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Before fitting the PCA, we standardized the answers to each question to have variance of 1 and mean of 0.  To handle missing data, we excluded every respondent who answered only four or fewer of the 7 questions. Otherwise, missing values were imputed using the average response to a given question by other respondents in the same year.   Principle Components Analysis performs a total least squares regression on a number of variables to find the dimensions that can explain the most (or least) amount of variance in the data. Each principle component is an eigenvector of the data's covariance matrix ($D^TD$) (\[D^TD\])  and the amount of variance it explains is the corresponding eigenvalue. ## Resulting measure  The first principle component of the 7 gender questions from the GSS explained 36% of the variance in the data