Avoiding Inferential Errors in Public Health Research: The Statistical Modelling of Physical Activity Behavior
DOI:
https://doi.org/10.6000/1929-6029.2014.03.04.7Keywords:
Count Regression, Inference error, Measurement, physical activity, Health behavior.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.
References
McCully SN, Don BP, Updegraff JA. Using the Internet to Help With Diet, Weight, and Physical Activity: Results From the Health Information National Trends Survey (HINTS). J Med Inter Res 2013; 15(8). http://dx.doi.org/10.2196/jmir.2612 DOI: https://doi.org/10.2196/jmir.2612
Boone-Heinonen J, Diez Roux AV, Kiefe CI, Lewis CE, Guilkey DK, Gordon-Larsen P. Neighborhood socioeconomic status predictors of physical activity through young to middle adulthood: The CARDIA study. Soc Sci Med 2011; 72(5): 641-9. http://dx.doi.org/10.1016/j.socscimed.2010.12.013 DOI: https://doi.org/10.1016/j.socscimed.2010.12.013
Sallis JF, Richard Hofstetter C, Faucher P, Elder JP, Blanchard J, Caspersen CJ, et al. A multivariate study of determinants of vigorous exercise in a community sample. Prevent Med 1989; 18(1): 20-34. http://dx.doi.org/10.1016/0091-7435(89)90051-0 DOI: https://doi.org/10.1016/0091-7435(89)90051-0
Jago R, Fox KR, Page AS, Brockman R, Thompson JL. Parent and child physical activity and sedentary time: do active parents foster active children? BMC Public Health 2010; 10(1): 194. http://dx.doi.org/10.1186/1471-2458-10-194 DOI: https://doi.org/10.1186/1471-2458-10-194
Vandewater EA, Shim M-s, Caplovitz AG. Linking obesity and activity level with children's television and video game use. J Adoles 2004; 27(1): 71-85. http://dx.doi.org/10.1016/j.adolescence.2003.10.003 DOI: https://doi.org/10.1016/j.adolescence.2003.10.003
Long JS, Freese J. Regression Models for Categorical Dependent Variables Using Stata. Second ed. College Station, Texas: Stata Press 2006.
Long JS. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, California: Sage Publications 1997.
Cameron AC, Trivedi. PK. Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests. J Appl Economet 1986; 1: 29-53. http://dx.doi.org/10.1002/jae.3950010104 DOI: https://doi.org/10.1002/jae.3950010104
Colin CA, Trivedi PK. Regression analysis of count data. Cambridge, UK: Cambridge Univ. 1998.
Health Information National Trends Survey [Internet]. National Cancer Institute 2013.
Carroll-Scott A, Gilstad-Hayden K, Rosenthal L, Peters SM, McCaslin C, Joyce R, et al. Disentangling neighborhood contextual associations with child body mass index, diet, and physical activity: The role of built, socioeconomic, and social environments. Soc Sci Med 2013; 95: 106-14. http://dx.doi.org/10.1016/j.socscimed.2013.04.003 DOI: https://doi.org/10.1016/j.socscimed.2013.04.003
Worsley A, Wang WC, Hunter W. Gender differences in the influence of food safety and health concerns on dietary and physical activity habits. Food Policy 2013; 41: 184-92. http://dx.doi.org/10.1016/j.foodpol.2013.05.011 DOI: https://doi.org/10.1016/j.foodpol.2013.05.011
Scheers T, Philippaerts R, Lefevre J. Compliance with different physical activity recommendations and its association with socio-demographic characteristics using an objective measure. BMC Public Health 2013; 13(136): 10.1186. DOI: https://doi.org/10.1186/1471-2458-13-136
Strong LL, Anderson CB, Miranda PY, Bondy ML, Zhou R, Etzel C, et al. Gender differences in sociodemographic and behavioral influences of physical activity in Mexican-origin adolescents. J Phys Activ Health 2012; 9(6): 829-39. DOI: https://doi.org/10.1123/jpah.9.6.829
Lämmle L, Worth A, Bös K. Socio-demographic correlates of physical activity and physical fitness in German children and adolescents. Eur J Public Health 2012; 22(6): 880-4. http://dx.doi.org/10.1093/eurpub/ckr191 DOI: https://doi.org/10.1093/eurpub/ckr191
Poston Jr DL. The statistical modeling of the fertility of Chinese women. J Modern Appl Statist Method 2002; 1(2): 47. DOI: https://doi.org/10.22237/jmasm/1036109160
StataCorp [Internet]. StataCorp LP. 2013.
Vuong QH. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica: J Economet Soc 1989: 307-33. http://dx.doi.org/10.2307/1912557 DOI: https://doi.org/10.2307/1912557
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