The relationship between body mass index and socioeconomic and demographic indicators: evidence from Australia

Abstract

Objectives

This paper explores the association of body mass index (BMI) with socioeconomic and demographic factors using data from the 6th wave of the Household, Income and Labour Dynamics in Australia (HILDA) Survey.

Methods

This study applies a stereotype logit model (SLM) to assess 10,875 individuals on the relationship between BMI and socioeconomic and demographic indicators.

Results

Aggregate results from the SLM show a positive (and concave) association between age and higher BMI. Further, males are more likely than females to have higher BMI. Higher BMI is positively associated with long-term health problems, reduced prosperity, being married, and being born in Australia and negatively associated with possessing a diploma or above.

Conclusions

Results show that there is a positive and concave relationship between age and higher BMI. Further, males tend to have higher BMI as compared to females. Higher BMI is also positively related to long-term health problems, reduced prosperity, being married and being born in Australia. Negative association with BMI is observed on those possessing a diploma and above.

Appendix: Explanation of a stereotype logit model

Consider a BMI outcome variable Y with c ordered categorical outcomes y _i denoted by i = 1, 2,….., c, and let X ₁, X ₂, …, X _p denote a set of p covariates. The ordinal polytomous regression model can be written as:

$$ { \Pr }(Y = y_{i} |X_{1} , \, X_{2} , \ldots ,X_{p} ) = \frac{{{ \exp }(\alpha_{i} \, + \, \beta_{i1} X_{1} \, + \, \beta_{i2} X_{2} \, + \ldots + \, \beta_{ip} X_{p} )}}{{\sum\limits_{i \, = \, 1}^{c} {{ \exp }(\alpha_{i} + \beta_{i1} X_{1} + \beta_{i2} X_{2} + \ldots + \, \beta_{ip} X_{p} )} }} $$

(1)

where α _c  = 0 and β _ck = 0(k = 1, 2,….., p) to assure identifiability. The log-probability ratios for equation (1) are formed by comparing each response category (y _i ) with a reference category (y _c ). Assuming the first category as the reference category, the log-probability ratio can be expressed as follows:

$$ \log \left[ {\frac{{\Pr (Y = y_{i} |X_{1, \, } X_{2, \, } \ldots X_{p} )}}{{\Pr (Y = y_{1} |X_{1, \, } X_{2, \, } \ldots X_{p} )}}} \right] = \alpha_{i} + \beta_{i1} X_{1} + \beta_{i2} X_{2} + \ldots + \beta_{ip} X_{p} $$

(2)

where i = 2 to c.

The regression coefficient β _ip for the pth covariate X _p corresponds to the log-probability ratio comparing (Y = y _i ) versus (Y = y ₁) for a unit increase in X _p . From the above equation we note that the ordinal nature is not accounted for in any way. To build the ordinality into the model, Anderson (1984) imposed the relationship β _ik  = ϕβ _k , where β _k is a list of new parameters and the ϕ _i values can be thought of as the scores attached to the response y _i . By substituting β _ik  = ϕβ _k into equation (2) a stereotype model can be written as:

$$ { \log }\left[ {\frac{{\Pr (Y = \, y_{i} |X_{1, \, } X_{2, \, } \ldots X_{p} )}}{{\Pr (Y \, = \, y_{1} |X_{1, \, } X_{2, \, } \ldots X_{p} )}}} \right] = \alpha_{i} + \phi_{i} (\beta_{1} X_{1} + \beta_{2} X_{2} + \ldots + \beta_{ip} X_{p} ) $$

(3)

A stereotype model determines a set of parameters {ϕ _i } for the dependent variable and a single parameter β _k for each covariate.