Factor Analysis Anthony Sealey University of Toronto This material is distributed under an Attribution-NonCommercial-ShareAlike 3.0 Unported Creative Commons License, the full details of which may be found online here: You may re-use, edit, or redistribute the content provided that the original source is cited, it is for non- commercial purposes, and provided it is distributed under a similar license.

The key component of the construction of indexes is a reliability analysis based on standardized Cronbach’s alpha scores, which helps us to determine the extent to which potential indicators of a latent variable are a good fit with each other.

Factor Analysis __________________________ Factor Analysis falls within a broad category of methodological approaches that are useful for identifying patterns and commonalities in sets of indicators that might be conceptualized using a variety of alternative sets of concepts.

Other similar approaches include: 1) principal components analysis 2) cluster analysis 3) multidimensional scaling

Not only is factor analysis only one of a variety of comparable approaches, but there is a variety of approaches to factor analysis. We will focus on one in particular that can be a helpful complement to the identification and construction of indexes.

Instead of relying on Cronbach’s alpha to assess the extent of the fit of the indicators of each measure in isolation from other indicators of other measures, we can use factor analysis to simultaneously assess the extent to which different sets of indicators correspond to unique concepts that are identifiable in the data.

Put more simply: factor analysis allows us to simultaneously assess the degree of fit of the indicators of multiple measures.

e.g. Measures of ‘Authoritarianism’ vs. ‘Feminism’ vs. ‘Moral Traditionalism’ vs. ‘Democratic Values’.

A worked example …

Let’s try using World Values Survey data to try to determine whether ‘abortion’ is really a ‘social progressivism’ issue at all. Is it instead really a feminism issue? Perhaps we shouldn’t use it as a measure of social progressivism at all?

Recall that because of data availability, we’re confined to one measure of feminism. Let’s use a varimax rotated factor analysis to determine whether abortion fits better with the feminist dimension or the other social progressivism indicators.

To do so we can use this SPSS code: factor /variables socprogin1 socprogin2 socprogin3 femism1 /print initial det kmo repr extraction rotation fscore univaratiate /format blank(0.20) /criteria factors(2) /extraction paf /rotation varimax.

To do so we can use this SPSS code: factor /variables socprogin1 socprogin2 socprogin3 femism1 /print initial det kmo repr extraction rotation fscore univaratiate /format blank(0.20) /criteria factors(2) /extraction paf /rotation varimax. here we ask the program to include these variables

To do so we can use this SPSS code: factor /variables socprogin1 socprogin2 socprogin3 femism1 /print initial det kmo repr extraction rotation fscore univaratiate /format blank(0.20) /criteria factors(2) /extraction paf /rotation varimax. here we ask the program to ignore any factor loadings less than 0.20

To do so we can use this SPSS code: factor /variables socprogin1 socprogin2 socprogin3 femism1 /print initial det kmo repr extraction rotation fscore univaratiate /format blank(0.20) /criteria factors(2) /extraction paf /rotation varimax. here we ask the program to locate exactly two factors for us

In this case the key output to look for is the ‘rotated factor matrix’: here we see that our three indicators load best together on the first factor

In this case the key output to look for is the ‘rotated factor matrix’: while this blank indicates that femism1 does not fit well with these indicators

In this case the key output to look for is the ‘rotated factor matrix’: but notice that ‘socprog1’ also loads nearly as highly on the second factor with ‘femism1’

Interestingly, ‘socprog1’ is not the indicator for outlooks on abortion. abortion indicator is ‘socprog3’

What have we learned? 1)That the indicator of outlooks on abortion clearly fits better with our other indicators of social progressivism than with the feminism indicator.

What have we learned? 2)That if anything, the social progressivism indicator that fits the best with our feminist indicator is the indicator of attitudes towards homosexuality (socprog1).

Assignment Three ______________________ Building Measures

Finally! ______________________ A focus on course objective #3: Developing a marked level of expertise with one key data set.

Choosing a Data Set: Webstats vs. SPSS vs. R

Key Fields in Political Science (and Public Policy) __________________________ 1) Canadian Politics 2) Comparative Politics 3) Development Politics 4) International Relations 5) Political Theory

Exercise Objectives __________________________ 1) To identify and meet colleagues who share common academic interests. 2) To begin to discuss and decide upon which key data sets that members of your field group will develop a marked level of expertise with.

Field Group Placement __________________________ Canada Group _____________________________ IR Group _____________________________ Developing Group _____________________________ Comparative Group _____________________________ Theory Group _____________________________

Exercise Objectives __________________________ 1) To identify and meet colleagues who share common academic interests. 2) To begin to discuss and decide upon which key data sets that members of your field group will develop a marked level of expertise with.