3.4 CFA with Missing Data using Mplus
After launching Mplus a screen displaying the Mplus syntax editor appears. Unlike Amos and LISREL, Mplus cannot directly read an SPSS file. Instead, raw data must be saved as an ASCII file in free or fixed format. If a file is saved in free format Mplus does not understand blanks to be missing. A number code must be entered in the raw data and specified to mean missing in the Mplus syntax. Open SPSS, choose File → New → Syntax, and enter the following in the SPSS Syntax Editor window:
privtown govtresp compete homosex abortion euthanas (SYSMIS=-1)
SAVE TRANSLATE OUTFILE='c:\temp\CFA\values.dat'
/TYPE=TAB /MAP /REPLACE.
This syntax recodes missing values as -1 and writes a tab-delimited text file to the C:\temp\CFA directory.
The Mplus syntax for the confirmatory factor model to be tested is the following:
TITLE: Two Factor Model with Missing Data;
DATA FILE IS values_full.dat;
VARIABLE: NAMES ARE privtown govtresp compete
homosex abortion euthanas;
ANALYSIS: TYPE = missing h1
MODEL: economic BY privtown govtresp compete;
morals BY homosex abortion euthanas govtresp;
The TITLE line provides a short description for the analysis. The DATA statement specifies the pathname for the tab-delimited raw data file to be analyzed. The NAMES ARE portion of the VARIABLE statement lists the names of the variables in the order they appear in the data file. The MISSING ARE option tells Mplus to interpret the value -1 as missing for all variables. The TYPE = missing option to the ANALYSIS statement tells Mplus to use an estimator appropriate for the presence of missing data, and the h1 requests a chi-square statistic for model fit. Convergence may be very slow for models with many parameters and missing data if a χ2 test is requested, and in such cases the h1 may be excluded. The MODEL statement tells Mplus that there are two latent predictor variables and six outcome variables. The OUTPUT statement here requests that standardized estimates and modification indices appear in the output file. See section 2.4 above for additional information on the rules of Mplus syntax.
To begin the estimation, click on Run
. A text output file appears and is saved in the working directory. For this model, the file is the following:
The overall model fit appears quite good. The χ2 test yields a value of 7.409 (df=7), which has a corresponding p-value of .388. This p-value is too high to reject the null of a good fit. Additionally, the RMSEA is only .007, offering further evidence that the model fits the data well.
Under the Model Results heading, the unstandardized loadings appear along with standard errors, the ratio of the estimates to their standard errors, and two standardized estimates. The Est./S.E. column can be used to evaluate significance. If the absolute value of the number in this column is greater than 1.96 the estimate can be interpreted as significant at the .05 level. In this case all of the unconstrained estimates have Est/SE ratios greater than 1.96.
The unstandardized weights are highly sensitive to model constraints, whereas the standardized regression weights provide more intuitive information about the strength of loadings. The column StdYX is equivalent to the standardized estimates provided by Amos and LISREL. GOVTRESP has low standardized loadings on both factors (.156 for ECONOMIC and .161 for MORALS), suggesting that it is a weak indicator of both economic and moral values. However, the other indicators have moderate to strong standardized loadings. For PRIVTOWN the loading is .615, for COMPETE it is .691, for HOMOSEX it is .637, for ABORTION it is .783, and for EUTHANAS it is .667.
The squared multiple correlations provide information on how much variance the factors account for in the observed variables. Despite receiving a path from both latent variables, GOVTRESP has a very low R2 of only .050. The remaining R2 statistics are, in order of increasing magnitude, PRIVTOWN (.378), HOMOSEX (.406), EUTHANAS (.445), COMPETE (.478), and ABORTION (.614). Finally, the correlation between the two common factors is a very small -.018, and the covariance estimate of -.050 is not statistically distinguishable from zero.