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r:path_analysis [2022/11/15 13:00] – hkimscilr:path_analysis [2024/11/04 10:28] (current) – [Introduction] hkimscil
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 ====== Path Analysis ====== ====== Path Analysis ======
-===== Lavaan 2 ===== +{{:r:pasted:20230529-234519.png}} 
- +====== Introduction ======
- +
-{{youtube>_tTPHt4cPwI}} +
-<code> +
-model <- ' +
-    # labeling path from mastery to interest +
-    interest ~ a*mastery + perfgoal + ses +
- +
-    # labeling path from interest to achieve.  +
-    # Adding labeled path from +
-    # mastery to achieve +
-    achieve ~ e*anxiety + b*interest + c*mastery +
-     +
-    # predicting anxiety and labeling path from mastery +
-    anxiety ~ perfgoal + d*mastery +
-    # estimtating the variances and covariances of  +
-    # the exogenous variables (ses, mastery,performance) +
-    mastery~~mastery +
-    perfgoal~~perfgoal +
-    ses~~ses +
- +
-    mastery~~perfgoal+ses +
-    perfgoal~~ses +
- +
-    # estimating the variances of residuals  +
-    # for endogenous variables  +
-    # (interest, anxiety, achieve) +
-    interest~~interest +
-    anxiety~~anxiety +
-    achieve~~achieve +
- +
-    # estimating the covariance of residuals  +
-    # for interest and anxiety +
-    interest~~anxiety +
-    # calculating specific indirect effect  +
-    # of mastery on achieve via interest +
-    SIE1:=a*b +
-    # calculating specific indirect effect of  +
-    # mastery on achieve via anxiety +
-    SIE2:=d*e +
-    # calculating total indirect effect of  +
-    # mastery on achievement via mediators +
-    TIE:=SIE1+SIE2 +
-    # calculating total effect of mastery on achieve +
-    TE:=TIE+c' +
-     +
-    # using naive bootstrap to obtain standard errors +
-    fit <- sem(model, data=processdata, se="bootstrap") +
-    summary(fit,fit.measures=TRUE) +
-     +
-    # using 'parameterEstimates' function will give  +
-    # us confidence intervals based on naive bootstrap.  +
-    # A standard approach to testing indirect effects. +
-    parameterEstimates(fit) +
- +
-</code> +
----- +
-===== Lavaan 3: Testing data normality ===== +
- +
-{{youtube>HvYW_GeHpD8}} +
-<code> +
-processdata <- read.csv("http://commres.net/wiki/_media/r/path_analysis_datan_binw.csv") +
-str(processdata) +
-# install.packages("MVN") +
-library(MVN) +
-newdata <- processdata[c("achieve", "interest", "anxiety")] +
-str(newdata) +
-</code> +
-Use the 'mvn' function to evalue normality +
- +
-Multivariate normality is evidenced by p-values associated with multivariate skewness and kurtosis statistics that are > .05. In those cases where both the skewness and kurtosis results are non-significant (p's > .05), then the data are assumed to follow a multivariate normal distribution where p > .05 (Korkmaz, Goksuluk, & Zarasiz, 2014, 2019).  +
- +
-You can also use plots to explore possible multivariate outliers. Moreover, you can examine univariate tests of normality (the default is Shapiro-Wilk test, but can be changed if desired). A significant test result regarding a specific variable indicates a significant departure from normality.  +
-<code> +
-mvn(newdata, mvnTest="mardia") +
-mvn(newdata, multivariatePlot="qq") +
-mvn(newdata, multivariateOutlierMethod="quan") +
-</code> +
- +
-You can generate univariate plot as well to evaluate distribution of the endogenous variables for non-normality. Skewness values approaching 2 or kurtoisis values over 7 may be considered indicative of more "significant problems" with non-normality (Curran, et al., 1996).  +
-<code> +
-mvn(newdata, univariatePlot="histogram") +
-mvn(newdata, univariatePlot="box") +
- +
-model <- ' +
-    interest ~ mastery + perfgoal + ses  +
-    achieve ~ anxiety + interest + mastery  +
-    anxiety ~ perfgoal + mastery  +
-    # variances +
-    mastery ~~ mastery +
-    perfgoal ~~ perfgoal +
-    ses ~~ ses +
-     +
-    mastery ~~ perfgoal + ses +
-    perfgoal ~~ ses +
-     +
-    interest ~~ interest +
-    anxiety ~~ anxiety +
-    achieve ~~ achieve +
-    interest~~anxiety  +
-' +
-</code> +
-We will fit the model using the 'estimator' argument at set it equal to "MLM." This will result in the Satorra-Bentler model chi-square being computed. We will also use the 'se' argument and set it to "roburst." +
-<code> +
-fit <- sem(model, data=processdata, estimator = "MLM", se="roburst") +
-summary(fit,fit.measures=TRUE) +
-</code> +
----- +
-reference +
-{{youtube>8r9bUKUVecc?small}} +
- +
-see [[https://www.rensvandeschoot.com/tutorials/lme4/|lme4 tutorial]] +
- +
-====== Path Analysis 2 ======+
 {{youtube>UGIVPtFKwc0}} {{youtube>UGIVPtFKwc0}}
  
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     * The number of unique (non-redundent) source of information     * The number of unique (non-redundent) source of information
     * $p(p+1)/2$     * $p(p+1)/2$
-    * The number of parameters (paths) specified in model +  * The number of parameters (paths) specified in model 
-  * Just-identified (df = 0) +    * Just-identified (df = 0) 
-    * Model can be estimated, but cannot be assessed +      * Model can be estimated, but cannot be assessed 
-  * Over-identified (df > 0) +    * Over-identified (df > 0) 
-    * Model can be estimated and assessed +      * Model can be estimated and assessed 
-  * Under-identified (df < 0) +    * Under-identified (df < 0) 
-    * Model cannot be either estimated or assessed+      * Model cannot be either estimated or assessed
  
   * Exogenous and    * Exogenous and 
Line 224: Line 111:
 </code> </code>
  
 +----
 +<code>
 +# my own 
 +# pbt model 
 +specmod5 <- '
 +    # Directional relations (path)
 +    intention ~ a*attitude + b*norms + c*control
 +    behavior ~ d*intention 
 +    # Covariances 
 +    attitude ~~ norms + control
 +    norms ~~ control    
 +    ad := a*d
 +    bd := b*d
 +    cd := c*d
 +'
 +fitmod5 <- sem(specmod5, data=df)
 +summary(fitmod5, fit.measures=TRUE, rsquare=TRUE)
 +</code>
 ====== Output ====== ====== Output ======
 <code> <code>
Line 553: Line 458:
  
 </code> </code>
-===== Lavaan in R: explanation =====+===== specmod5 ===== 
 +<code> 
 +> specmod5 <- " 
 ++     # Directional relations (path) 
 ++     intention ~ attitude + norms + control 
 ++     behavior ~ intention + norms 
 ++     # Covariances  
 ++     attitude ~~ norms + control 
 ++     norms ~~ control     
 ++ " 
 +> fitmod5 <- sem(specmod5, data=df) 
 +> summary(fitmod5, fit.measures=TRUE, rsquare=TRUE) 
 +lavaan 0.6-12 ended normally after 18 iterations
  
 +  Estimator                                         ML
 +  Optimization method                           NLMINB
 +  Number of model parameters                        13
 +
 +  Number of observations                           199
 +
 +Model Test User Model:
 +                                                      
 +  Test statistic                                 1.781
 +  Degrees of freedom                                 2
 +  P-value (Chi-square)                           0.410
 +
 +Model Test Baseline Model:
 +
 +  Test statistic                               182.295
 +  Degrees of freedom                                10
 +  P-value                                        0.000
 +
 +User Model versus Baseline Model:
 +
 +  Comparative Fit Index (CFI)                    1.000
 +  Tucker-Lewis Index (TLI)                       1.006
 +
 +Loglikelihood and Information Criteria:
 +
 +  Loglikelihood user model (H0)              -1258.396
 +  Loglikelihood unrestricted model (H1)      -1257.506
 +                                                      
 +  Akaike (AIC)                                2542.792
 +  Bayesian (BIC)                              2585.605
 +  Sample-size adjusted Bayesian (BIC)         2544.421
 +
 +Root Mean Square Error of Approximation:
 +
 +  RMSEA                                          0.000
 +  90 Percent confidence interval - lower         0.000
 +  90 Percent confidence interval - upper         0.136
 +  P-value RMSEA <= 0.05                          0.569
 +
 +Standardized Root Mean Square Residual:
 +
 +  SRMR                                           0.018
 +
 +Parameter Estimates:
 +
 +  Standard errors                             Standard
 +  Information                                 Expected
 +  Information saturated (h1) model          Structured
 +
 +Regressions:
 +                   Estimate  Std.Err  z-value  P(>|z|)
 +  intention ~                                         
 +    attitude          0.352    0.058    6.068    0.000
 +    norms             0.153    0.059    2.577    0.010
 +    control           0.275    0.058    4.740    0.000
 +  behavior ~                                          
 +    intention         0.443    0.068    6.525    0.000
 +    norms             0.034    0.068    0.493    0.622
 +
 +Covariances:
 +                   Estimate  Std.Err  z-value  P(>|z|)
 +  attitude ~~                                         
 +    norms             0.200    0.064    3.128    0.002
 +    control           0.334    0.070    4.748    0.000
 +  norms ~~                                            
 +    control           0.220    0.065    3.411    0.001
 +
 +Variances:
 +                   Estimate  Std.Err  z-value  P(>|z|)
 +   .intention         0.530    0.053    9.975    0.000
 +   .behavior          0.698    0.070    9.975    0.000
 +    attitude          0.928    0.093    9.975    0.000
 +    norms             0.830    0.083    9.975    0.000
 +    control           0.939    0.094    9.975    0.000
 +
 +R-Square:
 +                   Estimate
 +    intention         0.369
 +    behavior          0.199
 +
 +</code>
 +
 +===== Lavaan in R: explanation =====
 {{youtube>QP-v6RwsZjY?start=251}} {{youtube>QP-v6RwsZjY?start=251}}
 Path analysis in R with Lavaan (introduction) Path analysis in R with Lavaan (introduction)
Line 572: Line 572:
  
 <code> <code>
-processdata<-read.csv("path analysis dataN BinW.csv", header=TRUE, sep=",")+# processdata<-read.csv("path analysis dataN BinW.csv", header=TRUE, sep=",") 
 +processdata<-read.csv("http://commres.net/wiki/_media/r/path_analysis_datan_binw.csv",  
 +                       header=TRUE, sep=",", fileEncoding="UTF-8-BOM")
 </code> </code>
  
Line 630: Line 632:
   * Step 2: Use 'lavaan' function to run analysis. Here, I will be saving  the results in an R object called 'fit' (arbitrarily named). Inside  the parenthesis are arguments separated by commas. The first argument contains the name of the object containing the model syntax (see above). The object is named 'model' (again, arbitrarily named above). Next, we have the 'data' argument. This identifies the object (i.e., data frame)  containing the raw data.    * Step 2: Use 'lavaan' function to run analysis. Here, I will be saving  the results in an R object called 'fit' (arbitrarily named). Inside  the parenthesis are arguments separated by commas. The first argument contains the name of the object containing the model syntax (see above). The object is named 'model' (again, arbitrarily named above). Next, we have the 'data' argument. This identifies the object (i.e., data frame)  containing the raw data. 
 <code> <code>
-fit<-lavaan(model,data=processdata)+fit<-lavaan(model, data=processdata)
 </code> </code>
   * The 'summary' function can be used to obtain various fit measures and the parameter estimates for the model   * The 'summary' function can be used to obtain various fit measures and the parameter estimates for the model
 <code> <code>
-summary(fit,fit.measures=TRUE)+summary(fit, fit.measures=TRUE)
 </code> </code>
   * To obtain standardized estimates, use the 'standardized' argument (setting it to TRUE) when using the 'summary' function. You will need to interpret the Std.all column in the output, as it will provide standardized estimates for all measured variables in the model.   * To obtain standardized estimates, use the 'standardized' argument (setting it to TRUE) when using the 'summary' function. You will need to interpret the Std.all column in the output, as it will provide standardized estimates for all measured variables in the model.
 <code> <code>
-summary(fit,fit.measures=TRUE,standardized=TRUE,rsquare=TRUE)+summary(fit, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE)
 </code> </code>
  
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 </code> </code>
   * Note: Modification indices represent the expected decrease in model chi-square after freeing a given parameter (Schumacker & Lomax, 2004). The EPC is an estimate of the model parameter itself. A MI value of 3.84 or greater may be considered "significant" (at the .05) level. Warning: This is totally an empirically based approach to model specification. Consult your theory when using these!     * Note: Modification indices represent the expected decrease in model chi-square after freeing a given parameter (Schumacker & Lomax, 2004). The EPC is an estimate of the model parameter itself. A MI value of 3.84 or greater may be considered "significant" (at the .05) level. Warning: This is totally an empirically based approach to model specification. Consult your theory when using these!  
 +
 +output 
 +
 +<code>
 +> # install.packages("lavaan")
 +> 
 +> # processdata<-read.csv("path analysis dataN BinW.csv", header=TRUE, sep=",")
 +> processdata<-read.csv("http://commres.net/wiki/_media/r/path_analysis_datan_binw.csv", 
 ++                        header=TRUE, sep=",", fileEncoding="UTF-8-BOM")
 +> 
 +> str(processdata)
 +'data.frame': 140 obs. of  9 variables:
 + $ id      : int  1 2 3 4 5 6 7 8 9 10 ...
 + $ ses     : int  1 0 0 1 1 1 0 0 1 1 ...
 + $ genderid: int  1 0 1 1 1 1 0 0 0 0 ...
 + $ perfgoal: num  29.5 29.5 30.4 33.5 28.7 ...
 + $ achieve : num  6.12 1.62 4.5 2.38 5.12 ...
 + $ mastery : num  5.71 1.43 1.29 2.29 4.57 ...
 + $ interest: num  6 4 2 4 5.5 4 4 5 4.5 4 ...
 + $ anxiety : num  1.67 6.33 3.67 3.67 3.67 ...
 + $ pgoal_MS: int  0 0 1 1 0 1 0 1 0 0 ...
 +> library(lavaan)
 +> 
 +> # model specification
 +> model <- '
 ++   # equation where interest is predicted by ses 
 ++   # & mastery and performance goals
 ++   interest ~ mastery + perfgoal + ses
 ++   
 ++   # equation where achieve is predicted by 
 ++   # interest and anxiety
 ++   achieve ~ anxiety + interest + mastery
 ++ 
 ++   # equation where anxiety is predicted 
 ++   # by mastery and performance goals
 ++   anxiety ~ perfgoal + mastery
 ++ 
 ++   # estimating the variances of 
 ++   # the exogenous variables (ses, mastery,performance)
 ++   mastery ~~ mastery
 ++   perfgoal ~~ perfgoal
 ++   ses ~~ ses
 ++ 
 ++   # estimtating the covariances of the exogenous 
 ++   # variables (ses, mastery,performance)
 ++   mastery ~~ perfgoal + ses
 ++   perfgoal ~~ ses
 ++ 
 ++   # estimating the residual variances 
 ++   # for endogenous variables (interest, anxiety, achieve)
 ++   interest ~~ interest
 ++   anxiety ~~ anxiety
 ++   achieve ~~ achieve
 ++ 
 ++   # estimating the covariance of residuals 
 ++   # for interest and anxiety
 ++   interest ~~ anxiety '
 +> 
 +> fit<-lavaan(model, data=processdata)
 +> summary(fit, fit.measures=TRUE)
 +lavaan 0.6.16 ended normally after 27 iterations
 +
 +  Estimator                                         ML
 +  Optimization method                           NLMINB
 +  Number of model parameters                        18
 +
 +  Number of observations                           140
 +
 +Model Test User Model:
 +                                                      
 +  Test statistic                                29.231
 +  Degrees of freedom                                 3
 +  P-value (Chi-square)                           0.000
 +
 +Model Test Baseline Model:
 +
 +  Test statistic                               202.409
 +  Degrees of freedom                                15
 +  P-value                                        0.000
 +
 +User Model versus Baseline Model:
 +
 +  Comparative Fit Index (CFI)                    0.860
 +  Tucker-Lewis Index (TLI)                       0.300
 +
 +Loglikelihood and Information Criteria:
 +
 +  Loglikelihood user model (H0)              -1391.274
 +  Loglikelihood unrestricted model (H1)      -1376.659
 +                                                      
 +  Akaike (AIC)                                2818.548
 +  Bayesian (BIC)                              2871.498
 +  Sample-size adjusted Bayesian (SABIC)       2814.548
 +
 +Root Mean Square Error of Approximation:
 +
 +  RMSEA                                          0.250
 +  90 Percent confidence interval - lower         0.172
 +  90 Percent confidence interval - upper         0.336
 +  P-value H_0: RMSEA <= 0.050                    0.000
 +  P-value H_0: RMSEA >= 0.080                    1.000
 +
 +Standardized Root Mean Square Residual:
 +
 +  SRMR                                           0.074
 +
 +Parameter Estimates:
 +
 +  Standard errors                             Standard
 +  Information                                 Expected
 +  Information saturated (h1) model          Structured
 +
 +Regressions:
 +                   Estimate  Std.Err  z-value  P(>|z|)
 +  interest ~                                          
 +    mastery           0.708    0.088    8.066    0.000
 +    perfgoal         -0.035    0.040   -0.879    0.380
 +    ses               0.520    0.242    2.154    0.031
 +  achieve ~                                           
 +    anxiety          -0.040    0.054   -0.747    0.455
 +    interest          0.211    0.060    3.527    0.000
 +    mastery           0.345    0.079    4.358    0.000
 +  anxiety ~                                           
 +    perfgoal          0.025    0.045    0.556    0.578
 +    mastery          -0.387    0.097   -4.009    0.000
 +
 +Covariances:
 +                   Estimate  Std.Err  z-value  P(>|z|)
 +  mastery ~~                                          
 +    perfgoal         -0.935    0.361   -2.590    0.010
 +    ses               0.170    0.061    2.805    0.005
 +  perfgoal ~~                                         
 +    ses              -0.226    0.128   -1.768    0.077
 + .interest ~~                                         
 +   .anxiety           0.059    0.181    0.329    0.742
 +
 +Variances:
 +                   Estimate  Std.Err  z-value  P(>|z|)
 +    mastery           1.944    0.232    8.367    0.000
 +    perfgoal          8.936    1.068    8.367    0.000
 +    ses               0.249    0.030    8.367    0.000
 +   .interest          1.895    0.227    8.367    0.000
 +   .anxiety           2.410    0.288    8.367    0.000
 +   .achieve           0.988    0.118    8.367    0.000
 +
 +> summary(fit, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE)
 +lavaan 0.6.16 ended normally after 27 iterations
 +
 +  Estimator                                         ML
 +  Optimization method                           NLMINB
 +  Number of model parameters                        18
 +
 +  Number of observations                           140
 +
 +Model Test User Model:
 +                                                      
 +  Test statistic                                29.231
 +  Degrees of freedom                                 3
 +  P-value (Chi-square)                           0.000
 +
 +Model Test Baseline Model:
 +
 +  Test statistic                               202.409
 +  Degrees of freedom                                15
 +  P-value                                        0.000
 +
 +User Model versus Baseline Model:
 +
 +  Comparative Fit Index (CFI)                    0.860
 +  Tucker-Lewis Index (TLI)                       0.300
 +
 +Loglikelihood and Information Criteria:
 +
 +  Loglikelihood user model (H0)              -1391.274
 +  Loglikelihood unrestricted model (H1)      -1376.659
 +                                                      
 +  Akaike (AIC)                                2818.548
 +  Bayesian (BIC)                              2871.498
 +  Sample-size adjusted Bayesian (SABIC)       2814.548
 +
 +Root Mean Square Error of Approximation:
 +
 +  RMSEA                                          0.250
 +  90 Percent confidence interval - lower         0.172
 +  90 Percent confidence interval - upper         0.336
 +  P-value H_0: RMSEA <= 0.050                    0.000
 +  P-value H_0: RMSEA >= 0.080                    1.000
 +
 +Standardized Root Mean Square Residual:
 +
 +  SRMR                                           0.074
 +
 +Parameter Estimates:
 +
 +  Standard errors                             Standard
 +  Information                                 Expected
 +  Information saturated (h1) model          Structured
 +
 +Regressions:
 +                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 +  interest ~                                                            
 +    mastery           0.708    0.088    8.066    0.000    0.708    0.558
 +    perfgoal         -0.035    0.040   -0.879    0.380   -0.035   -0.060
 +    ses               0.520    0.242    2.154    0.031    0.520    0.147
 +  achieve ~                                                             
 +    anxiety          -0.040    0.054   -0.747    0.455   -0.040   -0.053
 +    interest          0.211    0.060    3.527    0.000    0.211    0.294
 +    mastery           0.345    0.079    4.358    0.000    0.345    0.379
 +  anxiety ~                                                             
 +    perfgoal          0.025    0.045    0.556    0.578    0.025    0.045
 +    mastery          -0.387    0.097   -4.009    0.000   -0.387   -0.327
 +
 +Covariances:
 +                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 +  mastery ~~                                                            
 +    perfgoal         -0.935    0.361   -2.590    0.010   -0.935   -0.224
 +    ses               0.170    0.061    2.805    0.005    0.170    0.244
 +  perfgoal ~~                                                           
 +    ses              -0.226    0.128   -1.768    0.077   -0.226   -0.151
 + .interest ~~                                                           
 +   .anxiety           0.059    0.181    0.329    0.742    0.059    0.028
 +
 +Variances:
 +                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 +    mastery           1.944    0.232    8.367    0.000    1.944    1.000
 +    perfgoal          8.936    1.068    8.367    0.000    8.936    1.000
 +    ses               0.249    0.030    8.367    0.000    0.249    1.000
 +   .interest          1.895    0.227    8.367    0.000    1.895    0.606
 +   .anxiety           2.410    0.288    8.367    0.000    2.410    0.884
 +   .achieve           0.988    0.118    8.367    0.000    0.988    0.613
 +
 +R-Square:
 +                   Estimate
 +    interest          0.394
 +    anxiety           0.116
 +    achieve           0.387
 +
 +> 
 +> parameterEstimates(fit)
 +        lhs op      rhs    est    se      z pvalue ci.lower ci.upper
 +1  interest  ~  mastery  0.708 0.088  8.066  0.000    0.536    0.880
 +2  interest  ~ perfgoal -0.035 0.040 -0.879  0.380   -0.114    0.043
 +3  interest  ~      ses  0.520 0.242  2.154  0.031    0.047    0.994
 +4   achieve  ~  anxiety -0.040 0.054 -0.747  0.455   -0.146    0.066
 +5   achieve  ~ interest  0.211 0.060  3.527  0.000    0.094    0.328
 +6   achieve  ~  mastery  0.345 0.079  4.358  0.000    0.190    0.500
 +7   anxiety  ~ perfgoal  0.025 0.045  0.556  0.578   -0.063    0.113
 +8   anxiety  ~  mastery -0.387 0.097 -4.009  0.000   -0.576   -0.198
 +9   mastery ~~  mastery  1.944 0.232  8.367  0.000    1.488    2.399
 +10 perfgoal ~~ perfgoal  8.936 1.068  8.367  0.000    6.842   11.029
 +11      ses ~~      ses  0.249 0.030  8.367  0.000    0.191    0.308
 +12  mastery ~~ perfgoal -0.935 0.361 -2.590  0.010   -1.642   -0.227
 +13  mastery ~~      ses  0.170 0.061  2.805  0.005    0.051    0.288
 +14 perfgoal ~~      ses -0.226 0.128 -1.768  0.077   -0.476    0.024
 +15 interest ~~ interest  1.895 0.227  8.367  0.000    1.451    2.339
 +16  anxiety ~~  anxiety  2.410 0.288  8.367  0.000    1.845    2.974
 +17  achieve ~~  achieve  0.988 0.118  8.367  0.000    0.757    1.220
 +18 interest ~~  anxiety  0.059 0.181  0.329  0.742   -0.295    0.414
 +> fitMeasures(fit)
 +                 npar                  fmin                 chisq 
 +               18.000                 0.104                29.231 
 +                   df                pvalue        baseline.chisq 
 +                3.000                 0.000               202.409 
 +          baseline.df       baseline.pvalue                   cfi 
 +               15.000                 0.000                 0.860 
 +                  tli                  nnfi                   rfi 
 +                0.300                 0.300                 0.278 
 +                  nfi                  pnfi                   ifi 
 +                0.856                 0.171                 0.868 
 +                  rni                  logl     unrestricted.logl 
 +                0.860             -1391.274             -1376.659 
 +                  aic                   bic                ntotal 
 +             2818.548              2871.498               140.000 
 +                 bic2                 rmsea        rmsea.ci.lower 
 +             2814.548                 0.250                 0.172 
 +       rmsea.ci.upper        rmsea.ci.level          rmsea.pvalue 
 +                0.336                 0.900                 0.000 
 +       rmsea.close.h0 rmsea.notclose.pvalue     rmsea.notclose.h0 
 +                0.050                 1.000                 0.080 
 +                  rmr            rmr_nomean                  srmr 
 +                0.122                 0.122                 0.074 
 +         srmr_bentler   srmr_bentler_nomean                  crmr 
 +                0.074                 0.074                 0.088 
 +          crmr_nomean            srmr_mplus     srmr_mplus_nomean 
 +                0.088                 0.074                 0.074 
 +                cn_05                 cn_01                   gfi 
 +               38.428                55.335                 0.941 
 +                 agfi                  pgfi                   mfi 
 +                0.587                 0.134                 0.911 
 +                 ecvi 
 +                0.466 
 +> modificationIndices(fit)
 +        lhs op      rhs     mi    epc sepc.lv sepc.all sepc.nox
 +19 interest ~~  achieve 25.396 -2.899  -2.899   -2.118   -2.118
 +23  achieve ~~  anxiety  6.669  6.803   6.803    4.408    4.408
 +24  achieve ~~  mastery 22.476 -1.743  -1.743   -1.257   -1.257
 +25  achieve ~~ perfgoal  2.763 -0.406  -0.406   -0.137   -0.137
 +26  achieve ~~      ses 20.541  0.186   0.186    0.376    0.376
 +27  anxiety ~~  mastery  0.921  0.765   0.765    0.354    0.354
 +28  anxiety ~~ perfgoal  0.921 -3.576  -3.576   -0.771   -0.771
 +29  anxiety ~~      ses  0.921 -0.061  -0.061   -0.078   -0.078
 +30 interest  ~  achieve 25.396 -2.933  -2.933   -2.106   -2.106
 +32  achieve  ~ perfgoal  4.551 -0.062  -0.062   -0.146   -0.146
 +33  achieve  ~      ses 22.431  0.837   0.837    0.329    0.329
 +34  anxiety  ~ interest  0.921 -0.502  -0.502   -0.538   -0.538
 +35  anxiety  ~  achieve  1.119  1.922   1.922    1.478    1.478
 +36  anxiety  ~      ses  0.921 -0.261  -0.261   -0.079   -0.079
 +37  mastery  ~ interest  0.923 12.889  12.889   16.348   16.348
 +38  mastery  ~  achieve 22.801 -1.774  -1.774   -1.616   -1.616
 +39  mastery  ~  anxiety  0.921  0.318   0.318    0.376    0.376
 +43 perfgoal  ~  achieve  2.745 -0.410  -0.410   -0.174   -0.174
 +44 perfgoal  ~  anxiety  0.921 -1.484  -1.484   -0.820   -0.820
 +47      ses  ~ interest  0.923 -1.021  -1.021   -3.618   -3.618
 +48      ses  ~  achieve 20.964  0.190   0.190    0.484    0.484
 +49      ses  ~  anxiety  0.921 -0.025  -0.025   -0.083   -0.083
 +> 
 +> 
 +</code>
 +
 +
  
 ----------------------------- -----------------------------
Line 688: Line 1010:
   interest~~anxiety'   interest~~anxiety'
  
-  fit<-lavaan(model,data=processdata,auto.var=TRUE) +  fit<-lavaan(model, data=processdata, auto.var=TRUE) 
-  summary(fit,fit.measures=TRUE,standardized=TRUE,rsquare=TRUE)+  summary(fit, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE)
 </code> </code>
  
Line 748: Line 1070:
 CODING  CODING 
 <code> <code>
-processdata <- read.csv("http://commres.net/wiki/_media/r/path_analysis_datan_binw.csv")+processdata<-read.csv("http://commres.net/wiki/_media/r/path_analysis_datan_binw.csv",  
 +                       header=TRUE, sep=",", fileEncoding="UTF-8-BOM")
 str(processdata) str(processdata)
 library(lavaan) library(lavaan)
Line 768: Line 1091:
     interest~~anxiety      interest~~anxiety 
 ' '
-fit <- lavaan(model. data=processdata) +fit <- lavaan(model, data=processdata) 
-fit <- sem(model. data=processdata)+fit <- sem(model, data=processdata)
  
 summary(fit, fit.measures=TRUE) summary(fit, fit.measures=TRUE)
Line 797: Line 1120:
 </code> </code>
 ---- ----
 +===== Lavaan 2 =====
 +
 +
 +{{youtube>_tTPHt4cPwI}}
 +<code>
 +model <- '
 +    # labeling path from mastery to interest
 +    interest ~ a*mastery + perfgoal + ses
 +
 +    # labeling path from interest to achieve. 
 +    # Adding labeled path from
 +    # mastery to achieve
 +    achieve ~ e*anxiety + b*interest + c*mastery
 +    
 +    # predicting anxiety and labeling path from mastery
 +    anxiety ~ perfgoal + d*mastery
 +    # estimtating the variances and covariances of 
 +    # the exogenous variables (ses, mastery,performance)
 +    mastery~~mastery
 +    perfgoal~~perfgoal
 +    ses~~ses
 +
 +    mastery~~perfgoal+ses
 +    perfgoal~~ses
 +
 +    # estimating the variances of residuals 
 +    # for endogenous variables 
 +    # (interest, anxiety, achieve)
 +    interest~~interest
 +    anxiety~~anxiety
 +    achieve~~achieve
 +
 +    # estimating the covariance of residuals 
 +    # for interest and anxiety
 +    interest~~anxiety
 +    # calculating specific indirect effect 
 +    # of mastery on achieve via interest
 +    SIE1:=a*b
 +    # calculating specific indirect effect of 
 +    # mastery on achieve via anxiety
 +    SIE2:=d*e
 +    # calculating total indirect effect of 
 +    # mastery on achievement via mediators
 +    TIE:=SIE1+SIE2
 +    # calculating total effect of mastery on achieve
 +    TE:=TIE+c'
 +    
 +    # using naive bootstrap to obtain standard errors
 +    fit <- sem(model, data=processdata, se="bootstrap")
 +    summary(fit,fit.measures=TRUE)
 +    
 +    # using 'parameterEstimates' function will give 
 +    # us confidence intervals based on naive bootstrap. 
 +    # A standard approach to testing indirect effects.
 +    parameterEstimates(fit)
 +
 +</code>
 +----
 +===== Lavaan 3: Testing data normality =====
 +
 +{{youtube>HvYW_GeHpD8}}
 +<code>
 +processdata <- read.csv("http://commres.net/wiki/_media/r/path_analysis_datan_binw.csv")
 +str(processdata)
 +# install.packages("MVN")
 +library(MVN)
 +newdata <- processdata[c("achieve", "interest", "anxiety")]
 +str(newdata)
 +</code>
 +Use the 'mvn' function to evalue normality
 +
 +Multivariate normality is evidenced by p-values associated with multivariate skewness and kurtosis statistics that are > .05. In those cases where both the skewness and kurtosis results are non-significant (p's > .05), then the data are assumed to follow a multivariate normal distribution where p > .05 (Korkmaz, Goksuluk, & Zarasiz, 2014, 2019). 
 +
 +You can also use plots to explore possible multivariate outliers. Moreover, you can examine univariate tests of normality (the default is Shapiro-Wilk test, but can be changed if desired). A significant test result regarding a specific variable indicates a significant departure from normality. 
 +<code>
 +mvn(newdata, mvnTest="mardia")
 +mvn(newdata, multivariatePlot="qq")
 +mvn(newdata, multivariateOutlierMethod="quan")
 +</code>
 +
 +You can generate univariate plot as well to evaluate distribution of the endogenous variables for non-normality. Skewness values approaching 2 or kurtoisis values over 7 may be considered indicative of more "significant problems" with non-normality (Curran, et al., 1996). 
 +<code>
 +mvn(newdata, univariatePlot="histogram")
 +mvn(newdata, univariatePlot="box")
 +
 +model <- '
 +    interest ~ mastery + perfgoal + ses 
 +    achieve ~ anxiety + interest + mastery 
 +    anxiety ~ perfgoal + mastery 
 +    # variances
 +    mastery ~~ mastery
 +    perfgoal ~~ perfgoal
 +    ses ~~ ses
 +    
 +    mastery ~~ perfgoal + ses
 +    perfgoal ~~ ses
 +    
 +    interest ~~ interest
 +    anxiety ~~ anxiety
 +    achieve ~~ achieve
 +    interest~~anxiety 
 +'
 +</code>
 +We will fit the model using the 'estimator' argument at set it equal to "MLM." This will result in the Satorra-Bentler model chi-square being computed. We will also use the 'se' argument and set it to "roburst."
 +<code>
 +fit <- sem(model, data=processdata, estimator = "MLM", se="roburst")
 +summary(fit,fit.measures=TRUE)
 +</code>
 +----
 +reference
 +{{youtube>8r9bUKUVecc?small}}
 +
 +see [[https://www.rensvandeschoot.com/tutorials/lme4/|lme4 tutorial]]
 +
 +===== Exercise =====
 +Using mtcars in R
 +<code>
 +?mtcars
 +mtcars
 +str(mtcars)
 +df <- mtcars
 +</code>
 +
 +<code>
 +# model specfication
 +model <-'
 +  mpg ~ hp + gear + cyl + disp + carb + am + wt
 +  hp ~ cyl + disp + carb
 +'
 +# model fit
 +fit <- cfa(model, data = mtcars)
 +summary(fit, fit.measures = TRUE, standardized=T, rsquare=T)
 +semPaths(fit, 'std', layout = 'circle')
 +</code>
  
r/path_analysis.1668484800.txt.gz · Last modified: 2022/11/15 13:00 by hkimscil
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