2. Confirmatory Factor Analysis

In politics commentators often use the terms left and right to describe the ideological positions of politicians and voters, but it is not always clear what exactly these terms mean. In the United States, the political left is generally associated with favoring greater government involvement in the economy while the right is understood to favor market autonomy. Yet on moral issues such as abortion, assisted suicide, and gay marriage it is often the political right that favors a stronger regulatory role for government. Does a single dimension of values underlie Americans’ views on both economic and moral issues? Or are there in fact two distinct value dimensions driving citizen attitudes?

This example uses data from the American sample of the European Values Survey (European Values Group and World Values Survey Association, 2005) to determine whether a model with one or two common latent factors adequately describes attitudes on economic and moral issues. The survey queried a random sample of 1,200 respondents about their economic, political, and moral values. Three questions summarizing economic attitudes and three questions summarizing moral attitudes, all measured on 10-point scales, will be analyzed. The economic items asked respondents if they felt private ownership of industry should be increased (PRIVTOWN), if the government should take more responsibility to see that all people are provided for (GOVTRESP), and whether competition brings out the best or worst in people (COMPETE). The moral items asked respondents how they felt about homosexuality (HOMOSEX), legalized abortion (ABORTION), and assisted suicide (EUTHANAS).

In order to provide an example of the most basic and common approach to confirmatory factor analysis, most of this document will demonstrate examples that rely on maximum likelihood estimation (MLE). However, MLE assumes multivariate normality among the observed variables, and preliminary univariate diagnostics show strong deviations from normality for several of the variables. Alternative estimators exist for cases of non-normal data but for the most part lie outside the limited scope of this document. Section 4, however, does consider factor analysis with categorical indicators.

For this section missing data is handled by listwise deletion (all cases with missing observations on any indicator are removed). Section 3 will show an alternative approach for estimating a confirmatory factor model in the presence of missing data. Listwise deletion resulted in dropping 40 of the original 1,200 observations, leaving a sample size of 1,160. The data is saved as the SPSS file values.sav located in the folder C:\temp\CFA.