Avoiding Inferential Errors in Public Health Research: The Statistical Modelling of Physical Activity Behavior
Pages 384-391
Ann O. Amuta and Dudley Poston Jr
DOI: http://dx.doi.org/10.6000/1929-6029.2014.03.04.7
Published: 06 November 2014

Abstract:  Background: A review of the health behavior literature on the statistical modeling of days of physical activity (PA) indicates that in many instances linear regression models have been used. It is inappropriate statistically to model a count dependent variable such as days of physical activity with Ordinary Least Squares (OLS). Many count variables have skewed distributions, and, also, have a preponderance of zeroes. Count variables should not be treated as continuous and unbounded. If OLS is used, estimations of the regression will frequently turn out to be inefficient, inconsistent and biased, and such outcomes could well have incorrect impacts on health programs and policies.

Methods: We considered three statistical methods for modelling the distribution of days of PA data for respondents in the 2013 Health Information Trends Survey (HINTS). The three regression models analyzed were: Ordinary Least Squares (OLS), Negative Binomial (NBRM), and Zero-inflated Negative Binomial (ZINB). We used the exact same predictor variables in the three models. Our results illustrate the differences in the results.

Results: Our analyses of the PA data demonstrated that the ZINB model fits the observed PA data better than either the OLS or the NBRM models. The coefficients and standard errors differed in the zero-inflated count models from the other models. For instance, the ZINB coefficient for the association between income and PA behavior was not statistically significant (p>0.05), whereas in the NBRM and in the OLS models, it was statistically significant (p<0.05).

Conclusions: The inappropriate use of regression models could well lead to wrong statistical inferences. Our analyses of the number of days of moderate PA demonstrated that the ZINB count model fits the observed PA data much better than the OLS model and the NBRM.