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20.05.2024

A model of errors in BMI based on self-reported and measured anthropometrics with evidence from Brazilian data

verfasst von: Apostolos Davillas, Victor Hugo de Oliveira, Andrew M. Jones

Erschienen in: Empirical Economics

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Abstract

The economics of obesity literature implicitly assumes that measured anthropometrics are error-free and they are often treated as a gold standard when compared to self-reported data. We use factor mixture models to analyse measurement error in both self-reported and measured anthropometrics with nationally representative data from the 2013 National Health Survey in Brazil. A small but statistically significant fraction of measured anthropometrics are attributed to recording errors, while, as they are imprecisely recorded and due to reporting behaviour, only between 10 and 23% of our self-reported anthropometrics are free from any measurement error. Post-estimation analysis allows us to calculate hybrid anthropometric predictions that best approximate the true body weight and height distribution. BMI distributions based on the hybrid measures do not differ between our factor mixture models, with and without covariates, and are generally close to those based on measured data, while BMI based on self-reported data under-estimates the true BMI distribution. “Corrected self-reported BMI” measures, based on common methods to mitigate reporting error in self-reports using predictions from corrective equations, do not seem to be a good alternative to our “hybrid” BMI measures. Analysis of regression models for the association between BMI and health care utilization shows only small differences, concentrated at the far-right tails of the BMI distribution, when they are based on our hybrid measure as opposed to measured BMI. However, more pronounced differences are observed, at the lower and higher tails of BMI, when these are compared to self-reported or “corrected self-reported” BMI.

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1
These fabrication errors (if they exist) are unlikely to result in mean reversion/mean divergence but may be fairly random errors. Existing studies have shown evidence of misperception of body size (Zelenytė et al. 2021), suggesting that interviewers may not be able to accurately predict participants’ body weight/height (if not measured) and, thus, not be able to make guesses that may lead to mean reversion/mean divergence (i.e. guesswork that is strongly correlated with true body weight and height).
 
2
The factor mixture measurement error model proposed by Kapteyn and Ypma (2007) assumes that observed administrative income data are a mixture of correct matches and mismatches (with survey data). However, they argue that, over and above potential mismatches in the linkage between administrative and survey data, it is also likely that administrative and survey data may capture conceptually different things. As such, they argue that there is no loss of generality to assume that measurement error in administrative data may reflect different sources. Analogously, in our analysis measurement error in measured anthropometrics may reflect different sources (as described above), in particular interviewers’ errors related to entering values from the measurement equipment to the survey materials, fabrication of the measurement of anthropometrics by the interviewer or even physical measurements for the wrong household member.
 
3
Even in the case of fabricated interviews or when anthropometric measurement is not conducted for the intended respondent, this may be a strong assumption if quality control takes place. However, there is no such quality control undertaken in the dataset used in our analysis (as well as in many other multi-purpose social science datasets that collect anthropometrics).
 
4
Self-reported anthropometrics are collected as integer values (cm for height and Kg for weight), while the corresponding measured values are measured to one decimal point. In those cases where the respondent provided a non-integer value of their self-reported body weight and/or height (for example 61.5 kg), the interviewer recorded an integer value (such as 61 kg or 62 kg).
 
5
Mean reversion (ρ < 0) means that respondents with high (low) values of true anthropometric measures, relative to the true mean, tend to under-report (over-report) their body weight and height in self-reports; the opposite is the case for mean divergence (ρ > 0).
 
6
Moreover, one may argue that survey mode may influence measurement error in self-reported anthropometrics. For example, social desirability bias is much lower in the case of self-completion as opposed to the open interview (Bowling 2005); thus, assuming that being taller and not of excess weight is more socially desirable, shorter people and those with excess weight may have distinct reporting patterns across collection modes. However, existing studies do not confirm the presence of such influences in reporting errors. Davillas and Jones (2021) find that measurement errors in anthropometrics do not differ according to the mode of interview, with similar patterns observed when self-reported anthropometrics are collected using randomly assigned open interview and self-completion modes. Along similar lines, Cawley et al. (2015) who also discuss mean reversion in reporting error in weight highlight that interviewers do not amend/correct the self-reported anthropometrics based on measured data in their datasets and, thus, no additional interviewer effects are expected.
 
7
Typically, failures of measurement equipment may be also relevant for measurement error in physical measurements of anthropometrics. However, we believe that the risk of equipment failure is less relevant in our dataset given the prevention mechanisms/protocols we describe above.
 
8
The user-written Stata command “ky_fit” predicts the seven “hybrid” measures proposed by Meijer et al. (2012). Table 6 in Jenkins and Rios-Avila (2023b) provides the descriptions of the predictors (“hybrid” outcomes), with the corresponding derivation of the formulae presented in their appendix.
 
9
The mean square error is computed as \(E\left( {{\text{predictor}} - \xi } \right)^{2} = {\text{Bias}}^{2} + {\text{Variance}}\). Reliability measures are computed as follows: \({\text{Rel}}1\left( r \right) = {\text{cov}} \left( {\xi ,r} \right)/{\text{var}} \left( r \right)\), \({\text{Rel}}1\left( s \right) = {\text{cov}} \left( {\xi ,s} \right)/{\text{var}} \left( s \right)\), \({\text{Rel}}2\left( r \right) = {\text{cov}} \left( {\xi ,r} \right)^{2} /\left[ {{\text{var}} \left( \xi \right) \cdot {\text{var}} \left( r \right)} \right]\) and \({\text{Rel}}2\left( s \right) = {\text{cov}} \left( {\xi ,s} \right)^{2} /\left[ {{\text{var}} \left( \xi \right) \cdot {\text{var}} \left( s \right)} \right]\). Further details can be found in Jenkins and Rios-Avila (2023a).
 
11
In PNS-2019, that collected data in 2019, body weight and height were measured for a much smaller sub-sample of respondents, due to the difficulties in physical anthropometric measurements for the full survey sample selected for individual interviews (Reis et al. 2022). On the other hand, in PNS-2013, the anthropometric measurements were carried out on all residents selected for the individual interview, except pregnant women (Damacena et al. 2015). Collection of both self-reported and measured anthropometrics at the same wave is necessary for our research question and the estimation requirements of our factor mixture models. Given that measured anthropometrics are only available for a small fraction of the total survey sample in PNS-2019 and because time sensitivity is not a constraint for the scope and the nature of our research question for this study, we have used the PNS-2013 data for our analysis.
 
12
Figure 4 (Appendix) plots the absolute differences between the 1st and 2nd body weight and height physical measurement. The graph shows that the mass of the absolute difference is concentrated at zero, and there are a few observations with absolute differences between the 1st and 2nd measurement that exceeds 1.5 kg (for body weight) or 1.5 cm (for body height).
 
13
The corresponding kernel density distributions for self-reported and measured body weight, height and BMI are presented in Figure 5 (Appendix). It seems that both self-reported and measured body height data have approximately normally shaped distributions, although right-skewed distributions are observed for the case of body weight and BMI. This is important as our model assumes normality for the factor distributions and identification of the components of the mixture of normals stems from non-normality in the (joint) distribution of observed outcomes.
 
14
Existing studies in the economics of obesity literature that rely on self-reported anthropometrics often estimate corrective equations (or utilize the coefficients from existing equations) based on the relationship between measured and self-reported body weight and height data from alternative data sources (Cawley 2015). To mimic correction procedures for self-reported anthropometrics in the existing studies, we estimate analogous “corrective” equations by regressing measured weight and height data on self-reports and a vector of demographics (results from these equations are available in Appendix, Table 14). The predictions from these equations are used to calculate self-reports of body weight and height that are corrected for reporting error—these results from our "corrected self-reported BMI” measure as presented in Tables 10 and 11.
 
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Metadaten
Titel
A model of errors in BMI based on self-reported and measured anthropometrics with evidence from Brazilian data
verfasst von
Apostolos Davillas
Victor Hugo de Oliveira
Andrew M. Jones
Publikationsdatum
20.05.2024
Verlag
Springer Berlin Heidelberg
Erschienen in
Empirical Economics
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI
https://doi.org/10.1007/s00181-024-02616-w

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