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Further Comments on Boyle's "Path Analysis and Ordinal Data"

One of the more important contributions of Boyle's paper (1970) is his extension of the work of Borgatta (1968) and Labovitz (1967, 1970) on the consequences of assuming equal intervals for supposedly ordinal data. For example, his presentation of the source of distortions in regression and correlation coefficients via "zigzag" regression lines is a clear conceptual explanation of Labovitz's empirical findings. Thus, Boyle effectively advances the argument that distortions resulting from the use of parametric statistical techniques, and their attendant equalinterval assumption, may not be as serious as once was thought. Our comments on Boyle's paper primarily focus on some errors in his treatment of dummy variables in path analysis and on his proposals for recalibrating measures. We also attempt to extend and clarify some key statements in the paper.