Data-Mining Homogeneous Subgroups in Multiple Regression When Heteroscedasticity, Multicollinearity, and Missing Variables Confound Predictor Effects

Abstract

Multiple regression is not reliable to recover predictor slopes within homogeneous subgroups from heterogeneous samples. In contrast to Monte Carlo analysis, which assigns completely to the first-specified predictor the variation it shares with the remaining predictors, multiple regression does not assign this shared variation to any predictor, and it is sequestered in the residual term. This unassigned and confounding variation may correlate with specified predictors, lead to heteroscedasticity, and distort multicollinearity. I develop and test an iterative, sequential algorithm to estimate a two-part series of weighted least-square (WLS) multiple regressions for recovering the Monte Carlo predictor slopes in three homogeneous subgroups (each generated with 500 observations) of a heterogeneous sample [Formula: see text]. Each variable has a different nonnormal distribution. The algorithm mines each subgroup and then adjusts bias within it from 1) heteroscedasticity related to one, some, or all specified predictors and 2) “nonessential” multicollinearity. It recovers all three specified predictor slopes across the three subgroups in two scenarios, with one influenced also by two unspecified predictors. The algorithm extends adaptive analysis to discover and appraise patterns in field research and machine learning when predictors are inter-correlated, and even unspecified, in order to reveal unbiased outcome clusters in heterogeneous and homogeneous samples with nonnormal outcome and predictors.