, size = 4)
Standort
ggplot(valid, aes(x = factor(standort, labels = c("Flensburg", "Linz", "Tübingen", "Vechta")))) + # 1= Flensburg, 2= Linz, 3= München, 4= Stuttgart, 5= Tübingen, 6= Vechta, 7= andere
geom_bar() +
labs(title = "Count of participants by Standort") +
xlab("") +
geom_text(aes(label = ..count..), stat = "count", vjust = -0.3, size = 4)
Subject
fach_freq <- data.frame(table(valid$fach))
names(fach_freq) <- c("Combination of Subjects", "Frequency")
kable(fach_freq, format = "html")| Combination of Subjects | Frequency |
|---|---|
| 11, 12, 15 | 1 |
| 12 | 4 |
| 12, 13 | 12 |
| 12, 13, 14 | 1 |
| 12, 13, 18 | 1 |
| 12, 14 | 1 |
| 12, 15 | 3 |
| 12, 17 | 1 |
| 12, 18 | 1 |
| 12, 18, 39 | 2 |
| 12, 29 | 1 |
| 12, 31 | 4 |
| 12, 35 | 1 |
| 12, 39 | 10 |
| 12, 40 | 2 |
| 12, 43 | 1 |
| 13 | 1 |
| 13, 14 | 1 |
| 13, 14, 23, 35 | 1 |
| 13, 17 | 1 |
| 13, 17, 34 | 1 |
| 13, 18 | 2 |
| 13, 18, 31 | 1 |
| 13, 23 | 1 |
| 13, 31 | 2 |
| 13, 37 | 4 |
| 13, 43 | 1 |
| 13, 44 | 2 |
| 13, 50 | 1 |
| 13, 52 | 1 |
| 14, 18 | 1 |
| 14, 31 | 1 |
| 15 | 2 |
| 15, 31 | 2 |
| 15, 39 | 1 |
| 15, 43 | 2 |
| 16, 18, 31 | 1 |
| 17, 23 | 1 |
| 17, 34 | 1 |
| 17, 34, 41 | 1 |
| 18 | 2 |
| 18, 24 | 1 |
| 18, 30 | 2 |
| 18, 30, 43 | 1 |
| 18, 31 | 1 |
| 18, 35 | 2 |
| 18, 36 | 1 |
| 18, 37 | 1 |
| 18, 44 | 1 |
| 23, 31 | 1 |
| 25, 27 | 1 |
| 27 | 2 |
| 31 | 1 |
| 31, 39 | 8 |
| 31, 40 | 1 |
| 31, 44 | 1 |
| 31, 50 | 1 |
| 34 | 1 |
| 34, 36 | 1 |
| 35 | 1 |
| 35, 40 | 1 |
| 36, 44 | 1 |
| 37 | 1 |
| 37, 50 | 2 |
| 38, 43 | 1 |
| 39 | 4 |
| 39, 46 | 1 |
| 4 | 2 |
| 4, 11, 12 | 1 |
| 4, 11, 12, 15 | 1 |
| 4, 12, 15 | 2 |
| 4, 12, 18 | 1 |
| 4, 12, 29 | 1 |
| 4, 12, 37, 39 | 1 |
| 4, 12, 39 | 3 |
| 4, 12, 46 | 1 |
| 4, 12, 50 | 1 |
| 4, 13, 39 | 1 |
| 4, 15, 39 | 1 |
| 4, 15, 40 | 1 |
| 4, 17, 43 | 1 |
| 4, 18, 37 | 1 |
| 4, 31, 39 | 1 |
| 4, 35 | 1 |
| 4, 35, 40 | 1 |
| 40 | 2 |
| 40, 44 | 1 |
| 42, 51 | 1 |
| 44 | 2 |
| 5 | 1 |
| 5, 12, 39 | 3 |
| 5, 13 | 2 |
| 5, 14, 18 | 1 |
| 5, 17 | 2 |
| 5, 17, 44 | 1 |
| 5, 31 | 1 |
| 5, 31, 39 | 2 |
| 5, 31, 44 | 1 |
| 5, 34 | 3 |
| 5, 36 | 1 |
| 5, 37 | 1 |
| 5, 6 | 2 |
| 50, 51 | 2 |
| 51 | 15 |
| 51, 52 | 1 |
| 6, 13 | 1 |
| 6, 13, 50 | 1 |
| 6, 31 | 3 |
| 6, 34 | 1 |
| 6, 34, 43 | 1 |
| 6, 36 | 1 |
| 6, 44 | 1 |
| 6, 50 | 1 |
| 7, 13, 31 | 1 |
| 9, 12 | 2 |
Results FF2: CFA
4-factor-model (4-5 indicators)
Testing for factor structure and measurement invariance. We expect equal loading structure, but not equal intercept structure between treatment groups.
## wrangle data ##
valid_l <- valid %>%
mutate(id = 1:length(.$session), # create ID
tc = ifelse(tc_sr == 1 & tc_st == 2, 1,0)) %>% # create treatment check variable
dplyr::select("flen_AN1":"rel_4_sr", "tc", "id", "semester", -"tc_sr", -"tc_st") %>%
gather(key = "variable", value = "value", na.rm = T, 1:50) %>% # create long data set
mutate(treat = case_when( # create treatment variable
str_sub(variable, -3, -1) == "_st" ~ "transfer",
str_sub(variable, -3, -1) == "_sr" ~ "relationierung",
TRUE ~ NA_character_
),
variable = case_when( # rename variable
str_sub(variable, -3, -1) == "_st" ~ str_sub(variable, 1, -4),
str_sub(variable, -3, -1) == "_sr" ~ str_sub(variable, 1, -4),
TRUE ~ variable
)
)
valid_cfa <- valid_l %>%
dplyr::filter(!is.na(treat)) %>%
spread(key = "variable", value = "value") %>%
mutate(treat = case_when(
treat == "relationierung" ~ 1,
treat == "transfer" ~ 0
))
# get treatment check variable and add to data set
addtc <- valid_l %>%
dplyr::filter(variable == "tc") %>%
mutate(tc = value) %>%
dplyr::select(tc, id)
valid_cfa <- left_join(valid_cfa, addtc, by="id")
# the model
f4.model <- ' level: 1
transfer_w =~ t1*tfe_1 + t2*tfe_2 + t3*tfe_3 + t4*tfe_4 + t5*tfe_5
selektion_w =~ s1*sel_1 + s2*sel_2 + s3*sel_3 + s4*sel_4 + s5*sel_5
enrichment_w =~ e1*enr_1 + e2*enr_2 + e3*enr_3 + e4*enr_4 + e5*enr_5
relation_w =~ r1*rel_1 + r2*rel_2 + r3*rel_3 + r4*rel_4
level: 2
transfer_b =~ t1*tfe_1 + t2*tfe_2 + t3*tfe_3 + t4*tfe_4 + t5*tfe_5
selektion_b =~ s1*sel_1 + s2*sel_2 + s3*sel_3 + s4*sel_4 + s5*sel_5
enrichment_b =~ e1*enr_1 + e2*enr_2 + e3*enr_3 + e4*enr_4 + e5*enr_5
relation_b =~ r1*rel_1 + r2*rel_2 + r3*rel_3 + r4*rel_4
tfe_2 ~~ 0*tfe_2
sel_5 ~~ sel_1
enr_2 ~~ 0*enr_2
rel_3 ~~ 0*rel_3
'
fit_f4 <- sem(f4.model,
data = valid_cfa,
cluster = "id"
)
lavaanPlot(model = fit_f4,
node_options = list(shape = "box", fontname = "Helvetica"),
edge_options = list(color = "grey"),
coefs = TRUE)summary(fit_f4, fit.measures = TRUE) ## lavaan 0.6.17 ended normally after 67 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 105
## Number of equality constraints 15
##
## Used Total
## Number of observations 367 400
## Number of clusters [id] 197
##
## Model Test User Model:
##
## Test statistic 486.722
## Degrees of freedom 309
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 2185.145
## Degrees of freedom 342
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.904
## Tucker-Lewis Index (TLI) 0.893
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -10031.676
## Loglikelihood unrestricted model (H1) -9788.315
##
## Akaike (AIC) 20243.352
## Bayesian (BIC) 20594.835
## Sample-size adjusted Bayesian (SABIC) 20309.299
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.040
## 90 Percent confidence interval - lower 0.033
## 90 Percent confidence interval - upper 0.046
## P-value H_0: RMSEA <= 0.050 0.996
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual (corr metric):
##
## SRMR (within covariance matrix) 0.081
## SRMR (between covariance matrix) 0.108
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
##
## Level 1 [within]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## transfer_w =~
## tfe_1 (t1) 1.000
## tfe_2 (t2) 1.220 0.124 9.824 0.000
## tfe_3 (t3) 1.033 0.135 7.633 0.000
## tfe_4 (t4) 0.909 0.116 7.824 0.000
## tfe_5 (t5) 0.880 0.114 7.730 0.000
## selektion_w =~
## sel_1 (s1) 1.000
## sel_2 (s2) 0.738 0.087 8.506 0.000
## sel_3 (s3) 1.019 0.090 11.310 0.000
## sel_4 (s4) 1.153 0.095 12.073 0.000
## sel_5 (s5) 1.028 0.086 11.984 0.000
## enrichment_w =~
## enr_1 (e1) 1.000
## enr_2 (e2) 1.017 0.095 10.665 0.000
## enr_3 (e3) 1.037 0.096 10.838 0.000
## enr_4 (e4) 0.922 0.091 10.085 0.000
## enr_5 (e5) 0.906 0.095 9.487 0.000
## relation_w =~
## rel_1 (r1) 1.000
## rel_2 (r2) 1.137 0.131 8.652 0.000
## rel_3 (r3) 1.215 0.131 9.275 0.000
## rel_4 (r4) 1.000 0.120 8.314 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## transfer_w ~~
## selektion_w -0.029 0.029 -1.010 0.312
## enrichment_w 0.004 0.028 0.127 0.899
## relation_w 0.008 0.023 0.338 0.736
## selektion_w ~~
## enrichment_w -0.017 0.026 -0.671 0.502
## relation_w 0.006 0.022 0.268 0.789
## enrichment_w ~~
## relation_w 0.072 0.023 3.139 0.002
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .tfe_1 0.651 0.085 7.618 0.000
## .tfe_2 0.720 0.082 8.836 0.000
## .tfe_3 0.681 0.087 7.862 0.000
## .tfe_4 0.964 0.111 8.709 0.000
## .tfe_5 0.373 0.051 7.257 0.000
## .sel_1 0.595 0.076 7.823 0.000
## .sel_2 0.700 0.080 8.750 0.000
## .sel_3 0.640 0.082 7.820 0.000
## .sel_4 0.585 0.080 7.287 0.000
## .sel_5 0.727 0.090 8.100 0.000
## .enr_1 0.794 0.099 8.021 0.000
## .enr_2 0.946 0.085 11.092 0.000
## .enr_3 0.785 0.095 8.279 0.000
## .enr_4 0.762 0.093 8.230 0.000
## .enr_5 1.074 0.124 8.675 0.000
## .rel_1 0.611 0.073 8.356 0.000
## .rel_2 0.575 0.074 7.783 0.000
## .rel_3 0.409 0.047 8.625 0.000
## .rel_4 0.587 0.071 8.266 0.000
## transfer_w 0.268 0.062 4.304 0.000
## selektion_w 0.208 0.043 4.859 0.000
## enrichment_w 0.152 0.042 3.582 0.000
## relation_w 0.117 0.030 3.848 0.000
##
##
## Level 2 [id]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## transfer_b =~
## tfe_1 (t1) 1.000
## tfe_2 (t2) 1.220 0.124 9.824 0.000
## tfe_3 (t3) 1.033 0.135 7.633 0.000
## tfe_4 (t4) 0.909 0.116 7.824 0.000
## tfe_5 (t5) 0.880 0.114 7.730 0.000
## selektion_b =~
## sel_1 (s1) 1.000
## sel_2 (s2) 0.738 0.087 8.506 0.000
## sel_3 (s3) 1.019 0.090 11.310 0.000
## sel_4 (s4) 1.153 0.095 12.073 0.000
## sel_5 (s5) 1.028 0.086 11.984 0.000
## enrichment_b =~
## enr_1 (e1) 1.000
## enr_2 (e2) 1.017 0.095 10.665 0.000
## enr_3 (e3) 1.037 0.096 10.838 0.000
## enr_4 (e4) 0.922 0.091 10.085 0.000
## enr_5 (e5) 0.906 0.095 9.487 0.000
## relation_b =~
## rel_1 (r1) 1.000
## rel_2 (r2) 1.137 0.131 8.652 0.000
## rel_3 (r3) 1.215 0.131 9.275 0.000
## rel_4 (r4) 1.000 0.120 8.314 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .sel_1 ~~
## .sel_5 0.109 0.050 2.196 0.028
## transfer_b ~~
## selektion_b 0.068 0.047 1.442 0.149
## enrichment_b 0.238 0.057 4.203 0.000
## relation_b 0.108 0.039 2.744 0.006
## selektion_b ~~
## enrichment_b -0.030 0.056 -0.529 0.597
## relation_b -0.029 0.042 -0.695 0.487
## enrichment_b ~~
## relation_b 0.214 0.053 4.062 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .tfe_1 2.676 0.072 37.083 0.000
## .tfe_2 2.713 0.072 37.578 0.000
## .tfe_3 2.414 0.082 29.348 0.000
## .tfe_4 2.979 0.071 42.248 0.000
## .tfe_5 2.058 0.067 30.724 0.000
## .sel_1 3.828 0.072 53.186 0.000
## .sel_2 4.441 0.070 63.103 0.000
## .sel_3 3.907 0.072 53.929 0.000
## .sel_4 3.782 0.077 49.136 0.000
## .sel_5 3.432 0.080 43.036 0.000
## .enr_1 3.558 0.078 45.757 0.000
## .enr_2 3.625 0.079 45.862 0.000
## .enr_3 3.859 0.080 48.368 0.000
## .enr_4 3.691 0.076 48.393 0.000
## .enr_5 3.615 0.081 44.655 0.000
## .rel_1 4.451 0.067 66.925 0.000
## .rel_2 4.630 0.067 69.546 0.000
## .rel_3 4.561 0.062 73.563 0.000
## .rel_4 4.543 0.060 75.278 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .tfe_2 0.000
## .enr_2 0.000
## .rel_3 0.000
## .tfe_1 0.241 0.084 2.864 0.004
## .tfe_3 0.499 0.112 4.468 0.000
## .tfe_4 0.105 0.091 1.149 0.251
## .tfe_5 0.345 0.069 4.983 0.000
## .sel_1 0.077 0.067 1.142 0.253
## .sel_2 0.255 0.079 3.215 0.001
## .sel_3 0.043 0.066 0.662 0.508
## .sel_4 0.025 0.067 0.376 0.707
## .sel_5 0.201 0.088 2.285 0.022
## .enr_1 0.064 0.081 0.794 0.427
## .enr_3 0.079 0.081 0.970 0.332
## .enr_4 0.140 0.081 1.724 0.085
## .enr_5 0.138 0.103 1.336 0.182
## .rel_1 0.175 0.070 2.497 0.013
## .rel_2 0.092 0.064 1.444 0.149
## .rel_4 0.036 0.058 0.628 0.530
## transfer_b 0.281 0.073 3.867 0.000
## selektion_b 0.504 0.096 5.275 0.000
## enrichment_b 0.610 0.109 5.621 0.000
## relation_b 0.297 0.071 4.211 0.000
4-factor-model (4 indicators)
Ausschluss von enr_5, tfe_4, sel_2 aufgrund geringer Ladung und inhaltlich geringer Passung
- tfe_4: Voraussetzung stark betont
- enr_5: bei anderen: Differenz betont
- sel_2: aktive Lehrerrolle
# Ausschluss von enr_5, tfe_4, sel_2 aufgrund geringer Ladung und inhaltlich geringer Passung
# tfe_4: Voraussetzung stark betont
# enr_5: bei anderen: Differenz betont
# sel_2: aktive Lehrerrolle
f4.model2 <- 'level: 1
transfer_w =~ t1*tfe_1 + t2*tfe_2 + t3*tfe_3 + t5*tfe_5
selektion_w =~ s1*sel_1 + s3*sel_3 + s4*sel_4 + s5*sel_5
enrichment_w =~ e1*enr_1 + e2*enr_2 + e3*enr_3 + e4*enr_4
relation_w =~ r1*rel_1 + r2*rel_2 + r3*rel_3 + r4*rel_4
level: 2
transfer_b =~ t1*tfe_1 + t2*tfe_2 + t3*tfe_3 + t5*tfe_5
selektion_b =~ s1*sel_1 + s3*sel_3 + s4*sel_4 + s5*sel_5
enrichment_b =~ e1*enr_1 + e2*enr_2 + e3*enr_3 + e4*enr_4
relation_b =~ r1*rel_1 + r2*rel_2 + r3*rel_3 + r4*rel_4
tfe_2 ~~ 0*tfe_2
sel_5 ~~ sel_1
enr_2 ~~ 0*enr_2
rel_3 ~~ 0*rel_3
'
fit_f4.2 <- sem(f4.model2,
data = valid_cfa,
cluster = "id",
std.lv=TRUE
)
lavaanPlot(model = fit_f4.2,
node_options = list(shape = "box", fontname = "Helvetica"),
edge_options = list(color = "grey"),
coefs = TRUE)summary(fit_f4.2, fit.measures = TRUE)## lavaan 0.6.17 ended normally after 58 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 90
## Number of equality constraints 16
##
## Used Total
## Number of observations 373 400
## Number of clusters [id] 197
##
## Model Test User Model:
##
## Test statistic 298.755
## Degrees of freedom 214
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1708.532
## Degrees of freedom 240
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.942
## Tucker-Lewis Index (TLI) 0.935
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -8565.580
## Loglikelihood unrestricted model (H1) -8416.203
##
## Akaike (AIC) 17279.160
## Bayesian (BIC) 17569.357
## Sample-size adjusted Bayesian (SABIC) 17334.577
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.033
## 90 Percent confidence interval - lower 0.023
## 90 Percent confidence interval - upper 0.041
## P-value H_0: RMSEA <= 0.050 1.000
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual (corr metric):
##
## SRMR (within covariance matrix) 0.082
## SRMR (between covariance matrix) 0.099
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Observed
## Observed information based on Hessian
##
##
## Level 1 [within]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## transfer_w =~
## tfe_1 (t1) 0.501 0.049 10.275 0.000
## tfe_2 (t2) 0.643 0.049 13.107 0.000
## tfe_3 (t3) 0.542 0.054 10.088 0.000
## tfe_5 (t5) 0.477 0.044 10.831 0.000
## selektion_w =~
## sel_1 (s1) 0.544 0.044 12.411 0.000
## sel_3 (s3) 0.571 0.043 13.323 0.000
## sel_4 (s4) 0.669 0.044 15.076 0.000
## sel_5 (s5) 0.586 0.049 11.938 0.000
## enrichment_w =~
## enr_1 (e1) 0.575 0.046 12.403 0.000
## enr_2 (e2) 0.621 0.046 13.505 0.000
## enr_3 (e3) 0.580 0.048 12.043 0.000
## enr_4 (e4) 0.581 0.045 12.943 0.000
## relation_w =~
## rel_1 (r1) 0.424 0.042 10.117 0.000
## rel_2 (r2) 0.499 0.041 12.199 0.000
## rel_3 (r3) 0.548 0.035 15.777 0.000
## rel_4 (r4) 0.433 0.037 11.684 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## transfer_w ~~
## selektion_w -0.252 0.118 -2.133 0.033
## enrichment_w -0.137 0.132 -1.033 0.301
## relation_w -0.041 0.129 -0.319 0.750
## selektion_w ~~
## enrichment_w -0.018 0.160 -0.113 0.910
## relation_w -0.001 0.158 -0.006 0.995
## enrichment_w ~~
## relation_w 0.529 0.129 4.095 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .tfe_1 0.686 0.087 7.849 0.000
## .tfe_2 0.716 0.086 8.364 0.000
## .tfe_3 0.665 0.085 7.863 0.000
## .tfe_5 0.346 0.052 6.715 0.000
## .sel_1 0.609 0.078 7.784 0.000
## .sel_3 0.653 0.084 7.733 0.000
## .sel_4 0.579 0.086 6.703 0.000
## .sel_5 0.716 0.091 7.854 0.000
## .enr_1 0.843 0.105 8.018 0.000
## .enr_2 0.895 0.087 10.230 0.000
## .enr_3 0.778 0.098 7.952 0.000
## .enr_4 0.683 0.090 7.572 0.000
## .rel_1 0.635 0.075 8.442 0.000
## .rel_2 0.578 0.074 7.849 0.000
## .rel_3 0.377 0.048 7.816 0.000
## .rel_4 0.587 0.072 8.198 0.000
## transfer_w 1.000
## selektion_w 1.000
## enrichment_w 1.000
## relation_w 1.000
##
##
## Level 2 [id]:
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## transfer_b =~
## tfe_1 (t1) 0.501 0.049 10.275 0.000
## tfe_2 (t2) 0.643 0.049 13.107 0.000
## tfe_3 (t3) 0.542 0.054 10.088 0.000
## tfe_5 (t5) 0.477 0.044 10.831 0.000
## selektion_b =~
## sel_1 (s1) 0.544 0.044 12.411 0.000
## sel_3 (s3) 0.571 0.043 13.323 0.000
## sel_4 (s4) 0.669 0.044 15.076 0.000
## sel_5 (s5) 0.586 0.049 11.938 0.000
## enrichment_b =~
## enr_1 (e1) 0.575 0.046 12.403 0.000
## enr_2 (e2) 0.621 0.046 13.505 0.000
## enr_3 (e3) 0.580 0.048 12.043 0.000
## enr_4 (e4) 0.581 0.045 12.943 0.000
## relation_b =~
## rel_1 (r1) 0.424 0.042 10.117 0.000
## rel_2 (r2) 0.499 0.041 12.199 0.000
## rel_3 (r3) 0.548 0.035 15.777 0.000
## rel_4 (r4) 0.433 0.037 11.684 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .sel_1 ~~
## .sel_5 0.132 0.055 2.407 0.016
## transfer_b ~~
## selektion_b 0.355 0.140 2.543 0.011
## enrichment_b 0.676 0.132 5.122 0.000
## relation_b 0.399 0.140 2.852 0.004
## selektion_b ~~
## enrichment_b -0.151 0.140 -1.079 0.280
## relation_b -0.133 0.139 -0.957 0.339
## enrichment_b ~~
## relation_b 0.418 0.118 3.551 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## .tfe_1 2.675 0.071 37.871 0.000
## .tfe_2 2.705 0.072 37.662 0.000
## .tfe_3 2.410 0.081 29.633 0.000
## .tfe_5 2.059 0.067 30.647 0.000
## .sel_1 3.840 0.068 56.728 0.000
## .sel_3 3.894 0.068 57.022 0.000
## .sel_4 3.772 0.072 52.600 0.000
## .sel_5 3.435 0.075 45.721 0.000
## .enr_1 3.549 0.073 48.946 0.000
## .enr_2 3.615 0.074 49.100 0.000
## .enr_3 3.849 0.075 51.599 0.000
## .enr_4 3.689 0.071 51.689 0.000
## .rel_1 4.444 0.063 70.641 0.000
## .rel_2 4.614 0.064 72.058 0.000
## .rel_3 4.559 0.058 78.570 0.000
## .rel_4 4.550 0.057 79.878 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .tfe_2 0.000
## .enr_2 0.000
## .rel_3 0.000
## .tfe_1 0.230 0.086 2.678 0.007
## .tfe_3 0.492 0.111 4.415 0.000
## .tfe_5 0.352 0.070 5.034 0.000
## .sel_1 0.122 0.073 1.670 0.095
## .sel_3 0.068 0.069 0.987 0.324
## .sel_4 0.017 0.071 0.244 0.807
## .sel_5 0.200 0.090 2.231 0.026
## .enr_1 0.079 0.085 0.924 0.355
## .enr_3 0.164 0.087 1.881 0.060
## .enr_4 0.119 0.077 1.545 0.122
## .rel_1 0.164 0.070 2.347 0.019
## .rel_2 0.116 0.064 1.817 0.069
## .rel_4 0.039 0.058 0.671 0.502
## transfer_b 1.000
## selektion_b 1.000
## enrichment_b 1.000
## relation_b 1.000Standardized Solution
standardizedSolution(fit_f4.2)## lhs op rhs label est.std se z pvalue ci.lower
## 1 transfer_w =~ tfe_1 t1 0.517 0.048 10.779 0.000 0.423
## 2 transfer_w =~ tfe_2 t2 0.605 0.045 13.499 0.000 0.518
## 3 transfer_w =~ tfe_3 t3 0.554 0.048 11.449 0.000 0.459
## 4 transfer_w =~ tfe_5 t5 0.629 0.052 12.037 0.000 0.527
## 5 selektion_w =~ sel_1 s1 0.572 0.042 13.697 0.000 0.490
## 6 selektion_w =~ sel_3 s3 0.577 0.042 13.814 0.000 0.495
## 7 selektion_w =~ sel_4 s4 0.660 0.041 15.915 0.000 0.579
## 8 selektion_w =~ sel_5 s5 0.569 0.042 13.402 0.000 0.486
## 9 enrichment_w =~ enr_1 e1 0.531 0.042 12.782 0.000 0.450
## 10 enrichment_w =~ enr_2 e2 0.549 0.038 14.263 0.000 0.474
## 11 enrichment_w =~ enr_3 e3 0.549 0.042 13.033 0.000 0.467
## 12 enrichment_w =~ enr_4 e4 0.575 0.043 13.495 0.000 0.492
## 13 relation_w =~ rel_1 r1 0.469 0.043 10.848 0.000 0.385
## 14 relation_w =~ rel_2 r2 0.548 0.043 12.619 0.000 0.463
## 15 relation_w =~ rel_3 r3 0.666 0.040 16.841 0.000 0.589
## 16 relation_w =~ rel_4 r4 0.492 0.041 12.127 0.000 0.412
## 17 tfe_1 ~~ tfe_1 0.733 0.050 14.764 0.000 0.635
## 18 tfe_2 ~~ tfe_2 0.633 0.054 11.666 0.000 0.527
## 19 tfe_3 ~~ tfe_3 0.693 0.054 12.939 0.000 0.588
## 20 tfe_5 ~~ tfe_5 0.604 0.066 9.172 0.000 0.475
## 21 sel_1 ~~ sel_1 0.673 0.048 14.075 0.000 0.579
## 22 sel_3 ~~ sel_3 0.667 0.048 13.827 0.000 0.572
## 23 sel_4 ~~ sel_4 0.564 0.055 10.299 0.000 0.457
## 24 sel_5 ~~ sel_5 0.676 0.048 13.970 0.000 0.581
## 25 enr_1 ~~ enr_1 0.718 0.044 16.275 0.000 0.632
## 26 enr_2 ~~ enr_2 0.699 0.042 16.532 0.000 0.616
## 27 enr_3 ~~ enr_3 0.698 0.046 15.089 0.000 0.608
## 28 enr_4 ~~ enr_4 0.669 0.049 13.642 0.000 0.573
## 29 rel_1 ~~ rel_1 0.780 0.041 19.193 0.000 0.700
## 30 rel_2 ~~ rel_2 0.699 0.048 14.676 0.000 0.606
## 31 rel_3 ~~ rel_3 0.556 0.053 10.547 0.000 0.453
## 32 rel_4 ~~ rel_4 0.758 0.040 19.034 0.000 0.680
## 33 transfer_w ~~ transfer_w 1.000 0.000 NA NA 1.000
## 34 selektion_w ~~ selektion_w 1.000 0.000 NA NA 1.000
## 35 enrichment_w ~~ enrichment_w 1.000 0.000 NA NA 1.000
## 36 relation_w ~~ relation_w 1.000 0.000 NA NA 1.000
## 37 transfer_w ~~ selektion_w -0.252 0.118 -2.133 0.033 -0.484
## 38 transfer_w ~~ enrichment_w -0.137 0.132 -1.033 0.301 -0.396
## 39 transfer_w ~~ relation_w -0.041 0.129 -0.319 0.750 -0.295
## 40 selektion_w ~~ enrichment_w -0.018 0.160 -0.113 0.910 -0.333
## 41 selektion_w ~~ relation_w -0.001 0.158 -0.006 0.995 -0.310
## 42 enrichment_w ~~ relation_w 0.529 0.129 4.095 0.000 0.276
## 43 tfe_1 ~1 0.000 0.000 NA NA 0.000
## 44 tfe_2 ~1 0.000 0.000 NA NA 0.000
## 45 tfe_3 ~1 0.000 0.000 NA NA 0.000
## 46 tfe_5 ~1 0.000 0.000 NA NA 0.000
## 47 sel_1 ~1 0.000 0.000 NA NA 0.000
## 48 sel_3 ~1 0.000 0.000 NA NA 0.000
## 49 sel_4 ~1 0.000 0.000 NA NA 0.000
## 50 sel_5 ~1 0.000 0.000 NA NA 0.000
## 51 enr_1 ~1 0.000 0.000 NA NA 0.000
## 52 enr_2 ~1 0.000 0.000 NA NA 0.000
## 53 enr_3 ~1 0.000 0.000 NA NA 0.000
## 54 enr_4 ~1 0.000 0.000 NA NA 0.000
## 55 rel_1 ~1 0.000 0.000 NA NA 0.000
## 56 rel_2 ~1 0.000 0.000 NA NA 0.000
## 57 rel_3 ~1 0.000 0.000 NA NA 0.000
## 58 rel_4 ~1 0.000 0.000 NA NA 0.000
## 59 transfer_w ~1 0.000 0.000 NA NA 0.000
## 60 selektion_w ~1 0.000 0.000 NA NA 0.000
## 61 enrichment_w ~1 0.000 0.000 NA NA 0.000
## 62 relation_w ~1 0.000 0.000 NA NA 0.000
## 63 transfer_b =~ tfe_1 t1 0.722 0.077 9.425 0.000 0.572
## 64 transfer_b =~ tfe_2 t2 1.000 0.000 NA NA 1.000
## 65 transfer_b =~ tfe_3 t3 0.612 0.064 9.570 0.000 0.486
## 66 transfer_b =~ tfe_5 t5 0.626 0.055 11.352 0.000 0.518
## 67 selektion_b =~ sel_1 s1 0.842 0.081 10.423 0.000 0.684
## 68 selektion_b =~ sel_3 s3 0.909 0.082 11.145 0.000 0.749
## 69 selektion_b =~ sel_4 s4 0.981 0.076 12.984 0.000 0.833
## 70 selektion_b =~ sel_5 s5 0.795 0.076 10.434 0.000 0.645
## 71 enrichment_b =~ enr_1 e1 0.899 0.096 9.377 0.000 0.711
## 72 enrichment_b =~ enr_2 e2 1.000 0.000 NA NA 1.000
## 73 enrichment_b =~ enr_3 e3 0.820 0.079 10.388 0.000 0.665
## 74 enrichment_b =~ enr_4 e4 0.860 0.076 11.259 0.000 0.710
## 75 relation_b =~ rel_1 r1 0.723 0.087 8.331 0.000 0.553
## 76 relation_b =~ rel_2 r2 0.825 0.077 10.725 0.000 0.675
## 77 relation_b =~ rel_3 r3 1.000 0.000 NA NA 1.000
## 78 relation_b =~ rel_4 r4 0.910 0.119 7.632 0.000 0.676
## 79 tfe_2 ~~ tfe_2 0.000 0.000 NA NA 0.000
## 80 sel_1 ~~ sel_5 0.847 0.295 2.874 0.004 0.269
## 81 enr_2 ~~ enr_2 0.000 0.000 NA NA 0.000
## 82 rel_3 ~~ rel_3 0.000 0.000 NA NA 0.000
## 83 tfe_1 ~~ tfe_1 0.479 0.111 4.329 0.000 0.262
## 84 tfe_3 ~~ tfe_3 0.626 0.078 8.006 0.000 0.473
## 85 tfe_5 ~~ tfe_5 0.608 0.069 8.804 0.000 0.473
## 86 sel_1 ~~ sel_1 0.291 0.136 2.141 0.032 0.025
## 87 sel_3 ~~ sel_3 0.173 0.148 1.167 0.243 -0.118
## 88 sel_4 ~~ sel_4 0.037 0.148 0.252 0.801 -0.253
## 89 sel_5 ~~ sel_5 0.368 0.121 3.043 0.002 0.131
## 90 enr_1 ~~ enr_1 0.192 0.172 1.112 0.266 -0.146
## 91 enr_3 ~~ enr_3 0.328 0.129 2.533 0.011 0.074
## 92 enr_4 ~~ enr_4 0.261 0.131 1.988 0.047 0.004
## 93 rel_1 ~~ rel_1 0.478 0.125 3.813 0.000 0.232
## 94 rel_2 ~~ rel_2 0.319 0.127 2.509 0.012 0.070
## 95 rel_4 ~~ rel_4 0.172 0.217 0.791 0.429 -0.254
## 96 transfer_b ~~ transfer_b 1.000 0.000 NA NA 1.000
## 97 selektion_b ~~ selektion_b 1.000 0.000 NA NA 1.000
## 98 enrichment_b ~~ enrichment_b 1.000 0.000 NA NA 1.000
## 99 relation_b ~~ relation_b 1.000 0.000 NA NA 1.000
## 100 transfer_b ~~ selektion_b 0.355 0.140 2.543 0.011 0.081
## 101 transfer_b ~~ enrichment_b 0.676 0.132 5.122 0.000 0.417
## 102 transfer_b ~~ relation_b 0.399 0.140 2.852 0.004 0.125
## 103 selektion_b ~~ enrichment_b -0.151 0.140 -1.079 0.280 -0.426
## 104 selektion_b ~~ relation_b -0.133 0.139 -0.957 0.339 -0.406
## 105 enrichment_b ~~ relation_b 0.418 0.118 3.551 0.000 0.187
## 106 tfe_1 ~1 3.858 0.387 9.956 0.000 3.098
## 107 tfe_2 ~1 4.203 0.340 12.380 0.000 3.538
## 108 tfe_3 ~1 2.718 0.216 12.576 0.000 2.294
## 109 tfe_5 ~1 2.705 0.199 13.600 0.000 2.315
## 110 sel_1 ~1 5.938 0.552 10.763 0.000 4.857
## 111 sel_3 ~1 6.197 0.649 9.548 0.000 4.925
## 112 sel_4 ~1 5.535 0.511 10.834 0.000 4.534
## 113 sel_5 ~1 4.657 0.408 11.401 0.000 3.857
## 114 enr_1 ~1 5.546 0.653 8.496 0.000 4.267
## 115 enr_2 ~1 5.819 0.447 13.021 0.000 4.943
## 116 enr_3 ~1 5.444 0.523 10.415 0.000 4.420
## 117 enr_4 ~1 5.456 0.539 10.114 0.000 4.399
## 118 rel_1 ~1 7.581 0.803 9.439 0.000 6.007
## 119 rel_2 ~1 7.638 0.777 9.828 0.000 6.115
## 120 rel_3 ~1 8.313 0.537 15.466 0.000 7.259
## 121 rel_4 ~1 9.574 1.313 7.289 0.000 6.999
## 122 transfer_b ~1 0.000 0.000 NA NA 0.000
## 123 selektion_b ~1 0.000 0.000 NA NA 0.000
## 124 enrichment_b ~1 0.000 0.000 NA NA 0.000
## 125 relation_b ~1 0.000 0.000 NA NA 0.000
## ci.upper
## 1 0.611
## 2 0.693
## 3 0.649
## 4 0.732
## 5 0.654
## 6 0.659
## 7 0.742
## 8 0.653
## 9 0.612
## 10 0.624
## 11 0.632
## 12 0.659
## 13 0.554
## 14 0.633
## 15 0.744
## 16 0.571
## 17 0.830
## 18 0.740
## 19 0.798
## 20 0.733
## 21 0.766
## 22 0.761
## 23 0.671
## 24 0.771
## 25 0.805
## 26 0.781
## 27 0.789
## 28 0.765
## 29 0.859
## 30 0.793
## 31 0.659
## 32 0.836
## 33 1.000
## 34 1.000
## 35 1.000
## 36 1.000
## 37 -0.020
## 38 0.122
## 39 0.212
## 40 0.296
## 41 0.308
## 42 0.782
## 43 0.000
## 44 0.000
## 45 0.000
## 46 0.000
## 47 0.000
## 48 0.000
## 49 0.000
## 50 0.000
## 51 0.000
## 52 0.000
## 53 0.000
## 54 0.000
## 55 0.000
## 56 0.000
## 57 0.000
## 58 0.000
## 59 0.000
## 60 0.000
## 61 0.000
## 62 0.000
## 63 0.872
## 64 1.000
## 65 0.737
## 66 0.734
## 67 1.000
## 68 1.069
## 69 1.129
## 70 0.944
## 71 1.087
## 72 1.000
## 73 0.975
## 74 1.009
## 75 0.893
## 76 0.976
## 77 1.000
## 78 1.144
## 79 0.000
## 80 1.425
## 81 0.000
## 82 0.000
## 83 0.696
## 84 0.779
## 85 0.743
## 86 0.558
## 87 0.464
## 88 0.328
## 89 0.606
## 90 0.530
## 91 0.581
## 92 0.518
## 93 0.724
## 94 0.568
## 95 0.597
## 96 1.000
## 97 1.000
## 98 1.000
## 99 1.000
## 100 0.629
## 101 0.934
## 102 0.674
## 103 0.123
## 104 0.140
## 105 0.649
## 106 4.617
## 107 4.869
## 108 3.142
## 109 3.094
## 110 7.019
## 111 7.469
## 112 6.536
## 113 5.458
## 114 6.826
## 115 6.695
## 116 6.469
## 117 6.513
## 118 9.155
## 119 9.161
## 120 9.366
## 121 12.148
## 122 0.000
## 123 0.000
## 124 0.000
## 125 0.000
Reliability
## McDonalds Omega for these factors ##
# Transfer
rel_data4.1.0 <- valid_cfa %>%
dplyr::filter(treat == 0) %>%
dplyr::select("tfe_1" , "tfe_2" , "tfe_3" , "tfe_5")
rel_tr_ctml <- MBESS::ci.reliability(rel_data4.1.0)$est
rel_tr_ctml_l <- MBESS::ci.reliability(rel_data4.1.0)$ci.lower
rel_tr_ctml_u <- MBESS::ci.reliability(rel_data4.1.0)$ci.upper
rel_data4.1.1 <- valid_cfa %>%
dplyr::filter(treat == 1) %>%
dplyr::select("tfe_1" , "tfe_2" , "tfe_3" , "tfe_5")
rel_tr_stp <- MBESS::ci.reliability(rel_data4.1.1)$est
rel_tr_stp_l <- MBESS::ci.reliability(rel_data4.1.1)$ci.lower
rel_tr_stp_u <- MBESS::ci.reliability(rel_data4.1.1)$ci.upper
# Selektion
rel_data4.2.0 <- valid_cfa %>%
dplyr::filter(treat == 0) %>%
dplyr::select("sel_1" , "sel_3" , "sel_4" , "sel_5")
rel_se_ctml <- MBESS::ci.reliability(rel_data4.2.0)$est
rel_se_ctml_l <- MBESS::ci.reliability(rel_data4.2.0)$ci.lower
rel_se_ctml_u <- MBESS::ci.reliability(rel_data4.2.0)$ci.upper
rel_data4.2.1 <- valid_cfa %>%
dplyr::filter(treat == 1) %>%
dplyr::select("sel_1" , "sel_3" , "sel_4" , "sel_5")
rel_se_stp <- MBESS::ci.reliability(rel_data4.2.1)$est
rel_se_stp_l <- MBESS::ci.reliability(rel_data4.2.1)$ci.lower
rel_se_stp_u <- MBESS::ci.reliability(rel_data4.2.1)$ci.upper
# Enrichment
rel_data4.3.0 <- valid_cfa %>%
dplyr::filter(treat == 0) %>%
dplyr::select("enr_1" , "enr_2" , "enr_3" , "enr_4")
rel_en_ctml <- MBESS::ci.reliability(rel_data4.3.0)$est
rel_en_ctml_l <- MBESS::ci.reliability(rel_data4.3.0)$ci.lower
rel_en_ctml_u <- MBESS::ci.reliability(rel_data4.3.0)$ci.upper
rel_data4.3.1 <- valid_cfa %>%
dplyr::filter(treat == 1) %>%
dplyr::select("enr_1" , "enr_2" , "enr_3" , "enr_4")
rel_en_stp <- MBESS::ci.reliability(rel_data4.3.1)$est
rel_en_stp_l <- MBESS::ci.reliability(rel_data4.3.1)$ci.lower
rel_en_stp_u <- MBESS::ci.reliability(rel_data4.3.1)$ci.upper
# Relationierung
rel_data4.4.0 <- valid_cfa %>%
dplyr::filter(treat == 0) %>%
dplyr::select("rel_1" , "rel_2" , "rel_3" , "rel_4")
rel_re_ctml <- MBESS::ci.reliability(rel_data4.4.0)$est
rel_re_ctml_l <- MBESS::ci.reliability(rel_data4.4.0)$ci.lower
rel_re_ctml_u <- MBESS::ci.reliability(rel_data4.4.0)$ci.upper
rel_data4.4.1 <- valid_cfa %>%
dplyr::filter(treat == 1) %>%
dplyr::select("rel_1" , "rel_2" , "rel_3" , "rel_4")
rel_re_stp <- MBESS::ci.reliability(rel_data4.4.1)$est
rel_re_stp_l <- MBESS::ci.reliability(rel_data4.4.1)$ci.lower
rel_re_stp_u <- MBESS::ci.reliability(rel_data4.4.1)$ci.upper- Transfer
- McDonalds \(\sf{\omega_{CTML}}\)= 0.621, 95%CI[NA, NA]
- McDonalds \(\sf{\omega_{STP}}\)= 0.818, 95%CI[NA, NA]
- Selektion
- McDonalds \(\sf{\omega_{CTML}}\)= 0.797, 95%CI[NA, NA]
- McDonalds \(\sf{\omega_{STP}}\)= 0.834, 95%CI[NA, NA]
- Enrichment
- McDonalds \(\sf{\omega_{CTML}}\)= 0.756, 95%CI[NA, NA]
- McDonalds \(\sf{\omega_{STP}}\)= 0.783, 95%CI[NA, NA]
- Relationierung
- McDonalds \(\sf{\omega_{CTML}}\)= 0.784, 95%CI[NA, NA]
- McDonalds \(\sf{\omega_{STP}}\)= 0.731, 95%CI[NA, NA]
Check 4 indicators with Study 1 data
Let’s see, if the data from item selection wave (exploratory, first data collection wave) fits the model with 4 indicators each factor.
# unfortunately I cannot share the data via this file
# however you can access the data on [link pending]
itemsel <- read_csv2(file = "https://raw.githubusercontent.com/j-5chneider/uzvvtp-las/master/data/pilot1.csv")
# rename variables to fit latest labels
itemsel <- itemsel %>%
mutate(tfe_1 = tfe_tfe_02,
tfe_2 = tfe_tfe_03,
tfe_3 = tfe_tfe_08,
tfe_4 = tfe_did_01,
tfe_5 = tfe_did_05,
sel_1 = tfo_sel_01,
sel_2 = tfo_sel_02,
sel_3 = tfo_sel_04,
sel_4 = tfo_sel_08,
sel_5 = tfo_sel_09,
enr_1 = tfo_enr_01,
enr_2 = tfo_enr_02,
enr_3 = tfo_enr_03,
enr_4 = tfo_enr_04,
enr_5 = tfo_enr_05,
rel_1 = rel_rel_02,
rel_2 = rel_rel_03,
rel_3 = rel_rel_08,
rel_4 = rel_rel_09)
f4.itemsel <- ' transfer =~ tfe_1 + tfe_2 + tfe_3 + tfe_5
selektion =~ sel_1 + sel_3 + sel_4 + sel_5
enrichment =~ enr_1 + enr_2 + enr_3 + enr_4
relation =~ rel_1 + rel_2 + rel_3 + rel_4
# tfe_2 ~~ 0*tfe_2 # Heywood Cases
# sel_5 ~~ sel_1
# enr_2 ~~ 0*enr_2
# rel_3 ~~ 0*rel_3
'
# without restrictions
fit_itemsel <- sem(f4.itemsel,
data = itemsel,
# cluster = "id", # there is no multilevel structure in wave 1
std.lv=TRUE
)
lavaanPlot(model = fit_itemsel,
node_options = list(shape = "box", fontname = "Helvetica"),
edge_options = list(color = "grey"),
coefs = TRUE)summary(fit_itemsel, fit.measures = TRUE)## lavaan 0.6.17 ended normally after 18 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 38
##
## Used Total
## Number of observations 203 399
##
## Model Test User Model:
##
## Test statistic 162.236
## Degrees of freedom 98
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 1263.053
## Degrees of freedom 120
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.944
## Tucker-Lewis Index (TLI) 0.931
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -4818.189
## Loglikelihood unrestricted model (H1) -4737.072
##
## Akaike (AIC) 9712.379
## Bayesian (BIC) 9838.280
## Sample-size adjusted Bayesian (SABIC) 9717.887
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.057
## 90 Percent confidence interval - lower 0.041
## 90 Percent confidence interval - upper 0.072
## P-value H_0: RMSEA <= 0.050 0.227
## P-value H_0: RMSEA >= 0.080 0.005
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.058
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## transfer =~
## tfe_1 0.824 0.080 10.367 0.000
## tfe_2 0.807 0.076 10.587 0.000
## tfe_3 0.792 0.082 9.617 0.000
## tfe_5 0.706 0.081 8.730 0.000
## selektion =~
## sel_1 0.759 0.078 9.671 0.000
## sel_3 0.955 0.084 11.341 0.000
## sel_4 0.955 0.091 10.536 0.000
## sel_5 0.868 0.101 8.590 0.000
## enrichment =~
## enr_1 1.056 0.096 11.020 0.000
## enr_2 0.900 0.088 10.206 0.000
## enr_3 1.087 0.092 11.841 0.000
## enr_4 0.811 0.103 7.911 0.000
## relation =~
## rel_1 0.768 0.078 9.893 0.000
## rel_2 1.011 0.078 13.013 0.000
## rel_3 0.986 0.081 12.111 0.000
## rel_4 0.988 0.078 12.723 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## transfer ~~
## selektion 0.221 0.086 2.588 0.010
## enrichment 0.489 0.073 6.717 0.000
## relation 0.317 0.079 4.003 0.000
## selektion ~~
## enrichment 0.300 0.082 3.663 0.000
## relation 0.363 0.076 4.750 0.000
## enrichment ~~
## relation 0.697 0.053 13.241 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .tfe_1 0.650 0.090 7.228 0.000
## .tfe_2 0.579 0.083 7.015 0.000
## .tfe_3 0.762 0.097 7.848 0.000
## .tfe_5 0.799 0.095 8.399 0.000
## .sel_1 0.701 0.088 7.941 0.000
## .sel_3 0.641 0.101 6.354 0.000
## .sel_4 0.843 0.117 7.226 0.000
## .sel_5 1.279 0.149 8.565 0.000
## .enr_1 0.987 0.129 7.660 0.000
## .enr_2 0.911 0.111 8.185 0.000
## .enr_3 0.815 0.117 6.969 0.000
## .enr_4 1.455 0.159 9.129 0.000
## .rel_1 0.778 0.088 8.857 0.000
## .rel_2 0.558 0.079 7.066 0.000
## .rel_3 0.692 0.089 7.781 0.000
## .rel_4 0.581 0.079 7.319 0.000
## transfer 1.000
## selektion 1.000
## enrichment 1.000
## relation 1.000
Results FF3: Experimental Study
We realized two different stimuli preceding a run through the
instrument each. The stimuli are descriptions of two theories from
education relevant to classroom practice: Cognitive Theory of Multimedia
Learning (CTML) vs. Strukturtheoretische Professionstheorie (SPT). The
conditions are varied within person and randomized in their order
between person. The conditions were designed to have an effect on the
subscale “Transfer”: The short description in the CTML-condition was
written to be especially suitable to beliefs of “Transfer”. In this
subscale we thus expect ratings to be higher in the CTML-condition
(vs. SPT-condition).
For the other subscales results will be computed exploratory.
The stimuli (German)
- CTML group: “Der „Spatial Contiguity Effect“ aus der Theorie des multimedialen Lernens, trifft Aussagen über die Kombination von Text und Bild in Lernmaterialien, beispielsweise bei der Gestaltung von Arbeitsblättern. Hierfür tragen Schroeder & Cenkci (2018) Befunde zusammen, ob Bilder und erklärender Text separat (getrennt nebeneinander) oder integriert (einzelne Textstücke direkt an relevanter Stelle im Bild) den Lernerfolg besser fördern. Das Ergebnis zeigt, dass integrierte Darstellungen einen positiven Effekt auf die Lernleistung besitzen. Dies gilt für computerbasierte Darstellungen, aber besonders für Darstellungen auf Arbeitsblättern. Wurden mobile Endgeräte verwendet, so konnte kein Unterschied in der Lernleistung zwischen den beiden Darstellungsformen festgestellt werden.”
- SPT group: “Im strukturtheoretischen Ansatz zur Professionalität im Lehrberuf adressiert Helsper (2004) das „Arbeitsbündnis zwischen Lehrperson und Schüler/-in“. Der Lehrerberuf ist aus dieser Perspektive durch Aufgaben und Anforderungen geprägt, die in sich widersprüchlich sind, also per se nicht aufgelöst werden können. So wird an Lehrpersonen beispielsweise die Anforderung gerichtet, sich als Person auf Lernende einzulassen und Nähe aufzubauen, andererseits müssen sie jedoch ihrer Rolle als Lehrperson gerecht werden, die z.B. bei der Notengebung eine gewisse Distanz gebietet (Nähe-Distanz-Antinomie). Beide Anforderungen vollauf zu realisieren ist nicht möglich und so scheint es für Lehrpersonen unmöglich „richtig“ zu handeln. Professionelles Handeln von Lehrpersonen äußert sich folglich darin, diese Widersprüche auszuhalten und sie sachgerecht zu bewältigen.”
Frequentist Data analysis
valid_exp <- valid_cfa %>%
dplyr::filter(tc == 1) # only include participants who
# answered the treatment check correctly
# Ausschluss von enr_5, tfe_4, sel_2 aufgrund geringer Ladung
exp.model <- 'level: 1
transfer_w =~ tfe_1 + tfe_2 + tfe_3 + tfe_5
selektion_w =~ sel_1 + sel_3 + sel_4 + sel_5
enrichment_w =~ enr_1 + enr_2 + enr_3 + enr_4
relation_w =~ rel_1 + rel_2 + rel_3 + rel_4
transfer_w ~ treat
selektion_w ~ treat
enrichment_w ~ treat
relation_w ~ treat
level: 2
transfer_b =~ tfe_1 + tfe_2 + tfe_3 + tfe_5
selektion_b =~ sel_1 + sel_3 + sel_4 + sel_5
enrichment_b =~ enr_1 + enr_2 + enr_3 + enr_4
relation_b =~ rel_1 + rel_2 + rel_3 + rel_4
tfe_2 ~~ 0*tfe_2
sel_5 ~~ sel_1
sel_5 ~~ 0*sel_5 # new in this model: Haywood Case
enr_2 ~~ 0*enr_2
rel_3 ~~ 0*rel_3
'
fit_exp <- sem(exp.model,
data = valid_exp,
cluster = "id"
)
lavaanPlot(model = fit_exp,
node_options = list(shape = "box", fontname = "Helvetica"),
edge_options = list(color = "grey"),
coefs = TRUE)# options(max.print=2000)
standardizedSolution(fit_exp)## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 transfer_w =~ tfe_1 0.611 0.063 9.656 0.000 0.487 0.735
## 2 transfer_w =~ tfe_2 0.829 0.068 12.107 0.000 0.695 0.964
## 3 transfer_w =~ tfe_3 0.405 0.083 4.865 0.000 0.242 0.568
## 4 transfer_w =~ tfe_5 0.529 0.073 7.205 0.000 0.385 0.672
## 5 selektion_w =~ sel_1 0.421 0.089 4.705 0.000 0.246 0.596
## 6 selektion_w =~ sel_3 0.654 0.087 7.529 0.000 0.484 0.825
## 7 selektion_w =~ sel_4 0.645 0.083 7.786 0.000 0.482 0.807
## 8 selektion_w =~ sel_5 0.440 0.081 5.456 0.000 0.282 0.598
## 9 enrichment_w =~ enr_1 0.464 0.105 4.418 0.000 0.258 0.670
## 10 enrichment_w =~ enr_2 0.442 0.089 4.941 0.000 0.267 0.618
## 11 enrichment_w =~ enr_3 0.371 0.117 3.181 0.001 0.142 0.599
## 12 enrichment_w =~ enr_4 0.610 0.102 5.975 0.000 0.410 0.810
## 13 relation_w =~ rel_1 0.088 0.113 0.781 0.435 -0.133 0.308
## 14 relation_w =~ rel_2 0.475 0.102 4.666 0.000 0.275 0.674
## 15 relation_w =~ rel_3 0.560 0.097 5.795 0.000 0.371 0.750
## 16 relation_w =~ rel_4 0.425 0.101 4.217 0.000 0.227 0.622
## 17 transfer_w ~ treat 0.038 0.066 0.572 0.568 -0.092 0.167
## 18 selektion_w ~ treat -0.121 0.070 -1.722 0.085 -0.259 0.017
## 19 enrichment_w ~ treat -0.030 0.080 -0.375 0.708 -0.187 0.127
## 20 relation_w ~ treat -0.257 0.088 -2.918 0.004 -0.430 -0.084
## 21 tfe_1 ~~ tfe_1 0.627 0.077 8.118 0.000 0.476 0.778
## 22 tfe_2 ~~ tfe_2 0.312 0.114 2.749 0.006 0.090 0.535
## 23 tfe_3 ~~ tfe_3 0.836 0.067 12.422 0.000 0.704 0.968
## 24 tfe_5 ~~ tfe_5 0.721 0.078 9.293 0.000 0.569 0.873
## 25 sel_1 ~~ sel_1 0.823 0.075 10.922 0.000 0.675 0.970
## 26 sel_3 ~~ sel_3 0.572 0.114 5.027 0.000 0.349 0.795
## 27 sel_4 ~~ sel_4 0.585 0.107 5.477 0.000 0.375 0.794
## 28 sel_5 ~~ sel_5 0.807 0.071 11.382 0.000 0.668 0.946
## 29 enr_1 ~~ enr_1 0.785 0.097 8.050 0.000 0.594 0.976
## 30 enr_2 ~~ enr_2 0.805 0.079 10.167 0.000 0.649 0.960
## 31 enr_3 ~~ enr_3 0.862 0.086 9.976 0.000 0.693 1.032
## 32 enr_4 ~~ enr_4 0.628 0.125 5.044 0.000 0.384 0.872
## 33 rel_1 ~~ rel_1 0.992 0.020 50.190 0.000 0.954 1.031
## 34 rel_2 ~~ rel_2 0.775 0.097 8.017 0.000 0.585 0.964
## 35 rel_3 ~~ rel_3 0.686 0.108 6.338 0.000 0.474 0.899
## 36 rel_4 ~~ rel_4 0.820 0.086 9.585 0.000 0.652 0.987
## 37 transfer_w ~~ transfer_w 0.999 0.005 199.623 0.000 0.989 1.008
## 38 selektion_w ~~ selektion_w 0.985 0.017 57.794 0.000 0.952 1.019
## 39 enrichment_w ~~ enrichment_w 0.999 0.005 207.134 0.000 0.990 1.009
## 40 relation_w ~~ relation_w 0.934 0.045 20.576 0.000 0.845 1.023
## 41 transfer_w ~~ selektion_w -0.059 0.108 -0.551 0.582 -0.270 0.151
## 42 transfer_w ~~ enrichment_w 0.094 0.119 0.791 0.429 -0.139 0.328
## 43 transfer_w ~~ relation_w 0.107 0.122 0.879 0.380 -0.132 0.346
## 44 selektion_w ~~ enrichment_w -0.052 0.131 -0.399 0.690 -0.309 0.205
## 45 selektion_w ~~ relation_w 0.022 0.157 0.142 0.887 -0.286 0.330
## 46 enrichment_w ~~ relation_w 0.602 0.134 4.488 0.000 0.339 0.865
## 47 treat ~~ treat 1.000 0.000 NA NA 1.000 1.000
## 48 tfe_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 49 tfe_2 ~1 0.000 0.000 NA NA 0.000 0.000
## 50 tfe_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 51 tfe_5 ~1 0.000 0.000 NA NA 0.000 0.000
## 52 sel_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 53 sel_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 54 sel_4 ~1 0.000 0.000 NA NA 0.000 0.000
## 55 sel_5 ~1 0.000 0.000 NA NA 0.000 0.000
## 56 enr_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 57 enr_2 ~1 0.000 0.000 NA NA 0.000 0.000
## 58 enr_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 59 enr_4 ~1 0.000 0.000 NA NA 0.000 0.000
## 60 rel_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 61 rel_2 ~1 0.000 0.000 NA NA 0.000 0.000
## 62 rel_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 63 rel_4 ~1 0.000 0.000 NA NA 0.000 0.000
## 64 treat ~1 0.981 0.000 NA NA 0.981 0.981
## 65 transfer_w ~1 0.000 0.000 NA NA 0.000 0.000
## 66 selektion_w ~1 0.000 0.000 NA NA 0.000 0.000
## 67 enrichment_w ~1 0.000 0.000 NA NA 0.000 0.000
## 68 relation_w ~1 0.000 0.000 NA NA 0.000 0.000
## 69 transfer_b =~ tfe_1 0.560 0.160 3.500 0.000 0.246 0.874
## 70 transfer_b =~ tfe_2 1.000 0.000 NA NA 1.000 1.000
## 71 transfer_b =~ tfe_3 0.853 0.109 7.828 0.000 0.639 1.067
## 72 transfer_b =~ tfe_5 0.818 0.089 9.205 0.000 0.644 0.992
## 73 selektion_b =~ sel_1 1.067 0.083 12.831 0.000 0.904 1.230
## 74 selektion_b =~ sel_3 0.812 0.078 10.424 0.000 0.659 0.965
## 75 selektion_b =~ sel_4 0.906 0.059 15.369 0.000 0.791 1.022
## 76 selektion_b =~ sel_5 1.000 0.000 NA NA 1.000 1.000
## 77 enrichment_b =~ enr_1 0.892 0.070 12.827 0.000 0.756 1.028
## 78 enrichment_b =~ enr_2 1.000 0.000 NA NA 1.000 1.000
## 79 enrichment_b =~ enr_3 0.998 0.065 15.259 0.000 0.869 1.126
## 80 enrichment_b =~ enr_4 0.922 0.075 12.282 0.000 0.775 1.069
## 81 relation_b =~ rel_1 0.931 0.096 9.741 0.000 0.743 1.118
## 82 relation_b =~ rel_2 0.838 0.084 9.981 0.000 0.673 1.002
## 83 relation_b =~ rel_3 1.000 0.000 NA NA 1.000 1.000
## 84 relation_b =~ rel_4 0.901 0.077 11.760 0.000 0.751 1.051
## 85 tfe_2 ~~ tfe_2 0.000 0.000 NA NA 0.000 0.000
## 86 sel_1 ~~ sel_5 -Inf NaN NA NA NaN NaN
## 87 sel_5 ~~ sel_5 0.000 0.000 NA NA 0.000 0.000
## 88 enr_2 ~~ enr_2 0.000 0.000 NA NA 0.000 0.000
## 89 rel_3 ~~ rel_3 0.000 0.000 NA NA 0.000 0.000
## 90 tfe_1 ~~ tfe_1 0.686 0.179 3.829 0.000 0.335 1.038
## 91 tfe_3 ~~ tfe_3 0.272 0.186 1.465 0.143 -0.092 0.637
## 92 tfe_5 ~~ tfe_5 0.331 0.145 2.277 0.023 0.046 0.616
## 93 sel_1 ~~ sel_1 -0.139 0.178 -0.783 0.434 -0.487 0.209
## 94 sel_3 ~~ sel_3 0.341 0.126 2.695 0.007 0.093 0.589
## 95 sel_4 ~~ sel_4 0.179 0.107 1.674 0.094 -0.031 0.388
## 96 enr_1 ~~ enr_1 0.204 0.124 1.647 0.100 -0.039 0.447
## 97 enr_3 ~~ enr_3 0.005 0.130 0.038 0.970 -0.251 0.261
## 98 enr_4 ~~ enr_4 0.150 0.138 1.081 0.280 -0.122 0.421
## 99 rel_1 ~~ rel_1 0.134 0.178 0.754 0.451 -0.214 0.483
## 100 rel_2 ~~ rel_2 0.299 0.141 2.124 0.034 0.023 0.574
## 101 rel_4 ~~ rel_4 0.189 0.138 1.367 0.172 -0.082 0.459
## 102 transfer_b ~~ transfer_b 1.000 0.000 NA NA 1.000 1.000
## 103 selektion_b ~~ selektion_b 1.000 0.000 NA NA 1.000 1.000
## 104 enrichment_b ~~ enrichment_b 1.000 0.000 NA NA 1.000 1.000
## 105 relation_b ~~ relation_b 1.000 0.000 NA NA 1.000 1.000
## 106 transfer_b ~~ selektion_b 0.050 0.129 0.386 0.700 -0.203 0.302
## 107 transfer_b ~~ enrichment_b 0.457 0.125 3.661 0.000 0.212 0.701
## 108 transfer_b ~~ relation_b 0.160 0.128 1.257 0.209 -0.090 0.411
## 109 selektion_b ~~ enrichment_b -0.192 0.105 -1.828 0.068 -0.397 0.014
## 110 selektion_b ~~ relation_b -0.113 0.106 -1.064 0.287 -0.320 0.095
## 111 enrichment_b ~~ relation_b 0.506 0.086 5.881 0.000 0.337 0.675
## 112 tfe_1 ~1 4.340 0.712 6.095 0.000 2.945 5.736
## 113 tfe_2 ~1 6.334 1.796 3.527 0.000 2.814 9.853
## 114 tfe_3 ~1 2.500 0.245 10.208 0.000 2.020 2.980
## 115 tfe_5 ~1 2.877 0.300 9.588 0.000 2.289 3.465
## 116 sel_1 ~1 4.991 0.527 9.463 0.000 3.957 6.025
## 117 sel_3 ~1 5.642 0.709 7.954 0.000 4.252 7.032
## 118 sel_4 ~1 4.566 0.473 9.663 0.000 3.640 5.492
## 119 sel_5 ~1 3.804 0.365 10.434 0.000 3.090 4.519
## 120 enr_1 ~1 4.345 0.481 9.030 0.000 3.402 5.288
## 121 enr_2 ~1 4.432 0.488 9.081 0.000 3.476 5.389
## 122 enr_3 ~1 4.274 0.416 10.271 0.000 3.459 5.090
## 123 enr_4 ~1 5.135 0.644 7.979 0.000 3.873 6.396
## 124 rel_1 ~1 6.507 0.697 9.335 0.000 5.141 7.874
## 125 rel_2 ~1 7.101 0.837 8.488 0.000 5.461 8.740
## 126 rel_3 ~1 7.283 0.735 9.913 0.000 5.843 8.723
## 127 rel_4 ~1 7.237 0.809 8.943 0.000 5.651 8.824
## 128 transfer_b ~1 0.000 0.000 NA NA 0.000 0.000
## 129 selektion_b ~1 0.000 0.000 NA NA 0.000 0.000
## 130 enrichment_b ~1 0.000 0.000 NA NA 0.000 0.000
## 131 relation_b ~1 0.000 0.000 NA NA 0.000 0.000
Did the participants respond too similar between the two stimuli (failed to implement strong stimuli)? Computing ICCs:
lavInspect(fit_exp, "icc")## tfe_1 tfe_2 tfe_3 tfe_5 sel_1 sel_3 sel_4 sel_5 enr_1 enr_2 enr_3 enr_4 rel_1
## 0.335 0.197 0.483 0.474 0.449 0.384 0.492 0.502 0.432 0.435 0.503 0.385 0.437
## rel_2 rel_3 rel_4 treat
## 0.386 0.451 0.454 0.000
BF Data Analysis (with predicted values)
# wrangle data again without missings
miss <- valid_exp %>%
dplyr::select(-c(enr_5, tfe_4, sel_2)) %>%
dplyr::filter(!complete.cases(.)) %>%
dplyr::select(id) %>%
unique()
valid_exp_nona <- valid_exp %>%
dplyr::select(-c(enr_5, tfe_4, sel_2)) %>%
dplyr::filter(!(id %in% miss$id) & id != 114 & id != 142) # filter out cases with missings
# in addition:
# id 114 and 142 seem to
# have answered only on one
# stimuli completely
# compute model without missings
fit_exp_nona <- sem(exp.model,
data = valid_exp_nona,
cluster = "id"
)
# extract predicted values from lavaan model
pred_exp <- data.frame(lavPredict(fit_exp_nona,
method = "regression",
append.data = T,
level = 1))
# compute BF
ttestBF(x = pred_exp$transfer_w[pred_exp$treat == 1],
y = pred_exp$transfer_w[pred_exp$treat == 0],
paired = T,
nullInterval = c(-Inf, 0) # Expectation was a negative effect
)## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 -Inf<d<0 : 0.0312 ±0.13%
## [2] Alt., r=0.707 !(-Inf<d<0) : 1.26 ±0%
##
## Against denominator:
## Null, mu = 0
## ---
## Bayes factor type: BFoneSample, JZS
Results FF4: Convergent Validity
- We expect “Transfer” to have a moderate positive correlation with “umsetzung”
- We expect “Transfer” to have a negative correlation with “differenz”
- We expect “enrichment” to have a small positive correlation with “differenz”
- All other results will be computed exploratory
Reliability of Umsetzbarkeit and Unabhängigkeit
valid_fl <- valid_l %>%
dplyr::filter(str_sub(variable, 1, 5) == "flen_") %>%
spread(key = "variable", value = "value") %>%
dplyr::select(-treat, -semester)
valid_con <- left_join(valid_cfa, valid_fl, by = "id")Umsetzbarkeit
# Umsetzbarkeit
omega(valid_con |> dplyr::select(flen_UM1, flen_UM2, flen_UM3, flen_UM4), 1)## Omega
## Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip,
## digits = digits, title = title, sl = sl, labels = labels,
## plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option,
## covar = covar)
## Alpha: 0.68
## G.6: 0.63
## Omega Hierarchical: 0.69
## Omega H asymptotic: 1
## Omega Total 0.69
##
## Schmid Leiman Factor loadings greater than 0.2
## g F1* h2 u2 p2
## flen_UM1 0.50 0.25 0.75 1
## flen_UM2 0.39 0.15 0.85 1
## flen_UM3 0.69 0.47 0.53 1
## flen_UM4 0.79 0.63 0.37 1
##
## With Sums of squares of:
## g F1*
## 1.5 0.0
##
## general/max 2.71e+16 max/min = 1
## mean percent general = 1 with sd = 0 and cv of 0
## Explained Common Variance of the general factor = 1
##
## The degrees of freedom are 2 and the fit is 0
## The number of observations was 400 with Chi Square = 0.48 with prob < 0.79
## The root mean square of the residuals is 0.01
## The df corrected root mean square of the residuals is 0.01
## RMSEA index = 0 and the 10 % confidence intervals are 0 0.064
## BIC = -11.5
##
## Compare this with the adequacy of just a general factor and no group factors
## The degrees of freedom for just the general factor are 2 and the fit is 0
## The number of observations was 400 with Chi Square = 0.48 with prob < 0.79
## The root mean square of the residuals is 0.01
## The df corrected root mean square of the residuals is 0.01
##
## RMSEA index = 0 and the 10 % confidence intervals are 0 0.064
## BIC = -11.5
##
## Measures of factor score adequacy
## g F1*
## Correlation of scores with factors 0.87 0
## Multiple R square of scores with factors 0.76 0
## Minimum correlation of factor score estimates 0.51 -1
##
## Total, General and Subset omega for each subset
## g F1*
## Omega total for total scores and subscales 0.69 0.69
## Omega general for total scores and subscales 0.69 0.69
## Omega group for total scores and subscales 0.00 0.00
Unabhängigkeit
# Unabhängigkeit
omega(valid_con |> dplyr::select(flen_WI1, flen_WI2, flen_WI3), 1)## Omega
## Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip,
## digits = digits, title = title, sl = sl, labels = labels,
## plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option,
## covar = covar)
## Alpha: 0.4
## G.6: 0.32
## Omega Hierarchical: 0.43
## Omega H asymptotic: 1
## Omega Total 0.43
##
## Schmid Leiman Factor loadings greater than 0.2
## g F1* h2 u2 p2
## flen_WI1 0.23 0.05 0.95 1
## flen_WI2 0.45 0.21 0.79 1
## flen_WI3 0.65 0.42 0.58 1
##
## With Sums of squares of:
## g F1*
## 0.67 0.00
##
## general/max 1.21e+16 max/min = 1
## mean percent general = 1 with sd = 0 and cv of 0
## Explained Common Variance of the general factor = 1
##
## The degrees of freedom are 0 and the fit is 0
## The number of observations was 400 with Chi Square = 0 with prob < NA
## The root mean square of the residuals is 0
## The df corrected root mean square of the residuals is NA
##
## Compare this with the adequacy of just a general factor and no group factors
## The degrees of freedom for just the general factor are 0 and the fit is 0
## The number of observations was 400 with Chi Square = 0 with prob < NA
## The root mean square of the residuals is 0
## The df corrected root mean square of the residuals is NA
##
## Measures of factor score adequacy
## g F1*
## Correlation of scores with factors 0.71 0
## Multiple R square of scores with factors 0.51 0
## Minimum correlation of factor score estimates 0.01 -1
##
## Total, General and Subset omega for each subset
## g F1*
## Omega total for total scores and subscales 0.43 0.43
## Omega general for total scores and subscales 0.43 0.43
## Omega group for total scores and subscales 0.00 0.00
Frequentist Data Analysis
con.model <- 'level: 1
transfer_w =~ tfe_1 + tfe_2 + tfe_3 + tfe_5
selektion_w =~ sel_1 + sel_3 + sel_4 + sel_5
enrichment_w =~ enr_1 + enr_2 + enr_3 + enr_4
relation_w =~ rel_1 + rel_2 + rel_3 + rel_4
level: 2
transfer_b =~ tfe_1 + tfe_2 + tfe_3 + tfe_5
selektion_b =~ sel_1 + sel_3 + sel_4 + sel_5
enrichment_b =~ enr_1 + enr_2 + enr_3 + enr_4
relation_b =~ rel_1 + rel_2 + rel_3 + rel_4
umsetzung =~ flen_UM1 + flen_UM2 + flen_UM3 + flen_UM4
differenz =~ flen_WI1 + flen_WI2 + flen_WI3
tfe_2 ~~ 0*tfe_2
sel_5 ~~ sel_1
enr_2 ~~ 0*enr_2
rel_3 ~~ 0*rel_3
'
fit_con <- sem(con.model,
data = valid_con,
cluster = "id"
)Covariances not shown in plot.
lavaanPlot(model = fit_con,
node_options = list(shape = "box", fontname = "Helvetica"),
edge_options = list(color = "grey"),
coefs = TRUE)standardizedSolution(fit_con)## lhs op rhs est.std se z pvalue ci.lower ci.upper
## 1 transfer_w =~ tfe_1 0.597 0.062 9.573 0.000 0.474 0.719
## 2 transfer_w =~ tfe_2 0.794 0.066 12.020 0.000 0.665 0.924
## 3 transfer_w =~ tfe_3 0.421 0.077 5.471 0.000 0.270 0.572
## 4 transfer_w =~ tfe_5 0.493 0.072 6.833 0.000 0.351 0.634
## 5 selektion_w =~ sel_1 0.448 0.082 5.459 0.000 0.287 0.608
## 6 selektion_w =~ sel_3 0.633 0.087 7.321 0.000 0.464 0.803
## 7 selektion_w =~ sel_4 0.639 0.083 7.666 0.000 0.476 0.803
## 8 selektion_w =~ sel_5 0.341 0.090 3.793 0.000 0.165 0.517
## 9 enrichment_w =~ enr_1 0.412 0.108 3.823 0.000 0.201 0.623
## 10 enrichment_w =~ enr_2 0.401 0.090 4.451 0.000 0.224 0.577
## 11 enrichment_w =~ enr_3 0.355 0.128 2.770 0.006 0.104 0.606
## 12 enrichment_w =~ enr_4 0.582 0.121 4.819 0.000 0.345 0.818
## 13 relation_w =~ rel_1 0.282 0.101 2.783 0.005 0.083 0.480
## 14 relation_w =~ rel_2 0.589 0.110 5.341 0.000 0.373 0.805
## 15 relation_w =~ rel_3 0.549 0.098 5.622 0.000 0.357 0.740
## 16 relation_w =~ rel_4 0.321 0.108 2.969 0.003 0.109 0.533
## 17 tfe_1 ~~ tfe_1 0.644 0.074 8.665 0.000 0.498 0.790
## 18 tfe_2 ~~ tfe_2 0.369 0.105 3.514 0.000 0.163 0.575
## 19 tfe_3 ~~ tfe_3 0.823 0.065 12.690 0.000 0.696 0.950
## 20 tfe_5 ~~ tfe_5 0.757 0.071 10.654 0.000 0.618 0.896
## 21 sel_1 ~~ sel_1 0.800 0.073 10.897 0.000 0.656 0.944
## 22 sel_3 ~~ sel_3 0.599 0.110 5.464 0.000 0.384 0.814
## 23 sel_4 ~~ sel_4 0.591 0.107 5.549 0.000 0.383 0.800
## 24 sel_5 ~~ sel_5 0.884 0.061 14.438 0.000 0.764 1.004
## 25 enr_1 ~~ enr_1 0.830 0.089 9.341 0.000 0.656 1.004
## 26 enr_2 ~~ enr_2 0.839 0.072 11.636 0.000 0.698 0.981
## 27 enr_3 ~~ enr_3 0.874 0.091 9.616 0.000 0.696 1.052
## 28 enr_4 ~~ enr_4 0.662 0.140 4.712 0.000 0.386 0.937
## 29 rel_1 ~~ rel_1 0.921 0.057 16.162 0.000 0.809 1.032
## 30 rel_2 ~~ rel_2 0.654 0.130 5.038 0.000 0.399 0.908
## 31 rel_3 ~~ rel_3 0.699 0.107 6.527 0.000 0.489 0.909
## 32 rel_4 ~~ rel_4 0.897 0.069 12.908 0.000 0.761 1.033
## 33 transfer_w ~~ transfer_w 1.000 0.000 NA NA 1.000 1.000
## 34 selektion_w ~~ selektion_w 1.000 0.000 NA NA 1.000 1.000
## 35 enrichment_w ~~ enrichment_w 1.000 0.000 NA NA 1.000 1.000
## 36 relation_w ~~ relation_w 1.000 0.000 NA NA 1.000 1.000
## 37 transfer_w ~~ selektion_w -0.084 0.102 -0.821 0.412 -0.284 0.116
## 38 transfer_w ~~ enrichment_w 0.030 0.119 0.256 0.798 -0.202 0.263
## 39 transfer_w ~~ relation_w 0.100 0.111 0.898 0.369 -0.118 0.318
## 40 selektion_w ~~ enrichment_w -0.004 0.132 -0.032 0.974 -0.262 0.254
## 41 selektion_w ~~ relation_w 0.127 0.137 0.923 0.356 -0.142 0.396
## 42 enrichment_w ~~ relation_w 0.524 0.137 3.828 0.000 0.255 0.792
## 43 tfe_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 44 tfe_2 ~1 0.000 0.000 NA NA 0.000 0.000
## 45 tfe_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 46 tfe_5 ~1 0.000 0.000 NA NA 0.000 0.000
## 47 sel_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 48 sel_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 49 sel_4 ~1 0.000 0.000 NA NA 0.000 0.000
## 50 sel_5 ~1 0.000 0.000 NA NA 0.000 0.000
## 51 enr_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 52 enr_2 ~1 0.000 0.000 NA NA 0.000 0.000
## 53 enr_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 54 enr_4 ~1 0.000 0.000 NA NA 0.000 0.000
## 55 rel_1 ~1 0.000 0.000 NA NA 0.000 0.000
## 56 rel_2 ~1 0.000 0.000 NA NA 0.000 0.000
## 57 rel_3 ~1 0.000 0.000 NA NA 0.000 0.000
## 58 rel_4 ~1 0.000 0.000 NA NA 0.000 0.000
## 59 transfer_w ~1 0.000 0.000 NA NA 0.000 0.000
## 60 selektion_w ~1 0.000 0.000 NA NA 0.000 0.000
## 61 enrichment_w ~1 0.000 0.000 NA NA 0.000 0.000
## 62 relation_w ~1 0.000 0.000 NA NA 0.000 0.000
## 63 transfer_b =~ tfe_1 0.564 0.124 4.551 0.000 0.321 0.806
## 64 transfer_b =~ tfe_2 1.000 0.000 NA NA 1.000 1.000
## 65 transfer_b =~ tfe_3 0.818 0.081 10.131 0.000 0.660 0.976
## 66 transfer_b =~ tfe_5 0.804 0.077 10.480 0.000 0.654 0.955
## 67 selektion_b =~ sel_1 0.952 0.075 12.630 0.000 0.805 1.100
## 68 selektion_b =~ sel_3 0.893 0.075 11.965 0.000 0.747 1.039
## 69 selektion_b =~ sel_4 0.947 0.061 15.413 0.000 0.827 1.068
## 70 selektion_b =~ sel_5 0.981 0.078 12.557 0.000 0.828 1.134
## 71 enrichment_b =~ enr_1 0.942 0.078 12.073 0.000 0.789 1.095
## 72 enrichment_b =~ enr_2 1.000 0.000 NA NA 1.000 1.000
## 73 enrichment_b =~ enr_3 0.928 0.072 12.844 0.000 0.787 1.070
## 74 enrichment_b =~ enr_4 0.888 0.072 12.282 0.000 0.747 1.030
## 75 relation_b =~ rel_1 0.857 0.080 10.721 0.000 0.701 1.014
## 76 relation_b =~ rel_2 0.842 0.075 11.264 0.000 0.695 0.988
## 77 relation_b =~ rel_3 1.000 0.000 NA NA 1.000 1.000
## 78 relation_b =~ rel_4 0.983 0.089 11.066 0.000 0.809 1.157
## 79 umsetzung =~ flen_UM1 0.490 0.067 7.302 0.000 0.359 0.622
## 80 umsetzung =~ flen_UM2 0.381 0.073 5.210 0.000 0.238 0.525
## 81 umsetzung =~ flen_UM3 0.693 0.061 11.356 0.000 0.574 0.813
## 82 umsetzung =~ flen_UM4 0.790 0.061 12.874 0.000 0.670 0.911
## 83 differenz =~ flen_WI1 0.172 0.095 1.818 0.069 -0.013 0.358
## 84 differenz =~ flen_WI2 0.495 0.106 4.656 0.000 0.287 0.703
## 85 differenz =~ flen_WI3 0.675 0.128 5.280 0.000 0.424 0.925
## 86 tfe_2 ~~ tfe_2 0.000 0.000 NA NA 0.000 0.000
## 87 sel_1 ~~ sel_5 1.312 2.140 0.613 0.540 -2.883 5.507
## 88 enr_2 ~~ enr_2 0.000 0.000 NA NA 0.000 0.000
## 89 rel_3 ~~ rel_3 0.000 0.000 NA NA 0.000 0.000
## 90 tfe_1 ~~ tfe_1 0.682 0.140 4.886 0.000 0.409 0.956
## 91 tfe_3 ~~ tfe_3 0.331 0.132 2.502 0.012 0.072 0.590
## 92 tfe_5 ~~ tfe_5 0.353 0.124 2.856 0.004 0.111 0.595
## 93 sel_1 ~~ sel_1 0.093 0.144 0.647 0.518 -0.189 0.374
## 94 sel_3 ~~ sel_3 0.203 0.133 1.519 0.129 -0.059 0.464
## 95 sel_4 ~~ sel_4 0.103 0.116 0.884 0.377 -0.125 0.331
## 96 sel_5 ~~ sel_5 0.038 0.153 0.249 0.804 -0.262 0.338
## 97 enr_1 ~~ enr_1 0.112 0.147 0.764 0.445 -0.176 0.401
## 98 enr_3 ~~ enr_3 0.139 0.134 1.033 0.302 -0.124 0.401
## 99 enr_4 ~~ enr_4 0.211 0.129 1.638 0.101 -0.041 0.463
## 100 rel_1 ~~ rel_1 0.265 0.137 1.930 0.054 -0.004 0.534
## 101 rel_2 ~~ rel_2 0.291 0.126 2.314 0.021 0.045 0.538
## 102 rel_4 ~~ rel_4 0.034 0.175 0.197 0.844 -0.308 0.376
## 103 flen_UM1 ~~ flen_UM1 0.760 0.066 11.540 0.000 0.631 0.889
## 104 flen_UM2 ~~ flen_UM2 0.855 0.056 15.308 0.000 0.745 0.964
## 105 flen_UM3 ~~ flen_UM3 0.519 0.085 6.131 0.000 0.353 0.685
## 106 flen_UM4 ~~ flen_UM4 0.375 0.097 3.864 0.000 0.185 0.565
## 107 flen_WI1 ~~ flen_WI1 0.970 0.033 29.790 0.000 0.907 1.034
## 108 flen_WI2 ~~ flen_WI2 0.755 0.105 7.181 0.000 0.549 0.961
## 109 flen_WI3 ~~ flen_WI3 0.544 0.173 3.156 0.002 0.206 0.883
## 110 transfer_b ~~ transfer_b 1.000 0.000 NA NA 1.000 1.000
## 111 selektion_b ~~ selektion_b 1.000 0.000 NA NA 1.000 1.000
## 112 enrichment_b ~~ enrichment_b 1.000 0.000 NA NA 1.000 1.000
## 113 relation_b ~~ relation_b 1.000 0.000 NA NA 1.000 1.000
## 114 umsetzung ~~ umsetzung 1.000 0.000 NA NA 1.000 1.000
## 115 differenz ~~ differenz 1.000 0.000 NA NA 1.000 1.000
## 116 transfer_b ~~ selektion_b 0.161 0.114 1.415 0.157 -0.062 0.384
## 117 transfer_b ~~ enrichment_b 0.451 0.108 4.180 0.000 0.239 0.662
## 118 transfer_b ~~ relation_b 0.192 0.118 1.628 0.104 -0.039 0.424
## 119 transfer_b ~~ umsetzung 0.002 0.107 0.015 0.988 -0.208 0.211
## 120 transfer_b ~~ differenz 0.182 0.130 1.403 0.161 -0.072 0.436
## 121 selektion_b ~~ enrichment_b -0.163 0.104 -1.570 0.116 -0.366 0.040
## 122 selektion_b ~~ relation_b -0.191 0.105 -1.824 0.068 -0.397 0.014
## 123 selektion_b ~~ umsetzung 0.180 0.098 1.832 0.067 -0.013 0.373
## 124 selektion_b ~~ differenz 0.225 0.114 1.966 0.049 0.001 0.449
## 125 enrichment_b ~~ relation_b 0.453 0.088 5.133 0.000 0.280 0.626
## 126 enrichment_b ~~ umsetzung -0.014 0.100 -0.139 0.890 -0.209 0.182
## 127 enrichment_b ~~ differenz -0.180 0.122 -1.477 0.140 -0.419 0.059
## 128 relation_b ~~ umsetzung 0.002 0.100 0.016 0.987 -0.195 0.198
## 129 relation_b ~~ differenz -0.468 0.128 -3.655 0.000 -0.719 -0.217
## 130 umsetzung ~~ differenz 0.173 0.111 1.563 0.118 -0.044 0.390
## 131 tfe_1 ~1 4.209 0.555 7.583 0.000 3.121 5.297
## 132 tfe_2 ~1 5.900 1.213 4.865 0.000 3.523 8.277
## 133 tfe_3 ~1 2.507 0.218 11.499 0.000 2.080 2.934
## 134 tfe_5 ~1 2.594 0.215 12.040 0.000 2.172 3.016
## 135 sel_1 ~1 5.000 0.486 10.277 0.000 4.046 5.953
## 136 sel_3 ~1 5.709 0.675 8.459 0.000 4.386 7.032
## 137 sel_4 ~1 4.828 0.504 9.576 0.000 3.840 5.816
## 138 sel_5 ~1 3.837 0.339 11.306 0.000 3.172 4.502
## 139 enr_1 ~1 4.690 0.554 8.471 0.000 3.605 5.775
## 140 enr_2 ~1 4.493 0.461 9.738 0.000 3.588 5.397
## 141 enr_3 ~1 4.461 0.425 10.493 0.000 3.628 5.294
## 142 enr_4 ~1 4.900 0.532 9.206 0.000 3.856 5.943
## 143 rel_1 ~1 6.344 0.633 10.019 0.000 5.103 7.585
## 144 rel_2 ~1 7.094 0.865 8.198 0.000 5.398 8.790
## 145 rel_3 ~1 6.843 0.628 10.892 0.000 5.612 8.075
## 146 rel_4 ~1 7.601 0.898 8.468 0.000 5.841 9.360
## 147 flen_UM1 ~1 4.348 0.230 18.876 0.000 3.896 4.799
## 148 flen_UM2 ~1 2.823 0.159 17.748 0.000 2.511 3.135
## 149 flen_UM3 ~1 3.760 0.202 18.579 0.000 3.363 4.157
## 150 flen_UM4 ~1 3.670 0.198 18.522 0.000 3.282 4.059
## 151 flen_WI1 ~1 3.943 0.211 18.684 0.000 3.529 4.357
## 152 flen_WI2 ~1 2.382 0.140 17.068 0.000 2.108 2.655
## 153 flen_WI3 ~1 2.310 0.136 16.928 0.000 2.042 2.577
## 154 transfer_b ~1 0.000 0.000 NA NA 0.000 0.000
## 155 selektion_b ~1 0.000 0.000 NA NA 0.000 0.000
## 156 enrichment_b ~1 0.000 0.000 NA NA 0.000 0.000
## 157 relation_b ~1 0.000 0.000 NA NA 0.000 0.000
## 158 umsetzung ~1 0.000 0.000 NA NA 0.000 0.000
## 159 differenz ~1 0.000 0.000 NA NA 0.000 0.000
BF Data Analysis (with predicted values)
pred_con <- data.frame(lavPredict(fit_con, method = "regression", level = 2))Correlation Transfer ~~ Unsetzbarkeit
correlationBF(y = pred_con$transfer_b, x = pred_con$umsetzung,
#rscale = .3, # width of prior: standard
nullInterval = c(.3, 1) # assumption was medium effect
)## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 0.3<rho<1 : 8.35e-06 ±NA%
## [2] Alt., r=0.333 !(0.3<rho<1) : 0.218 ±NA%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*Correlation Transfer ~~ Unabhängigkeit
correlationBF(y = pred_con$transfer_b, x = pred_con$differenz,
# rscale = .3, # width of prior: standard
nullInterval = c(-1, 0) # assumption was negative effect
)## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 -1<rho<0 : 0.0411 ±NA%
## [2] Alt., r=0.333 !(-1<rho<0) : 27.3 ±NA%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*Correlation Enrichment ~~ Unabhängigkeit
correlationBF(y = pred_con$enrichment_b, x = pred_con$differenz,
# rscale = .3, # width of prior: standard
nullInterval = c(.1, 1) # assumption was small effect
)## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 0.1<rho<1 : 0.000125 ±NA%
## [2] Alt., r=0.333 !(0.1<rho<1) : 68.3 ±NA%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*Correlation Relationierung ~~ Unabhängigkeit
(not preregistered, therefore exploratory)
correlationBF(y = pred_con$relation_b, x = pred_con$differenz,
# rscale = .3, # width of prior: standard
nullInterval = c(.1, 1) # assumption was small effect
)## Bayes factor analysis
## --------------
## [1] Alt., r=0.333 0.1<rho<1 : 6.72e-08 ±NA%
## [2] Alt., r=0.333 !(0.1<rho<1) : 1.15e+18 ±NA%
##
## Against denominator:
## Null, rho = 0
## ---
## Bayes factor type: BFcorrelation, Jeffreys-beta*
Used packages & Setup
installed.packages()[names(sessionInfo()$otherPkgs), "Version"]## knitr lavaan BayesFactor Matrix coda lavaanPlot
## "1.45" "0.6-17" "0.9.12-4.7" "1.6-5" "0.19-4" "0.8.1"
## rio psych lubridate forcats stringr dplyr
## "1.0.1" "2.4.1" "1.9.3" "1.0.0" "1.5.1" "1.1.4"
## purrr readr tidyr tibble ggplot2 tidyverse
## "1.0.2" "2.1.5" "1.3.1" "3.2.1" "3.4.4" "2.0.0"R.Version()## $platform
## [1] "x86_64-w64-mingw32"
##
## $arch
## [1] "x86_64"
##
## $os
## [1] "mingw32"
##
## $crt
## [1] "ucrt"
##
## $system
## [1] "x86_64, mingw32"
##
## $status
## [1] ""
##
## $major
## [1] "4"
##
## $minor
## [1] "3.1"
##
## $year
## [1] "2023"
##
## $month
## [1] "06"
##
## $day
## [1] "16"
##
## $`svn rev`
## [1] "84548"
##
## $language
## [1] "R"
##
## $version.string
## [1] "R version 4.3.1 (2023-06-16 ucrt)"
##
## $nickname
## [1] "Beagle Scouts"