Table 1 reports descriptive statistics for the final sample. As expected, BMI calculated from measured height and weight is higher than BMI based on self-reports, and underreporting is related to the level of BMI. Stratifying by BMI classification (underweight: BMI < 18.5, normal weight: 18.5 ≤ BMI < 25, overweight: ≤25 BMI < 30, and obese: BMI ≥ 30) shows that, on average, the underweight overreport BMI, whereas both men and women in the three other BMI statuses underreport. The obese underreport more than the overweight, who in turn underreport more than normal-weight individuals.
Defining obesity as BMI ≥ 30, obesity prevalence increases by four percentage points for both men and women when using measured values instead of self-reports. Notably, when defining obesity using waist circumference instead, prevalence increases to 35 % among women. The increase is less pronounced among men.
Regarding misclassification, Fig. 1 illustrates the relationship between BMI (calculated from objectively measured height and weight) and waist circumference. Observations that are inconsistently classified in the sense that they are classified as obese according to one of the definitions but not according to the other are located in the upper left and lower right squares of each graph. In this study we focus on the lower right squares and define misclassification as being obese according to the waist circumference definition but not according to the BMI definition. 15 % of female observations, and 6 % of male observations, are misclassified in this sense.
Fewer men (3 %) and women (2 %) are allocated to the upper left corners, and thus have a relatively high BMI but a slim waistline. Clearly, these observations also represent a type of misclassification, namely being classified as obese according to the BMI definition, but not according to the waist circumference definition. However, the small number of individuals belonging to this type of misclassification makes it difficult to perform a comprehensive analysis of the determinants, and the misclassification analysis in this study therefore focuses only on the first type of misclassification.Footnote 6
For the misreporting analysis, Tables 2 and 3 report the results from three different models. Model I includes three indicator variables for level of education in the x
vector. Model II includes the log of current household disposable income per consumption unit, and model III combines education and income. The first column reports the results from Eq. 1, where measured weight and height are used to calculate BMI to estimate “true” gradients. The second column contains the socioeconomic disparities based on self-reported information (Eq. 2). The third column shows the results from estimation of Eq. 3 and whether the estimates based on the self-reported data in column 2 are biased. The fourth column shows the results from estimation of Eq. 4 and whether there is any direct effect of socioeconomic status on the total bias.
For women (Table 2), the estimation of model I shows, as expected, that there are statistically significant educational disparities when using BMI calculated from both measured and self-reported weight and height.Footnote 7 These estimates are statistically significantly larger (i.e. more negative), by about 15 %, than the ones estimated from self-reported data. Hence, the estimated gradient based on self-reported values is biased towards zero. According to column 4, there is a direct effect of education on the bias for the highest education group (p < 0.05). Given the same level of true BMI, women in the highest educational group report weight and height in a way that results in less underreporting of BMI compared to the lowest educational group. Because women with higher education also tend to have lower BMI than those with lower education, and because women with lower BMI underreport BMI to a lesser extent than women with higher BMI, there is also an indirect effect of education on the bias. Following Eq. 5, the indirect effect is a combination of ρ and γ
meas, which for the highest educational group is (−0.045)*(−1.683) = 0.076, corresponding to about 26 % of the total bias.
In model II, using BMI calculated from measured weight and height results in a negative income gradient (p < 0.05). Using self-reported information gives a somewhat smaller, and less significant (p < 0.10), effect, but the difference between the two estimates is not significant (p > 0.10, column 3).
Combining education and income in model III shows that education seems to be a stronger correlate with BMI than income. Once controlling for education, income is insignificant (p > 0.10), and the size of the coefficient is reduced compared to model II. The negative correlation between education and BMI, however, remains statistically significant, although the sizes of the education coefficients are somewhat smaller compared to model I. The bias towards zero in the education gradient when using self-reported data remains very similar, as in model I.
Table 3 reports the male results. According to model I, there is a difference in BMI across educational groups also among men, where men in the highest educational groups differ by having a lower BMI (p < 0.10). However, this difference is smaller than among women. Compared to a man with 11 years of schooling at most, a man in the highest educational group (educ4) has about a 0.9 index point lower BMI. The income gradients in models II and III are positive, but small and insignificant.Footnote 8 Controlling for both income and education in model III gives results similar to those in model I. Hence, as for women, education appears as the strongest BMI-related socioeconomic variable in this sample, whereas income is less important.
Unlike the female results, there is no evidence of significant differences between the specifications with self-reported and measured information (column 3). However, column 4 shows a negative, and statistically significant (p < 0.05), direct effect for the highest educational group; given the same level of true BMI, men in the highest educational group tend to underreport BMI to a larger extent than those in the lowest educational group. Because men in higher educational groups tend to have lower BMI in general (column 1), and because men with higher BMI underreport more (column 4), the indirect effect is positive, and, consequently, the total bias in column 3 is smaller than the direct effect. The total bias (column 3) shows a tendency towards an overestimation of the education gradient (i.e. a more negative education effect) when using self-reported data. This means that, overall, men in the highest educational group underreport BMI to a larger extent than those in the lowest educational group, despite their lower BMI in general. The bias is not statistically significant though, and altogether male educational disparities in BMI calculated from self-reported weight and height seem to be less biased than corresponding female disparities.
Misreporting: sensitivity analysis
The robustness of the results presented in Tables 2 and 3 is explored in various ways.Footnote 9 The first robustness check aims at taking into account that the number of days between the first and second visit to the health care center is not the same for all observations. Although all participants were supposed to make their second visit to the health care center 14 days after the first visit, the number of days between the visits generally varies between 0 and 60 days, with some additional outlying observations. The median is the intended 14 days for both men and women.
As the time period between the visits increases, the risk that the observed difference between BMI calculated from self-reported and measured information is an actual weight difference, and not a misreport, increases (height reasonably does not change in the age groups included in the analysis). To deal with this issue, we repeat the analysis on a constrained sample, including only individuals with information on when the first and second visit took place and for who the number of days between the visits is 65 days at most. This reduces the sample by 137 female and 159 male observations. To explore whether the results from the main analysis remain when taking the different lengths of time between the visits into account, the number of days and its square are added as control variables in all regressions.Footnote 10
Among women, the number of days between the visits is indeed related to misreporting such that underreporting increases with the number of days. Compared to the main analysis, the bias in the educational gradient is somewhat reduced, and the statistical significance decreases somewhat.Footnote 11 For income, no differences to the main analyses are observed. Also among men, underreporting increases with the number of days between the visits, but the correlation is statistically insignificant. However, controlling for the number of days between visits in the misreporting regressions reduces the size and precision of the bias in the educational gradient also for men. The direct effect of educ4, which is significant at the 5 % level in the main analysis, loses its statistical significance. Overall, the qualitative conclusions based on this constrained sample analysis are the same as for the main analysis, but the results are somewhat weakened in terms of size and statistical significance once controlling for the number of days between visits and removing observations with long periods between them. This could indicate that part of the misreporting are actual weight changes rather than misreporting, but also when accounting for this, there is evidence of bias in female educational gradients based on self-reported data.
Another concern could be that, with time, participants learned that they would first be asked about their weight and height, which would be measured later. Hence, because of learning, individuals who were surveyed and examined towards of the end of the period could misreport to a lesser extent than those examined in the beginning. To explore this possibility, the second repeated analysis includes control for the within sex and municipality rank for when the second visit at the health care center occurred, and the square of this variable.Footnote 12 There is no apparent tendency that individuals who were examined towards the end of the period reported more accurately and the rank variables are not statistically significantly related to misreporting. Overall, the results from this alternative analysis are very similar to the results from the main analysis.
In a third round of robustness checks, the sample is repeatedly modified by excluding certain groups, with the purpose of ensuring that the results in the main analysis are not driven by a particular subgroup, and that results are not too sensitive to removal of these subgroups. Different age groups (74–76, 70–76, 65–69, 60–64, 55–59, …, 30–34), the different civil status groups (unmarried, divorced, and widow), and the immigration status groups (first and second generations) are removed, one by one, resulting in 15 repetitions of the analysis.
Among women, the bias in the estimate of educ3 when using self-reported BMI is statistically significant at the 5 % level in 12 out of the 15 repeated analyses, the bias in the estimate of educ4 is significant (with p < 0.05 or better) in all samples, and the direct effect of educ4 goes from being significant at the five percent level to being significant at the ten percent level in three cases.Footnote 13 Among men, the difference between estimates based on self-reported and measured BMI remains negative but statistically insignificant (p > 0.10) in all 15 samples. The direct effect of educ4 in the main analysis remains negative in all samples, and significant (with p < 0.05 or better) in half of the samples.Footnote 14 Overall, we conclude from this third part of the sensitivity analysis that the exact estimates vary somewhat across samples. Nevertheless, qualitatively, the key patterns from the main analysis are identified also in the majority of the subsamples explored. It is difficult to reveal any clear patterns for when the results change compared to the main analysis. The most consistent result throughout is that the results weaken when the age group 70–76 is removed, indicating that the biases observed in the main analysis might be stronger in this age group.
Turning to the misclassification analysis, Table 4 reports the results from estimation of Eq. 6. Among women, the tendency of being misclassified goes in opposite directions for education and income. The probability of being misclassified decreases with income, whereas it is (insignificantly) larger for women in the highest educational group. Because education and income are positively correlated, including only one of the variables also captures the correlation with the other. Consequently, including both education and income in model III strengthens the correlation with both income and education compared to model I and model II, respectively. According to model III, a 10 % higher income is related to a 0.75 percentage point decrease in the probability of being misclassified. The education variables remain positive but insignificant.
Among men, there is a negative correlation between misclassification and both the highest educational group and income. In model I, men in the highest educational group are 4.9 percentage points less likely to be misclassified than those in the lowest educational group. In model II, a 10 % higher income implies a 0.52 percentage points lower probability in being misclassified. When controlling for both income and education in model III, the association with income remains statistically significant (p < 0.05) whereas education loses its significance.
Systematic variation across income and education in misclassification implies that income and education gradients differ depending on the definition of obesity. Table 5 illustrates this implication by reporting the results from estimating Eq. 7, where obesity is defined in three different ways. For women, columns 1–2 show that educational differences increase when moving from BMI calculated from self-reports to BMI calculated from measured information to define obesity. This observation is in line with the misreporting analysis and the finding of a bias in the female educational gradient when using self-reported data on weight and height to calculate BMI (Table 2). When moving further, to obesity defined by waist circumference (column 3), the educ3 estimate remains similar in size. The educ4 estimate reduces in size, from around 13 percentage points to 5–8 percentage points, and becomes insignificant. This result reflects what Table 4 shows; women in the highest educational group tend to be misclassified more often, and hence the difference in obesity across educational groups depends on what definition is used. Similarly, because misclassification decreases with income (Table 4), the income gradient is significantly larger (p < 0.10 in model II and p < 0.05 in model III) for the waist circumference definition.
For men (columns 4–6) the coefficients of the education variables are basically the same for obesity defined by self-reported and measured BMI, which is in line with the results from the misreporting analysis (Table 3) where no bias in the education disparities was detected. Notably, using self-reported or measured BMI to define obesity, there are no statistically significant differences in obesity across education or income. However, when using waist circumference to define obesity, a negative education effect for the highest educational groups evolves. The size of this difference is about 8 percentage points (p < 0.05 in model I and p < 0.1 in model III). There is also a negative income gradient emerging, reflecting the result from the misreporting analysis that the probability of misclassification increases with income. However, the income coefficient is rather small and does not reach statistical significance.
Misclassification: sensitivity analysis
As for the misreporting analysis, the robustness of the results from the misclassification analysis is checked by repeating the analysis on modified samples where age groups, civil status groups and immigration groups are removed, one at a time, to ensure that the results in the main analysis are not driven by a particular subgroup.Footnote 15
Footnote 16 Among women, the tendency for those in the highest educational group to be misclassified more often remains in all repeated analyses. The association also remains statistically insignificant (p > 0.05) in all cases but one.Footnote 17 The negative correlation between misclassification and income remains negative in all 15 subsamples. Controlling for education (model III), it varies between −0.051 and −0.098. In terms of statistical significance, the clearest pattern is that the significance disappears (p > 0.10) when the four youngest age groups are removed (i.e. 30–34, 35–39, 40–44, and 45–49).Footnote 18 This result could imply that the negative correlation between income and misclassification is more apparent among those under the age of 50, but it could also be a result of smaller sample sizes.Footnote 19
Among men, those in the highest educational group are less likely to be misclassified in all 15 subsamples, but the difference compared with those in the lowest educational group is statistically significant (p < 0.05) in six cases only. Controlling for both education and income (model III) results in a rather stable association between income and misclassification, varying between −0.045 and −0.055, which is significant (p < 0.05) in nine out of the 15 subsamples.Footnote 20 Hence, as in the main analysis, the correlation between income and misclassification appears more stable and pronounced than the lower probability of those in the highest educational group to be misclassified. There is no clear indication as to whether this overall result from the main analysis would be sensitive to exclusion of any particular age, civil status or immigration status group.
The definition of obesity based on waist circumference takes only waist circumference, and not height, into account, whereas BMI is weight relative to height. There might therefore be a concern that the misclassification is related to height. The height variables are indeed jointly significantly related to misclassification such that the probability of being misclassified increases with height. However, adding controls for height does not have any major impact on the relationship between misclassification and education or income. The negative association between income and misclassification for women remains significant (with p < 0.05), and becomes stronger rather than weaker, when controlling for height. Among men, the negative association between misclassification and both income and education strengthens somewhat once controlling for height. Along the same lines, the emerging educational gradient among men which Table 5 observed remains also when height is controlled for in the obesity probability regressions, and it becomes stronger rather than weaker.
A final set of robustness checks regards the estimation method used in the misclassification analysis. The main analysis relies on linear probability models (LPM). A major and well-known shortcoming with the LPM is that it may well predict probabilities outside the unit interval . The non-linear probit and logit models are alternatives that eliminate this problem. As a robustness check, we therefore perform the misclassification analysis using probit and logit models, calculating average marginal effects as well as marginal effect at the mean. Overall, results are not particularly sensitive to estimation method. Among women, results are very similar irrespective of estimation method. Among men, results are also similar, although standard errors are somewhat smaller when using the non-linear models, resulting in somewhat improved significance levels.
The overall conclusion from the misclassification sensitivity analysis is that the results from the main analysis are robust to estimation method (i.e. whether LPM, logit or probit is used) and to whether height is included as a regressor or not. However, the exact estimates vary somewhat when different subgroups are removed, and results are somewhat sensitive to the exact sample. But it is difficult to reveal any clear patterns of when the results change compared to the main analysis.