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--- mediation_analysis [2024/10/31 08:52] – [Poking the above] hkimscil
+++ mediation_analysis [2024/11/03 22:37] (current) – [What about this output] hkimscil
@@ Line 861: / Line 861: @@
 그 외의 지수는?
 어떤 모델이 지금의 현상을 가장 잘 설명하는다고 판단하는가?
+  * Model fit
+    * Chi-square Test: p-value less than p-critical value (.05 for example) indicates that model does not fit well enough. p-value more than critical value means the model fits the data relatively well. The test is sensitive to the sample size and normality of the data.
+    * CFI (Comparative Fit Index): greater than .90 indicates good fit to the data. It is less sensitive to the sample size and normality of the data than chi-square test.
+    * TLI (Tucker-Lewis Index): greater than .95 (sometimes .90) indicates good fit. It is less sensitive to the sample size.
+    * RMSEA (Root Mean Square Error of Approximation): equal to or less than .08 (sometimes .10 is used) indicates good fit to the data.
+    * SRMR (Standard Root Mean square Residual): less than or equal to .08 indicates good fit to the data.
+| $\chi^2$  | $\text{CFI}$  | $\text{TLI}$  | $\text{RMSEA}$  | $\text{SRMR}$   |
+| $p \ge .05$  | $p \ge .90$  | $p \ge .95$  | $p \le .08$  | $p \le .08$  |
+Then what is SEM (Structural Equation Modeling)
+  * Relationships within and among variables and constructs
@@ Line 973: / Line 987: @@
 </code>
+====== e.g. with a categorical variable ======
+<code>
+# regression with job placement data
+df <- read.csv("http://commres.net/wiki/_media/r/plannedbehavior.csv")
+head(df)
+df<- within(df, {
+  norms.cat <- NA # need to initialize variable
+  norms.cat[norms < tmp[2]] <- "Low"
+  norms.cat[norms >= tmp[2] & norms < tmp[3]] <- "Middle"
+  norms.cat[norms >= tmp[3]] <- "High"
+} )
+head(df)
+med.m.01 <- '
+    # mediator
+    intention ~ a*attitude
+    behavior ~ b*intention
+    # direct effect c
+    behavior ~ c*attitude
+    # indirect effect
+    ab := a*b
+    # total effect
+    tot := c + ab
+    '
+fit <- sem(med.m.01, data = df,
+           meanstructure = T,
+           se = "boot", bootstrap = 500)
+summary(fit, fit.measures = T,
+        standardized = T,
+        ci = T)
+###
+mod.m.02 <- '
+    # mediator
+    intention ~ c(ag1,ag2,ag3)*attitude
+    behavior ~ c(bg1,bg2,bg3)*intention
+    # direct effect
+    behavior ~ c(cg1,cg2,cg3)*attitude
+    # indirect effect
+    abg1 := ag1*bg1 # for group 1
+    abg2 := ag2*bg2
+    abg3 := ag3*bg3
+    # tot effect
+    totalg1 := cg1 + (ag1*bg1)
+    totalg2 := cg2 + (ag2*bg2)
+    totalg3 := cg3 + (ag3*bg3)
+'
+fit.by.norms.cat <- sem(mod.m.02, data = df,
+                        group = "norms.cat",
+                        se = "boot", bootstrap = 500,
+                        meanstructure = T)
+summary(fit.by.norms.cat,
+        fit.measures = T,
+        standardized = T,
+        ci = T)
+all.constraints <- '
+    ag1 == ag2 == ag3
+    bg1 == bg2 == bg3
+    cg1 == cg2 == cg3
+'
+lavTestWald(fit.by.norms.cat,
+            constraints = all.constraints)
+lavTestWald(fit.by.norms.cat,
+            constraints = "ag1==ag2==ag3")
+lavTestWald(fit.by.norms.cat,
+            constraints = "bg1==bg2==bg3")
+lavTestWald(fit.by.norms.cat,
+            constraints = "cg1==cg2==cg3")
+# or
+full.mod.mediation <- '
+    # mediator
+    intention ~ a*attitude
+    behavior ~ b*intention + w*norms.cat
+    # define moderator
+    Z := w*b
+    # direct effect
+    behavior ~ c*attitude
+    # indirect effect
+    ab := a*b
+    # tot effect
+    total := c + (a*b)
+'
+full.mod <- sem (full.mod.mediation, data = df,
+                 se = "boot", bootstrap = 500,
+                 meanstructure = T)
+summary(full.mod, fit.measures = T,
+        stand = T, ci = T)
+</code>
 ====== e.gs ======
 <code>