From 41b0aa94b626771aa635bdb15cbe161d46a5d63e Mon Sep 17 00:00:00 2001 From: Duco Veen Date: Tue, 18 Apr 2023 17:42:08 +0200 Subject: [PATCH] update practical 1 SEM --- content/04_SEM/practical_01.html | 446 +++++++++++++++--- content/04_SEM/practical_01.qmd | 152 +++++- .../figure-html/unnamed-chunk-10-1.png | Bin 0 -> 45248 bytes .../figure-html/unnamed-chunk-16-1.png | Bin 0 -> 11735 bytes .../figure-html/unnamed-chunk-20-1.png | Bin 0 -> 14302 bytes .../figure-html/unnamed-chunk-5-1.png | Bin 0 -> 12450 bytes .../figure-html/unnamed-chunk-6-1.png | Bin 0 -> 12662 bytes index.Rmd | 6 +- index.html | 8 +- 9 files changed, 534 insertions(+), 78 deletions(-) create mode 100644 content/04_SEM/practical_01_files/figure-html/unnamed-chunk-10-1.png create mode 100644 content/04_SEM/practical_01_files/figure-html/unnamed-chunk-16-1.png create mode 100644 content/04_SEM/practical_01_files/figure-html/unnamed-chunk-20-1.png create mode 100644 content/04_SEM/practical_01_files/figure-html/unnamed-chunk-5-1.png create mode 100644 content/04_SEM/practical_01_files/figure-html/unnamed-chunk-6-1.png diff --git a/content/04_SEM/practical_01.html b/content/04_SEM/practical_01.html index fa3bb75..412367a 100644 --- a/content/04_SEM/practical_01.html +++ b/content/04_SEM/practical_01.html @@ -113,6 +113,12 @@

Table of contents

+
  • Examples +
    • @@ -199,7 +205,7 @@

    Confirmatory
  • Get some descriptions or summaries of the data.
    • -
    +
    Code 
    # For instance using
 summary(data)
    @@ -256,18 +262,18 @@

    Confirmatory

      -
    1. Fit a confirmatory factor analysis for the neuroticism factor using the cfa() function from lavaan. See ?cfa for more details.
      2. +
    2. Fit a confirmatory factor analysis for the neuroticism factor using the cfa() function from lavaan. See ?cfa for more details. Also create plots with the semPaths() function.

    First specify the model.

    -
    +
    Code 
    cfa.model <- 'Neu  =~ N1 + N2 + N3 + N4 + N5'

    Then we will fit the model and look at the results

    -
    +
    Code 
    fit.cfa <- cfa(cfa.model, data = data)
 summary(fit.cfa)
    @@ -312,19 +318,92 @@

    Confirmatory .N5 1.968 0.057 34.494 0.000 Neu 1.655 0.070 23.756 0.000

    +
    +Code +
    semPaths(fit.cfa, whatLabels = "est")
    +
    +
    +

    +
    -

    Using the cfa() function, you have to specify less in the model compared to the lavaan() function that we used in the lecture. What defaults are being used? Look in ?cfa() at the Details section. There you will find that cfa() is a wrapper function that actually uses lavaan() with specific defaults. Are intercepts for instance estimated or not?

    +

    Using the cfa() function, you have to specify less in the model compared to the lavaan() function that we used in the lecture. What defaults are being used? Look in ?cfa() at the Details section. There you will find that cfa() is a wrapper function that actually uses lavaan() with specific defaults. Are intercepts for instance estimated or not? Did you see them in the figures?

      +
    1. Rerun the analysis above, now include the meanstructure.
      2. +
    +
    +
    +Code +
    fit.cfa.means <- cfa(cfa.model, data = data, meanstructure = TRUE)
+summary(fit.cfa.means)
    +
    +
    +
    lavaan 0.6-12 ended normally after 26 iterations
+
+  Estimator                                         ML
+  Optimization method                           NLMINB
+  Number of model parameters                        15
+
+                                                  Used       Total
+  Number of observations                          2694        2800
+
+Model Test User Model:
+                                                      
+  Test statistic                               360.932
+  Degrees of freedom                                 5
+  P-value (Chi-square)                           0.000
+
+Parameter Estimates:
+
+  Standard errors                             Standard
+  Information                                 Expected
+  Information saturated (h1) model          Structured
+
+Latent Variables:
+                   Estimate  Std.Err  z-value  P(>|z|)
+  Neu =~                                              
+    N1                1.000                           
+    N2                0.952    0.023   40.826    0.000
+    N3                0.892    0.024   36.883    0.000
+    N4                0.677    0.024   27.818    0.000
+    N5                0.632    0.025   24.973    0.000
+
+Intercepts:
+                   Estimate  Std.Err  z-value  P(>|z|)
+   .N1                2.931    0.030   96.735    0.000
+   .N2                3.509    0.029  119.337    0.000
+   .N3                3.217    0.031  104.346    0.000
+   .N4                3.190    0.030  105.263    0.000
+   .N5                2.973    0.031   95.168    0.000
+    Neu               0.000                           
+
+Variances:
+                   Estimate  Std.Err  z-value  P(>|z|)
+   .N1                0.819    0.036   22.656    0.000
+   .N2                0.828    0.034   24.025    0.000
+   .N3                1.245    0.042   29.526    0.000
+   .N4                1.714    0.051   33.779    0.000
+   .N5                1.968    0.057   34.494    0.000
+    Neu               1.655    0.070   23.756    0.000
    +
    +
    +Code +
    semPaths(fit.cfa.means, whatLabels = "est")
    +
    +
    +

    +
    +
    +
    1. Now investigate the fitmeasures using the fitmeasures() function.
    -
    +
    Code -
    fitmeasures(fit.cfa)
    +
    fitmeasures(fit.cfa.means)
                   npar                fmin               chisq                  df 
-             10.000               0.067             360.932               5.000 
+             15.000               0.067             360.932               5.000 
              pvalue      baseline.chisq         baseline.df     baseline.pvalue 
               0.000            4724.621              10.000               0.000 
                 cfi                 tli                nnfi                 rfi 
@@ -332,52 +411,52 @@ 
    Confirmatory
                 nfi                pnfi                 ifi                 rni 
               0.924               0.462               0.925               0.925 
                logl   unrestricted.logl                 aic                 bic 
-         -23078.504          -22898.038           46177.007           46235.995 
+         -23078.504          -22898.038           46187.007           46275.489 
              ntotal                bic2               rmsea      rmsea.ci.lower 
-           2694.000           46204.222               0.163               0.149 
+           2694.000           46227.829               0.163               0.149 
      rmsea.ci.upper        rmsea.pvalue                 rmr          rmr_nomean 
-              0.177               0.000               0.142               0.142 
+              0.177               0.000               0.123               0.142 
                srmr        srmr_bentler srmr_bentler_nomean                crmr 
-              0.056               0.056               0.056               0.069 
+              0.049               0.049               0.056               0.056 
         crmr_nomean          srmr_mplus   srmr_mplus_nomean               cn_05 
-              0.069               0.056               0.056              83.630 
+              0.069               0.049               0.056              83.630 
               cn_01                 gfi                agfi                pgfi 
-            113.604               0.942               0.825               0.314 
+            113.604               0.985               0.940               0.246 
                 mfi                ecvi 
-              0.936               0.141
    + 0.936 0.145

    cfi seems nice, tli less so, rmsea is not looking to good.

    -
      +
      1. Now specify a CFA model for the 5 factors from the dataset.
      -
      +
      Code -
      cfa.model5 <- '
-Agr =~ A1 + A2 + A3 + A4 + A5
-Con =~ C1 + C2 + C3 + C4 + C5
-Ext =~ E1 + E2 + E3 + E4 + E5
-Neu =~ N1 + N2 + N3 + N4 + N5
-Ope =~ O1 + O2 + O3 + O4 + O5
-'
      +
      cfa.model5 <- '
+Agr =~ A1 + A2 + A3 + A4 + A5
+Con =~ C1 + C2 + C3 + C4 + C5
+Ext =~ E1 + E2 + E3 + E4 + E5
+Neu =~ N1 + N2 + N3 + N4 + N5
+Ope =~ O1 + O2 + O3 + O4 + O5
+'
      1. Investigate the fit and fitmeasures, what do you think?
      -
      +
      Code -
      fit.cfa5 <- cfa(cfa.model5, data = data)
-summary(fit.cfa5)
      +
      fit.cfa5 <- cfa(cfa.model5, data = data, meanstructure = TRUE)
+summary(fit.cfa5)
      lavaan 0.6-12 ended normally after 55 iterations
 
   Estimator                                         ML
   Optimization method                           NLMINB
-  Number of model parameters                        60
+  Number of model parameters                        85
 
                                                   Used       Total
   Number of observations                          2436        2800
@@ -444,6 +523,39 @@ 
      Confirmatory
   Neu ~~                                              
     Ope              -0.093    0.022   -4.138    0.000
 
+Intercepts:
+                   Estimate  Std.Err  z-value  P(>|z|)
+   .A1                2.406    0.029   84.421    0.000
+   .A2                4.797    0.024  200.773    0.000
+   .A3                4.599    0.027  173.111    0.000
+   .A4                4.688    0.030  155.808    0.000
+   .A5                4.544    0.026  176.499    0.000
+   .C1                4.525    0.025  180.839    0.000
+   .C2                4.372    0.027  163.624    0.000
+   .C3                4.300    0.026  164.403    0.000
+   .C4                2.550    0.028   91.427    0.000
+   .C5                3.306    0.033   99.953    0.000
+   .E1                2.979    0.033   90.132    0.000
+   .E2                3.154    0.033   96.489    0.000
+   .E3                3.984    0.027  145.509    0.000
+   .E4                4.409    0.030  148.357    0.000
+   .E5                4.391    0.027  161.359    0.000
+   .N1                2.944    0.032   92.214    0.000
+   .N2                3.518    0.031  113.259    0.000
+   .N3                3.225    0.032   99.822    0.000
+   .N4                3.202    0.032  100.717    0.000
+   .N5                2.971    0.033   90.348    0.000
+   .O1                4.813    0.023  210.888    0.000
+   .O2                2.685    0.031   85.347    0.000
+   .O3                4.450    0.024  182.271    0.000
+   .O4                4.925    0.024  203.784    0.000
+   .O5                2.469    0.027   92.049    0.000
+    Agr               0.000                           
+    Con               0.000                           
+    Ext               0.000                           
+    Neu               0.000                           
+    Ope               0.000                           
+
 Variances:
                    Estimate  Std.Err  z-value  P(>|z|)
    .A1                1.745    0.052   33.725    0.000
@@ -477,13 +589,24 @@ 
      Confirmatory
     Neu               1.689    0.073   23.034    0.000
     Ope               0.404    0.033   12.156    0.000
      -
      +
      +
      +
      Code -
      fitmeasures(fit.cfa5)
      +
      semPaths(fit.cfa5, whatLabels = "est")
      +
      +
      +

      +
      +
      +
      +
      +Code +
      fitmeasures(fit.cfa5)
                     npar                fmin               chisq                  df 
-             60.000               0.855            4165.467             265.000 
+             85.000               0.855            4165.467             265.000 
              pvalue      baseline.chisq         baseline.df     baseline.pvalue 
               0.000           18222.116             300.000               0.000 
                 cfi                 tli                nnfi                 rfi 
@@ -491,46 +614,261 @@ 
      Confirmatory
                 nfi                pnfi                 ifi                 rni 
               0.771               0.681               0.783               0.782 
                logl   unrestricted.logl                 aic                 bic 
-         -99840.238          -97757.504          199800.476          200148.363 
+         -99840.238          -97757.504          199850.476          200343.316 
              ntotal                bic2               rmsea      rmsea.ci.lower 
-           2436.000          199957.729               0.078               0.076 
+           2436.000          200073.251               0.078               0.076 
      rmsea.ci.upper        rmsea.pvalue                 rmr          rmr_nomean 
-              0.080               0.000               0.157               0.157 
+              0.080               0.000               0.151               0.157 
                srmr        srmr_bentler srmr_bentler_nomean                crmr 
-              0.075               0.075               0.075               0.078 
+              0.073               0.073               0.075               0.075 
         crmr_nomean          srmr_mplus   srmr_mplus_nomean               cn_05 
-              0.078               0.075               0.075             178.764 
+              0.078               0.073               0.075             178.764 
               cn_01                 gfi                agfi                pgfi 
-            189.003               0.862               0.830               0.703 
+            189.003               0.991               0.988               0.751 
                 mfi                ecvi 
-              0.449               1.759
      + 0.449 1.780

      Hm.. The fit is not so great. Perhaps we can look at modification indices. Beware, we are leaving the realm of confirmatory analysis now. We will look at the 5 best modifications.

      -
      +
      Code -
      modificationindices(fit.cfa5, sort. = TRUE, maximum.number = 5)
      +
      modificationindices(fit.cfa5, sort. = TRUE, maximum.number = 5)
          lhs op rhs      mi    epc sepc.lv sepc.all sepc.nox
-421  N1 ~~  N2 418.812  0.841   0.841    1.033    1.033
-119 Ext =~  N4 200.790  0.487   0.448    0.285    0.285
-158 Ope =~  E3 153.715  0.672   0.427    0.316    0.316
-438  N3 ~~  N4 134.104  0.403   0.403    0.283    0.283
-159 Ope =~  E4 122.558 -0.636  -0.404   -0.276   -0.276
      +451 N1 ~~ N2 418.812 0.841 0.841 1.033 1.033 +149 Ext =~ N4 200.790 0.487 0.448 0.285 0.285 +188 Ope =~ E3 153.715 0.672 0.427 0.316 0.316 +468 N3 ~~ N4 134.104 0.403 0.403 0.283 0.283 +189 Ope =~ E4 122.558 -0.636 -0.404 -0.276 -0.276

      We could also consider looking at Exploratory Factor Analyses, analyse the structure and collect new data to confirm it. Or perhaps we would like to adjust a questionnaire such that we replace items that seem to fit less well. All sort of things that could be done.

      - - - - - - - - - + + +
      +

      Examples

      +

      Since there where some questions about some more advanced SEM methods, I’ll present here a few examples with their sources. They can help you to try and work this out on your own data.

      +
      +

      Mediation example

      +

      This example come from the lavaan website which is a great resource.

      +

      First, some data is simulated that would go with a mediation model.

      +
      +
      +Code +
      set.seed(1234)
+X <- rnorm(100)
+M <- 0.5*X + rnorm(100)
+Y <- 0.7*M + rnorm(100)
+Data <- data.frame(X = X, Y = Y, M = M)
      +
      +
      +

      The rnorm() function let’s you simulate data from a normal distribution. Here 100 samples are taken from a standard normal distribution for X. The mediator is specified by the relationship of 0.5 times X plus unique variation, coming from a standard normal distribution. Y is then specified as 0.7 times the moderator plus unique variation, coming from a standard normal distribution. The data is then put in a dataframe.

      +

      Next we need to specify the lavaan model. To be able to read and understand the model this table might help:

      +
      +HTML5 Icon +
      +
      +
      +Code +
      model.med <- ' # direct effect
+             Y ~ c*X
+           # mediator
+             M ~ a*X
+             Y ~ b*M
+           # indirect effect (a*b)
+             ab := a*b
+           # total effect
+             total := c + (a*b)
+         '
      +
      +
      +

      Next we should fit the model. To get more reliable standard errors, we can make use of the option se = "bootstrap".

      +
      +
      +Code +
      fit.med <- sem(model.med, data = Data, se = "bootstrap")
+summary(fit.med)
      +
      +
      +
      lavaan 0.6-12 ended normally after 1 iterations
+
+  Estimator                                         ML
+  Optimization method                           NLMINB
+  Number of model parameters                         5
+
+  Number of observations                           100
+
+Model Test User Model:
+                                                      
+  Test statistic                                 0.000
+  Degrees of freedom                                 0
+
+Parameter Estimates:
+
+  Standard errors                            Bootstrap
+  Number of requested bootstrap draws             1000
+  Number of successful bootstrap draws            1000
+
+Regressions:
+                   Estimate  Std.Err  z-value  P(>|z|)
+  Y ~                                                 
+    X          (c)    0.036    0.116    0.312    0.755
+  M ~                                                 
+    X          (a)    0.474    0.098    4.837    0.000
+  Y ~                                                 
+    M          (b)    0.788    0.094    8.361    0.000
+
+Variances:
+                   Estimate  Std.Err  z-value  P(>|z|)
+   .Y                 0.898    0.149    6.044    0.000
+   .M                 1.054    0.178    5.917    0.000
+
+Defined Parameters:
+                   Estimate  Std.Err  z-value  P(>|z|)
+    ab                0.374    0.087    4.314    0.000
+    total             0.410    0.139    2.942    0.003
      +
      +
      +

      Finally, we can plot the model.

      +
      +
      +Code +
      semPaths(fit.med, whatLabels = 'est', edge.label.cex = 2)
      +
      +
      +

      +
      +
      +
      +
      +

      Latent Growth Curve example

      +

      This is a short simulated example I created:

      +

      We simulate some data where there are 5 timepoints. The mean intercept value is 2, the mean slope value is 0.7. The variance for the intercept is 1 and the variance for the slope is 0.5^2=0.25. The residual variance at each timepoint is 0.5^2=0.25.

      +
      +
      +Code +
      # Set seed for reproducibility
+set.seed(123)
+
+# Simulate data for latent growth curve model
+n <- 500 # sample size
+t <- 5  # number of time points
+time <- 1:t  # time variable
+intercept <- rnorm(n, mean = 2, sd = 1)  # intercept latent variable
+slope <- rnorm(n, mean = 0.7, sd = 0.5)  # slope latent variable
+observed_vars <- data.frame()
+
+for (i in 1:n) {
+  # Simulate observed variables for each participant
+  Y <- intercept[i] + slope[i] * time + rnorm(t, mean = 0, sd = 0.5)
+  observed_vars <- rbind(observed_vars, Y)
+}
+colnames(observed_vars) <- paste0("Y", time)
      +
      +
      +

      Now get your growth model specified.

      +
      +
      +Code +
      # Create lavaan model syntax
+growth_model <- "
+  # latent variables
+    intercept =~ 1 * Y1 + 1 * Y2 + 1 * Y3 + 1 * Y4 + 1 * Y5
+    slope =~ 1* Y1 + 2 * Y2 + 3* Y3 + 4 * Y4 + 5 * Y5
+"
      +
      +
      +

      Fit it, and look if the estimates are as we simulated them.

      +
      +
      +Code +
      # Fit the model to the simulated data
+fit.growth <- lavaan::growth(growth_model, data = observed_vars)
+
+# Summarize the model results
+summary(fit.growth)
      +
      +
      +
      lavaan 0.6-12 ended normally after 35 iterations
+
+  Estimator                                         ML
+  Optimization method                           NLMINB
+  Number of model parameters                        10
+
+  Number of observations                           500
+
+Model Test User Model:
+                                                      
+  Test statistic                                 7.641
+  Degrees of freedom                                10
+  P-value (Chi-square)                           0.664
+
+Parameter Estimates:
+
+  Standard errors                             Standard
+  Information                                 Expected
+  Information saturated (h1) model          Structured
+
+Latent Variables:
+                   Estimate  Std.Err  z-value  P(>|z|)
+  intercept =~                                        
+    Y1                1.000                           
+    Y2                1.000                           
+    Y3                1.000                           
+    Y4                1.000                           
+    Y5                1.000                           
+  slope =~                                            
+    Y1                1.000                           
+    Y2                2.000                           
+    Y3                3.000                           
+    Y4                4.000                           
+    Y5                5.000                           
+
+Covariances:
+                   Estimate  Std.Err  z-value  P(>|z|)
+  intercept ~~                                        
+    slope            -0.016    0.026   -0.592    0.554
+
+Intercepts:
+                   Estimate  Std.Err  z-value  P(>|z|)
+   .Y1                0.000                           
+   .Y2                0.000                           
+   .Y3                0.000                           
+   .Y4                0.000                           
+   .Y5                0.000                           
+    intercept         2.041    0.049   41.530    0.000
+    slope             0.697    0.023   30.037    0.000
+
+Variances:
+                   Estimate  Std.Err  z-value  P(>|z|)
+   .Y1                0.255    0.031    8.300    0.000
+   .Y2                0.257    0.022   11.745    0.000
+   .Y3                0.225    0.018   12.353    0.000
+   .Y4                0.260    0.025   10.507    0.000
+   .Y5                0.230    0.037    6.190    0.000
+    intercept         0.932    0.079   11.817    0.000
+    slope             0.245    0.017   14.280    0.000
      +
      +
      +

      Great, that looks good! Now let’s just finish with a plot of this model.

      +
      +
      +Code +
      semPaths(fit.growth, whatLabels = "est", edge.label.cex = 1)
      +
      +
      +

      +
      +
      +
      +
      diff --git a/content/04_SEM/practical_01.qmd b/content/04_SEM/practical_01.qmd index b4d830e..45a26ad 100644 --- a/content/04_SEM/practical_01.qmd +++ b/content/04_SEM/practical_01.qmd @@ -5,7 +5,7 @@ format: html: toc: true toc_float: true - code-fold: true + code-fold: show code-copy: true execute: echo: true @@ -43,7 +43,7 @@ data <- psych::bfi summary(data) ``` -4. **Fit a confirmatory factor analysis for the neuroticism factor using the `cfa()` function from `lavaan`. See `?cfa` for more details. ** +4. **Fit a confirmatory factor analysis for the neuroticism factor using the `cfa()` function from `lavaan`. See `?cfa` for more details. Also create plots with the `semPaths()` function. ** First specify the model. @@ -56,19 +56,29 @@ Then we will fit the model and look at the results ```{r} fit.cfa <- cfa(cfa.model, data = data) summary(fit.cfa) +semPaths(fit.cfa, whatLabels = "est") ``` -Using the `cfa()` function, you have to specify less in the model compared to the `lavaan()` function that we used in the lecture. What defaults are being used? Look in `?cfa()` at the Details section. There you will find that `cfa()` is a wrapper function that actually uses `lavaan()` with specific defaults. Are intercepts for instance estimated or not? +Using the `cfa()` function, you have to specify less in the model compared to the `lavaan()` function that we used in the lecture. What defaults are being used? Look in `?cfa()` at the Details section. There you will find that `cfa()` is a wrapper function that actually uses `lavaan()` with specific defaults. Are intercepts for instance estimated or not? Did you see them in the figures? -5. **Now investigate the fitmeasures using the `fitmeasures()` function.** +5. **Rerun the analysis above, now include the meanstructure.** ```{r} -fitmeasures(fit.cfa) +fit.cfa.means <- cfa(cfa.model, data = data, meanstructure = TRUE) +summary(fit.cfa.means) +semPaths(fit.cfa.means, whatLabels = "est") +``` + + +6. **Now investigate the fitmeasures using the `fitmeasures()` function.** + +```{r} +fitmeasures(fit.cfa.means) ``` `cfi` seems nice, `tli` less so, `rmsea` is not looking to good. -6. **Now specify a CFA model for the 5 factors from the dataset.** +7. **Now specify a CFA model for the 5 factors from the dataset.** ```{r} cfa.model5 <- ' @@ -84,8 +94,18 @@ Ope =~ O1 + O2 + O3 + O4 + O5 7. **Investigate the fit and fitmeasures, what do you think?** ```{r} -fit.cfa5 <- cfa(cfa.model5, data = data) +fit.cfa5 <- cfa(cfa.model5, data = data, meanstructure = TRUE) summary(fit.cfa5) +``` + + +```{r} +#| fig-height: 7 +semPaths(fit.cfa5, whatLabels = "est") +``` + + +```{r} fitmeasures(fit.cfa5) ``` @@ -97,21 +117,121 @@ modificationindices(fit.cfa5, sort. = TRUE, maximum.number = 5) We could also consider looking at Exploratory Factor Analyses, analyse the structure and collect new data to confirm it. Or perhaps we would like to adjust a questionnaire such that we replace items that seem to fit less well. All sort of things that could be done. - +# Examples + +Since there where some questions about some more advanced SEM methods, I'll present here a few examples with their sources. They can help you to try and work this out on your own data. + +## Mediation example + +This example come from the [lavaan website](https://lavaan.ugent.be/tutorial/mediation.html) which is a great resource. + +First, some data is simulated that would go with a mediation model. + +```{r} +set.seed(1234) +X <- rnorm(100) +M <- 0.5*X + rnorm(100) +Y <- 0.7*M + rnorm(100) +Data <- data.frame(X = X, Y = Y, M = M) +``` + +The `rnorm()` function let's you simulate data from a normal distribution. Here 100 samples are taken from a standard normal distribution for X. The mediator is specified by the relationship of 0.5 times X plus unique variation, coming from a standard normal distribution. Y is then specified as 0.7 times the moderator plus unique variation, coming from a standard normal distribution. The data is then put in a dataframe. + +Next we need to specify the lavaan model. To be able to read and understand the model this table might help: + +
      +HTML5 Icon +
      + +```{r} +model.med <- ' # direct effect + Y ~ c*X + # mediator + M ~ a*X + Y ~ b*M + # indirect effect (a*b) + ab := a*b + # total effect + total := c + (a*b) + ' +``` + +Next we should fit the model. To get more reliable standard errors, we can make use of the option `se = "bootstrap"`. + +```{r} +#| cache: true +fit.med <- sem(model.med, data = Data, se = "bootstrap") +summary(fit.med) +``` + +Finally, we can plot the model. + +```{r} +semPaths(fit.med, whatLabels = 'est', edge.label.cex = 2) +``` + +## Latent Growth Curve example + +This is a short simulated example I created: + +We simulate some data where there are 5 timepoints. The mean intercept value is 2, the mean slope value is 0.7. The variance for the intercept is 1 and the variance for the slope is 0.5^2=0.25. The residual variance at each timepoint is 0.5^2=0.25. + +```{r} +# Set seed for reproducibility +set.seed(123) + +# Simulate data for latent growth curve model +n <- 500 # sample size +t <- 5 # number of time points +time <- 1:t # time variable +intercept <- rnorm(n, mean = 2, sd = 1) # intercept latent variable +slope <- rnorm(n, mean = 0.7, sd = 0.5) # slope latent variable +observed_vars <- data.frame() + +for (i in 1:n) { + # Simulate observed variables for each participant + Y <- intercept[i] + slope[i] * time + rnorm(t, mean = 0, sd = 0.5) + observed_vars <- rbind(observed_vars, Y) +} +colnames(observed_vars) <- paste0("Y", time) + +``` +Now get your growth model specified. +```{r} +# Create lavaan model syntax +growth_model <- " + # latent variables + intercept =~ 1 * Y1 + 1 * Y2 + 1 * Y3 + 1 * Y4 + 1 * Y5 + slope =~ 1* Y1 + 2 * Y2 + 3* Y3 + 4 * Y4 + 5 * Y5 +" +``` + +Fit it, and look if the estimates are as we simulated them. + +```{r} +# Fit the model to the simulated data +fit.growth <- lavaan::growth(growth_model, data = observed_vars) +# Summarize the model results +summary(fit.growth) + +``` + +Great, that looks good! Now let's just finish with a plot of this model. + +```{r} +#| fig-height: 4 +#| fig-width: 7 +semPaths(fit.growth, whatLabels = "est", edge.label.cex = 1) +``` - - - - - - - - +## useful links +- [lavaan website](https://lavaan.ugent.be/) +- Descriptions of fitmeasures in SEM by David Kenny, see [here](https://davidakenny.net/cm/fit.htm). 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Practicals are walkthrough files that guide y - Basics, correlation, regression, summaries, reliability analysis: - [Lecture 1:](content/02_modelling/lecture_01.html) Basic plotting, summary, correlation and regression and model comparison. - [Practical 1:](content/02_modelling/practical_01.html) Basic plotting of data, summary, correlation and regression and model comparison. - - [Lecture 2:](content/02_modelling/lecture_01.html) Reliability analysis, Principal component analysis and exploratory factor analysis. + - [Lecture 2:](content/02_modelling/lecture_02.html) Reliability analysis, Principal component analysis and exploratory factor analysis. - [Practical 2:](content/02_modelling/practical_02.html) Practice with Reliability analysis, Principal component analysis and exploratory factor analysis. @@ -140,7 +140,5 @@ All lectures are in `html` format. Practicals are walkthrough files that guide y - lavaan: - [Lecture 1:](content/04_SEM/lecture_01.html) Intro to lavaan, CFA, modelfit, plotting your SEM models. - - [Practical 1:](content/04_SEM/practical_01.html) - - + - [Practical 1:](content/04_SEM/practical_01.html) CFA exercise, examples of mediation and latent growth curve modelling. diff --git a/index.html b/index.html index c3967d2..e0fd186 100644 --- a/index.html +++ b/index.html @@ -2066,7 +2066,7 @@

      Materials

    1. Practical 1: Basic plotting of data, summary, correlation and regression and model comparison.
      2. -
    2. Lecture 2: +
    3. Lecture 2: Reliability analysis, Principal component analysis and exploratory factor analysis.
    4. Practical 2: @@ -2110,9 +2110,9 @@

      Materials

      -
      5. +
    5. Practical 1: CFA +exercise, examples of mediation and latent growth curve modelling.
      6. +