Regression with Dummy Variables [Paperback]

Regression with Dummy Variables is a very useful book that includes, for most readers, more than they will ever need to know about incorporation of categorical or dummy variables into a regression equation and interpretation of the results. The book is not mathematically dense, relying heavily on verbal exposition rather than mathematics in developing its presentation. However, the author has a condensed, streamlined, no-frills writing style that enables her to present the material in a compact and rigorous manner.

For readers who have had a solid introduction to basic statistics and multiple regression analysis, the material is accessible, though some discussions, including interpretation of interaction effects involving more than one categorical variable, and categorical variables with more than two categories, require even the well prepared reader to pay very close attention and give careful consideration to the author's explanations. It's best to have a pocket calculator handy to reproduce some of the calculations just to make sure we understand what the author is doing.

It's embarrassing to have to admit, but one of the lessons I learned from Melissa Hardy's book is that, in my own work, in some instances I had been correctly interpreting interaction terms, but incorrectly interpreting corresponding main effects. Perhaps, as Berry and Feldman (1985) observe in their book Multiple Regression in Practice, many others have been making the same mistake. In any case, I've been reporting regression analysis results for nearly thirty years and until I belatedly found a technique using partial derivatives for interpreting interaction terms and their corresponding main effects, I was getting the main effects wrong (See Friedman and Necochea, 1988). Even when Friedman and Necohea's procedure enabled me to calculate the effects correctly, I didn't realize why my previous work sometimes gave misleading results. Many thanks to the author for setting me straight.

The section dealing with interaction effects tacitly raises an issue that the author, inexplicably, fails to address. Specifically construction of multiplicative interaction terms is an invitation to very high levels of multicollinearity. After all, the main effect terms used in construction of an interaction term remain in the equation after the interaction term has been added. With interval or ratio level data, grand mean centering is an effective means of dealing with what otherwise might be an intractable problem. However, grand mean centering does not have this salutary effect when working with dummy variables. As a result, if one tried to estimate the coefficients for Model 5, presented on pages 33 and 34, or Model 6, presented on pages 43 and 44, the estimates would be BLUE, but the standard errors would be enormous, the coefficient estimates would be misleadingly imprecise, and statistical power would be greatly diminished. Variance inflation factors and the condition index would be far larger than any known rule of thumb, and the equation would be, for all practical purposes, of no explanatory value.

It helps that the coefficients for Models 5 and 6 were estimated from a comparatively large sample (from information in the tables I take the sample size to be 3211), but I can't imagine a sample large enough to accommodate five or six interaction terms created with dummy variables. No, we're not talking about perfect multicollinearity, a phenomenon the author acknowledges as a consequence of failing to suppress a reference category, the so-called dummy variable trap. But I can't see how she could have avoided severe multicollinearity for Models 5 and 6.

Since we don't have access to the author's data set, we can't reproduce her results and check for ourselves. But since problems with multicollinearity are so commonplace when multiplicative interaction terms are used, I think the author has an obligation to conspicuously address this issue, especially since she rightly devotes a great deal of attention to statistical interaction. Otherwise, readers will almost certainly be frustrated and disappointed when they apply the otherwise very skillfully explained techniques included in Regression with Dummy Variables to their own data.

It also worth mentioning that for both Models 5 and 6 introduction of interaction terms increased the R-squared value by less than one percent. Again, given a sufficiently large sample, even a miniscule and substantively inconsequential R-squared increment can be statistically significant. I think the author should emphasize this, and acknowledged that her subsequent interpretation of statistical interaction in the earnings attainment process may be misleading: as a practical matter, the interaction effects really make no difference.

In most respects, this is a very useful book, one that taught me valuable lessons. The author's omissions in her discussion of of examples, however, are hard to understand. This is especially true with regard to the issue of multicollinearity.

Like most of the books in the Sage Quantitative Applications in the Social Sciences, this is clearly written and understandable. This is one of those rare statistics texts that is readable and useful. If you need to understand or use dummy variables in regression, this book will save you enormous amounts of time and frustration. Strongly recommended.

This book saved my life! It provided clear explanations and great examples of how to use and interpret regressions with dummy variables. I don't know how I would have passed without it. An extra bonus for people interested in strat--the examples deal with inequality.

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