#::::::::::::::::: PSY9140 SEM course Day 3 :::::::::::::::::::::::::::::### ################### (0) Preparations ####################################### # installing packages; has just to be done once. # install.packages("lavaan") # install.packages("psych") # install.packages("lavaanPlot") # install.packages("semPlot") # install.packages("semTable") # install.packages("ggcorrplot") # load packages. Has to be done each time R is started. library(lavaan) library(psych) library(lavaanPlot) library(semPlot) library(semTable) library(ggcorrplot) ################### (1) Exercise 1 ####################################### # load the datafile "data1.csv" as a dataframe with the name "df1" by using the "read.csv" command df1 <- read.csv("https://www.sv.uio.no/psi/personer/vit/tilmanns/psy9140/data1.csv") # descriptive statistics for all variables in "df1" by using "describe" from the "psych" package describe(df1) # (1) Specify a multiple regression model with body image (body ), depressive symptoms (dep) and # body mass index (bmi) as independent variable and dieting (diet) as dependent variable # Specify the model model <- "diet ~ body + dep + bmi body ~~ dep + bmi dep ~~ bmi" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df1) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE) # (2) Which independent variable is the strongest predictor of dieting? # Answer: The standardized regression coefficients show that body image is the strongest predictor (beta = -.315) # (3) How much variance is explained by all three independent variables together? # Answer: The standardized residual variance for diet provides information about R2. R2 = 1 - .778 = .222. # It is also possible to obtain information about R2 directly from lavaan by using the rsquare command: summary(fit, fit.measures = TRUE, standardized=TRUE, rsquare = TRUE) # (4) Estimate the model with and without correlations among the independent variables. # In which way do the results differ? # We can estimate the model without correlations among independent variables: model <- "diet ~ body + dep + bmi" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df1) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE) # Results show that variances of independent variables and covariances among independent variables are not estimated. # Moreover, only 2268 cases are used in the analyses because of missing data for some cases on the independent variable. # Missing data also lead to somewhat different estimates of the regression coefficients. ################### (2) Exercise 2 ####################################### # (1) Specify the multiple mediation model as depicted on the previous slide. # Specify the model in the next line model <- "diet ~ body + dep + girl dep ~ body + girl body ~ girl" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df1) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE) # (2) Point out the different mediational processes that can be estimated in the model. # Answer: Four mediational processes / indirect paths can be estimated: # girl-->body-->dep # girl-->dep-->diet # body-->dep-->diet # girl-->body-->dep-->diet # (3) Test one (or several) of them by using the := operator command. # The solution provided here tests all mediational paths simultaneously: model <- "diet ~ body_diet*body + dep_diet*dep + girl_diet*girl dep ~ body_dep*body + girl_dep*girl body ~ girl_body*girl # Indirect effects ind_body_dep_diet := body_dep*dep_diet ind_girl_body_dep := girl_body*body_dep ind_girl_body_diet := girl_body*body_diet ind_girl_dep_diet := girl_dep*dep_diet ind_girl_body_dep_diet := girl_body*body_dep*dep_diet # Total effects tot_body_diet := body_dep*dep_diet + body_diet tot_girl_dep := girl_body*body_dep + girl_dep tot_girl_diet := girl_dep*dep_diet + girl_body*body_diet + girl_body*body_dep*dep_diet + girl_diet" # (4) Use Sobel's test and/or bootstrapping (with 100 draws) to test for mediation. # The model is first run by using the Sobel's test (default) fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df1) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE) # Note that the Defined parameter names are shortened by lavaan # The model is now run by using bootstrapping (100 draws - you should have more draws, e.g., 5,000 but that takes time) fit <-sem(model, missing = "ML", meanstructure = TRUE, se = "bootstrap", bootstrap = 100, data = df1) # Providing output for the model summary(fit, fit.measures = TRUE, standardized =TRUE, ci = TRUE) # Providing bias corrected confidence intervals from the bootstrap parameterestimates(fit, boot.ci.type = "bca.simple") ################### (3) Exercise 3 ####################################### # load the datafile "data2.csv" as a dataframe with the name "df2" by using the "read.csv" command df2 <- read.csv("https://www.sv.uio.no/psi/personer/vit/tilmanns/psy9140/data2.csv") # descriptive statistics for all variables in "df2" describe(df2) # (1) Test the measure of Body Image by conducting a CFA # Specify the model in the next line model <- "body =~ body1 + body2 + body3 + body4 + body5 + body6 + body7" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df2) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE, modindices = TRUE) # (2) Modify the measurement model, if necessary. Use both results from the analyses (for instance # modification indices and factor loadings) and substantive considerations when modifying the model. # One possible solution is to remove body5 and body7 from the CFA to improve model fit. model <- "body =~ body1 + body2 + body3 + body4 + body6" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df2) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE, modindices = TRUE) # (3) Combine all factors in one model with correlations among latent factors model <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 # Covariances among latent factors diet ~~ dep diet ~~ body dep ~~ body" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df2) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE) # (4) Examine model fit. Does the model fit the data well? # Answer: The RMSEA, CFI, and TLI indicate that model fit is rather good. ################### (4) Exercise 4 ##################################### # (1) Specify and estimate the combined measurement and structural model depicted below. model <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 # Structural part of the model diet ~ dep diet ~ body dep ~ body" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df2) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE) # (2) Assess mediation by using the ":=" operator. Do the results differ from the mediation model based on mean scores? model <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 # Structural part of the model diet ~ b*dep diet ~ c*body dep ~ a*body # Mediation ab := a*b total := a*b + c" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df2) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE) ################### (5) Exercise 5 ####################################### # (1) Use parameter constraints in to examine whether the relationships between the variables are moderated by gender. # (2) Which paths show significant gender differences? # Model without constraints unconstraint_model <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 # Structural models diet ~ dep diet ~ body dep ~ body" # Model where regression coefficient for body-->dep is forced to be equal across gender constraint_model_a <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 # Structural models diet ~ dep diet ~ body dep ~ c(a,a)*body" # Model where regression coefficient for dep-->diet is forced to be equal across gender constraint_model_b <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 # Structural models diet ~ c(b,b)*dep diet ~ body dep ~ body" # Model where regression coefficient for body-->diet is forced to be equal across gender constraint_model_c <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 # Structural models diet ~ dep diet ~ c(c,c)*body dep ~ body" # Running the models fit_unconstraint <- sem(unconstraint_model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl") fit_constraint_a <- sem(constraint_model_a, missing = "ML", meanstructure = TRUE, data = df2, group = "girl") fit_constraint_b <- sem(constraint_model_b, missing = "ML", meanstructure = TRUE, data = df2, group = "girl") fit_constraint_c <- sem(constraint_model_c, missing = "ML", meanstructure = TRUE, data = df2, group = "girl") # Providing output for the models summary(fit_unconstraint, fit.measures = TRUE, standardized=TRUE) summary(fit_constraint_a, fit.measures = TRUE, standardized=TRUE) summary(fit_constraint_b, fit.measures = TRUE, standardized=TRUE) summary(fit_constraint_c, fit.measures = TRUE, standardized=TRUE) # Compare model fit for unconstraint and constraint models anova(fit_unconstraint, fit_constraint_a) anova(fit_unconstraint, fit_constraint_b) anova(fit_unconstraint, fit_constraint_c) # Only the regression coefficient for dep-->diet is significantly different for boys and girls, # as shown by the significant chi-square difference test. ################### (6) Exercise 6 ####################################### # (1) Conduct a multi group analysis for a CFA for depressive symptoms. # Do you find measurement invariance (equal factor loadings) across gender? model <- "dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6" # Running the model fit_unconstraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl") fit_constraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl", group.equal = c("loadings")) # Providing output for the model summary(fit_unconstraint, fit.measures = TRUE, standardized=TRUE) summary(fit_constraint, fit.measures = TRUE, standardized=TRUE) anova(fit_unconstraint, fit_constraint) # The chi-square difference test is not significant and indicates as such measurement invariance across gender. # (2) Examine measurement invariance across gender for dieting. # Which factor loadings have to be freed to improve model fit? model <- "diet =~ diet1 + diet2 + diet3 + diet4" # Running the models fit_unconstraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl") fit_constraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl", group.equal = c("loadings")) # Providing output for the model summary(fit_unconstraint, fit.measures = TRUE, standardized=TRUE) summary(fit_constraint, fit.measures = TRUE, standardized=TRUE) anova(fit_unconstraint, fit_constraint) # Chi-square difference tests show a clear difference in model fit between the two models, # thereby indicating that measurement invariance cannot be assumed. # We can use the lavTestScore() function to examine model fit when specific factor loadings are freed across groups lavTestScore(fit_constraint) # The results show that all three factor loadings may be freed to improve model fit # (3) Estimate the following structural model with depressive symptoms as predictor and dieting as # outcome variable in a two group analysis with measurement invariance. Is the relationship between # depressive symptoms and dieting moderated by gender? model <- "dep =~ dep1 + dep2 + dep3 + dep4 + dep5 + dep6 diet =~ diet1 + diet2 + diet3 + diet4 diet ~ dep" # Running the models fit_unconstraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl", group.equal = c("loadings")) fit_constraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl", group.equal = c("loadings", "regressions")) # Providing output for the model summary(fit_unconstraint, fit.measures = TRUE, standardized=TRUE) summary(fit_constraint, fit.measures = TRUE, standardized=TRUE) anova(fit_unconstraint, fit_constraint) # Chi-square difference test show a p-value of .055. As a result, there is no moderation by gender, # but the p-value is close to being significant. ################### (7) Exercise 7 ####################################### # (1) Use the anova or lavTestLRT function to compare the estimated model with a model without measurement invariance. model <- "# CFA body =~ body1 + body2 + body3 + body4 + body6 diet =~ diet1 + diet2 + diet3 + diet4 # Structural models diet ~ body" # Running the model without constraints fit_unconstraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl") # Running the model with constraints fit_constraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl", group.equal = c("loadings")) # Providing output for the model summary(fit_unconstraint, fit.measures = TRUE, standardized=TRUE) summary(fit_constraint, fit.measures = TRUE, standardized=TRUE) anova(fit_unconstraint, fit_constraint) # The chi-square difference tests indicate that the model with measurement invariance # has worse model fit than the model without measurement invariance # (2) Use the lavTestScore () function to obtain information about constraint parameters that may be freed lavTestScore(fit_constraint) # Results show that all factor loadings can be freed to obtain better model fit, but the factor loading of # the body4 indicator (.p4.) and diet2 (.p7.) provide the largest decrease in chi-square when freed. # (3) Use the group.partial = function to free one or several parameters (e.g., factor loadings) # We will here free .p4. and .p7. fit_partly_constraint <- sem(model, missing = "ML", meanstructure = TRUE, data = df2, group = "girl", group.equal = c("loadings"), group.partial = c("body =~ body4", "diet =~ diet2")) summary(fit_partly_constraint, fit.measures = TRUE, standardized=TRUE) # Even after freeing the two factor loadings, model fit is still not adequate. ################### (8) Exercise 8 ####################################### # (1) Transfer data from SPSS to R # installing package "foreign (has just to be done once. # install.packages("foreign") # Load package "foreign" library(foreign) # Load SPSS file as data frame df_cosmetics <- read.spss("https://www.sv.uio.no/psi/personer/vit/tilmanns/psy9140/cosmetics.sav", use.value.labels=FALSE, to.data.frame=TRUE) # descriptive statistics for all variables in "df_cosmetics" describe(df_cosmetics) # (2) Specify and estimate the following model # Specify the model model <- "wish ~ invest + satisfac invest ~~ satisfac" # Running the model fit <- sem(model, missing = "ML", meanstructure = TRUE, data = df_cosmetics) # Providing output for the model summary(fit, fit.measures = TRUE, standardized=TRUE)