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# DISCRIMINANT FUNCTION ANALYSIS

Discriminant function analysis (DFA) is used to classify cases into categorical variables from ordinal and interval variables. For example, we may want to classify which of two (or more) groups an individual belongs to: male or female; those who have been labor migrants versus those who have not; those who are high, middle, or low income; those in favor of something and those who are not; and so on.

DFA is a statistical method developed for handling this problem. It has been around for a long time (Fisher 1936) but, like most multivariate techniques, DFA has become more popular since user-friendly computer programs have made it easier to do.

Lambros Comitas and I used DFA in our study of two groups of people in Athens, Greece: those who had returned from having spent at least 5 years in West Germany as labor migrants and those who had never been out of Greece. We were trying to understand how the experience abroad might have affected the attitudes of Greek men and women about traditional gender roles (Bernard and Comitas 1978). Our sample consisted of 400 persons: 100 male migrants, 100 female migrants, 100 male nonmigrants, and 100 female nonmigrants. Using DFA, we were able to predict with 70% accuracy whether an informant had been a migrant on the basis of just five variables.

There are some things you need to be careful about in using DFA, however. Notice that our sample in the Athens study consisted of half migrants and half nonmigrants. That was because we used a disproportionate, stratified sampling design to ensure adequate representation of returned migrants in the study. Given our sample, we could have guessed whether one of our informants was a migrant with 50% accuracy, without any information about the informant at all.

Only a very small fraction of the population of Athens consists of former long-term labor migrants to West Germany. The chances of stopping an Athenian at random on the street and grabbing one of those returned labor migrants was less than 5% in 1977 when we did the study.

Suppose that, armed with the results of the DFA that Comitas and I did, I asked random Athenians five questions, the answers to which allow me to predict 70% of the time whether any respondent had been a long-term labor migrant to West Germany. No matter what the answers were to those questions, I’d be better off predicting that the random Athenian was not a returned migrant. I’d be right more than 95% of the time.

Furthermore, why not just ask the random survey respondent straight out: ‘‘Are you a returned long-term labor migrant from West Germany?’’ With such an innocuous question, presumably I’d have gotten a correct answer at least as often as our 70% prediction based on knowing five pieces of information.

DFA is a powerful classification device, but it is not really a prediction device. Still, many problems (like the one Comitas and I studied) are essentially about understanding things so you can classify them correctly. Livingstone and Lunt (1993) surveyed 217 people in Oxford, England, and divided them into six types, based on whether or not people were in debt, whether or not people had savings, and people who live exactly within their income (with neither savings nor debt). DFA, using a variety of variables (age, class, education, income, expenses, attitudes toward debt, etc.) correctly classified almost 95% of the cases into one of the six groups that Livingstone and Lunt had identified.

Gans and Wood (1985) used DFA technique for classifying Samoan women as ‘‘traditional’’ or ‘‘modern’’ with respect to their ideal family size. If women stated that they wanted three or fewer children, Gans and Wood placed them in a category they labeled ‘‘modern.’’ Women who said they wanted four or more children were labeled ‘‘traditional.’’ DFA showed that just six of the many variables that Gans and Wood had collected allowed them to classify correctly which category a woman belonged to in 75% of all cases. The variables were such things as age, owning a car, level of education, etc.

It would have been ridiculous for Gans and Wood to have asked women straight out: ‘‘Are you traditional or modern when it comes to the number of children you’d like?’’ DFA (combined with on-the-ground ethnography) gave them a good picture of the variables that go into Samoan women’s desired family size.

Similarly, Comitas and I were able to describe the attitudinal components of gender role changes by using DFA, and our prediction rate of 70% was significantly better than the 50% we’d have gotten by chance, given our sampling design. If you’re careful about how you interpret the results of a discriminant function analysis, it can be a really important addition to your statistical tool kit.

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