Background
Obesity and depression are two major diseases associated with numerous health complications 1. Obesity is linked with hypertension, dyslipidemia, diabetes mellitus, coronary heart disease, stroke, as well as increased all cause mortality 2. Depression contributes to increased risk of coronary heart disease, myocardial infarction, heart failure in patients with systolic hypertension, low bone mineral density, and increased mortality 345678.
Both diseases share common health complications but there is inconsistent findings concerning the relationship between obesity and depression. Some studies concluded that there was no relation between obesity and depression 910, while others reported that obese people had higher risk of depression 1112 or that heavier people were less depressed 1314. Goodman and Whitaker 15 showed that depressed adolescents are at increased risk for the development and persistence of obesity later in their life and Pine et al. 16 concluded that depression in childhood was positively associated with BMI during adulthood. In spite of the inconsistent findings overall it is believed that psychological distresses caused by obesity may lead to depression 17. Other researchers, for instance Rosmond 18, have even suggested that obesity and depression might be the same disease with different manifestations. The relation between obesity and depression could depend on factors such as sex, level of obesity, level of depression, socioeconomic status and family history of depression 17.
In this article we used the structural equation modeling (SEM) technique to assess the relation between BMI (as a proxy for obesity) and depression in a sample of 12,376 individuals from the province of Ontario as a subset of the 2002 Canadian Community Health Survey, Cycle 1.2 (CCHS1.2) dataset. The main objective was to examine the potential of the SEM technique for such complex analysis. This sample size is large enough to disentangle the complexity of the relation between obesity and depression. In addition, the results could be used as an approximation for Canadian population given that Ontario represents about 40% of the total Canadian population 19.
Methods
Data source
The CCHS1.2 is a crosssectional survey that contains information related to health status, health care utilization and health determinants for the Canadian population. The survey is based on a complex design, with stratification and multiple stages of selection, and unequal probabilities of selection to ensure adequate representation of young persons (15 to 24 years) and seniors (65 years and over) 20. The questionnaire was administered on the sample units selected from the area frames using the computerassisted interviewing (CAI) method. One person aged 15 years and over was randomly selected from the sampled households. The dataset contains information from 36,984 individuals with a response rate of 77.0% in Canada of which 12,376 respondents were from Ontario. There were 76 pregnant women who were excluded from the analysis.
Variables
The following variables have been suggested in the literature to be associated with the relation between depression and obesity:
Body mass index (BMI)
The CCHS1.2 survey used the respondents' selfreported measurements of height and weight to calculate the body mass index (BMI) which is an index of weighttosquared height (kg /m^{2}). In this analysis BMI has been used as a continuous variable as reported in the dataset.
Depression
Persistence of Major Depressive Episode is a continuous variable that identifies the longest period associated with a major depressive episode experienced by the respondent. We used this variable as the main proxy for depression.
Physical activity
To derive a physical activity index, the energy expenditure (EE) of participants in their leisure activities was estimated using the frequency and time per physical activity session as well as the metabolic energy cost (MET) value. This value is expressed as a multiple of the resting metabolic rate 2122. In this survey respondents were asked to specify the intensity level of their activities; therefore the MET values adopted correspond to the low intensity value of each activity.
Stress management
This variable was approximated by ability to handle unexpected and difficult problems in the dataset. Participants were asked to rate their ability in handling unexpected and difficult problems such as a family or personal crisis on a 5point Likert scale from excellent to poor so that higher scores relate to decreased ability in handling unexpected and difficult problems.
Socioeconomic status (SES)
Socioeconomic status is frequently measured by job status, income, and education 2324. We used a factor analysis technique to extract a latent variable from the variables of job status during the past year, multiple job status, income per household, income per person, and education. As a result, education did not load significantly on the factor; therefore, we removed it and made the SES factor with the other four variables.
Eating habits – eating attitudes test (EAT) index
This variable measures the extent of the symptoms and concerns characteristic of eating disorders 25. Higher scores of EAT index indicate higher risk of eating disorder.
Relatives with depression
This variable is a measure of the number of close relatives, including biological parents, siblings, and children who ever had at least one episode of being depressed.
Statistical analysis
The structural equation modeling is a method for representing, estimating and testing a theoretical network of mostly linear relations between variables that may be either directly observable or unobservable and may only be measured imperfectly. It is a generalization of both regression and factor analysis and comprises most of the linear modeling methods as "special cases". The procedure places emphasis on covariance structures rather than cases. The fundamental hypothesis in using SEM is that the covariance matrix of the observed variables is a function of a set of parameters. If the model is correct and the parameters are known, then the population covariance matrix would be exactly reproduced by SEM (except for sampling variation). SEM proceeds by assessing whether a sample covariance or correlation matrix is consistent with a hypothetical matrix implied by the model. The inputs are either raw data or sample moments computed from the data, and a model to be evaluated. The sample moments will include either correlations or variances and covariances. It may also include means and higher order moments 26.
The general SEM model can be decomposed into two submodels: a measurement model and a structural model. The measurement model defines relations between the observed and unobserved latent variables. The structural model defines relations among the unobserved variables by specifying the pattern by which particular latent variables directly or indirectly influence some other latent variables in the model.
SEM is mainly a confirmatory technique rather than exploratory and is more likely to be used to determine whether a certain model is valid, rather than to find a suitable model. However, SEM analysis often involves a certain degree of exploratory analysis. By convention, when graphically representing the model the observed variables are enclosed by rectangles or squares and latent variables are enclosed by ovals or circles. Residuals are always unobserved and are represented by ovals or circles.
In this work to evaluate the goodnessoffit of a model the root mean square error of approximation (RMSEA) statistic and the comparative fit index (CFI) were used as these are the most commonly used indices 26. The RMSEA estimates the lack of fit in a model compared to a saturated model. The estimated RMSEA is given by:
estimated RMSEA
=
F
^
0
d
f
model
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGLbqzcqqGZbWCcqqG0baDcqqGPbqAcqqGTbqBcqqGHbqycqqG0baDcqqGLbqzcqqGKbazcqqGGaaicqqGsbGucqqGnbqtcqqGtbWucqqGfbqrcqqGbbqqcqGH9aqpdaGcaaqaamaalaaabaGafmOrayKbaKaadaWgaaWcbaGaeGimaadabeaaaOqaaiabdsgaKjabdAgaMnaaBaaaleaacqqGTbqBcqqGVbWBcqqGKbazcqqGLbqzcqqGSbaBaeqaaaaaaeqaaaaa@4C4B@
where F^0=Max(χmodel2−dfmodelN,0)
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGgbGrgaqcamaaBaaaleaacqaIWaamaeqaaOGaeyypa0Jaemyta0KaemyyaeMaemiEaGNaeiikaGYaaSaaaeaaiiGacqWFhpWydaqhaaWcbaGaeeyBa0Maee4Ba8MaeeizaqMaeeyzauMaeeiBaWgabaGaeGOmaidaaOGaeyOeI0IaemizaqMaemOzay2aaSbaaSqaaiabb2gaTjabb+gaVjabbsgaKjabbwgaLjabbYgaSbqabaaakeaacqWGobGtaaGaeiilaWIaeGimaaJaeiykaKcaaa@4CD1@ and N is the sample size 27. For a perfect model F^0
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGgbGrgaqcamaaBaaaleaacqaIWaamaeqaaaaa@2EEB@ = 0. Values of RMSEA of 0.06 or less indicate a goodfitting model and a value larger than 0.10 is indicative of a poor model.
The comparative fit index (CFI) assesses fit relative to other models. It employs the noncentral χ^{2 }distribution with noncentrality parameters, τ_{i}. The larger τ_{i }indicates the greater model misspecification. For a perfect model τ_{i }= 0. The CFI is defined as:
CFI
=
1
−
τ
model
τ
indep
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGdbWqcqqGgbGrcqqGjbqscqGH9aqpcqaIXaqmcqGHsisldaWcaaqaaGGaciab=r8a0naaBaaaleaacqqGTbqBcqqGVbWBcqqGKbazcqqGLbqzcqqGSbaBaeqaaaGcbaGae8hXdq3aaSbaaSqaaiabbMgaPjabb6gaUjabbsgaKjabbwgaLjabbchaWbqabaaaaaaa@444E@
with
τ_{indep }= χindep2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFhpWydaqhaaWcbaGaeeyAaKMaeeOBa4MaeeizaqMaeeyzauMaeeiCaahabaGaeGOmaidaaaaa@364C@  df_{indep }and τ_{model }= χmodel2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFhpWydaqhaaWcbaGaeeyBa0Maee4Ba8MaeeizaqMaeeyzauMaeeiBaWgabaGaeGOmaidaaaaa@364E@  df_{model}.
The parameter τ_{indep }= χindep2
MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFhpWydaqhaaWcbaGaeeyAaKMaeeOBa4MaeeizaqMaeeyzauMaeeiCaahabaGaeGOmaidaaaaa@364C@  df_{indep }refers to the independence model which assumes zero population covariances among the observed variables 28. CFI values greater than 0.90 indicate reasonably good fit of the model 29. The analysis were performed using the AMOS software 30.
The Stunkard model
Stunkard et al. 31 suggested a model which encompasses a "genetic correlation" and an "environmental correlation" between depression and obesity. The "genetic correlation" refers to the likelihood that there might be a set of genes that promote both depression and obesity, while the "environmental correlation" underlines the possibility of existence of "common life experiences" that may promote both diseases. Although this model does not completely explain the physiological pathways between the two diseases, it has been used as an empirical framework in studies of genetic epidemiology 32.
We started the analysis with an adaptation of Stunkard's model. This model consists of two unobserved latent variables of Environ (for environment) and Genes and eight observed variables (Figure 1). The observed variables load on the latent variables (factors) in the following pattern:
<p>Figure 1</p>
Model 1 – SEM model with two latent variables of Environ and Genes (Stress M = Stress Management)
Model 1 – SEM model with two latent variables of Environ and Genes (Stress M = Stress Management).
a) Physical activity, SES, stress management, eating habits and gender which are usually considered as the components of the environment load on the first factor, Environ.
b) Gender and relatives with depression load on the second factor, Genes.
c) Both BMI and depression regress on the aforementioned factors.
Measurement errors associated with each observed variable were added with the assumption that these error terms were independent from each other.
This hypothesized model is a nonrecursive model, that is, it is a model with two structural equations where the dependent variable of each equation appears as a predictor variable in the other equation. In this model BMI and depression form a feedback loop; meaning that we can follow the path between these two variables on an infinite number of times without having to return to the other variables. This model states that BMI is directly influenced by depression and vice versa.
Results
A summary of descriptive statistics is given in Table 1. As this table shows about 50 percent of Ontarian suffer from overweight or obesity and approximately 12 percent of the respondents reported experiencing some period of major depressive episode. In this dataset variables of eating habit and relatives with depression have large numbers of missing values.
<p>Table 1</p>
Descriptive statistics of variables used in the analysis
Variables
N (%)
Mean
Std. Deviation
Min
Max
Gender
12376




Males
5660 (45.3)




Females
6716 (54.3)




Body Mass Index
10961
^{§}
25.75
4.84
9.60
57.80
Under/Normal weight
5449 (49.7)




Overweight
3710 (33.8)




Obese
1802 (16.4)




Depression (# years with MDElifetime)
12282
^{§}
0.41
8.20
0
67.00
No depression (0 years)
10826 (88.1)




Yes depression
1456 (11.9)




Physical Activity
12375
^{§}
2.27
2.34
0
28.70
Stress Management
12352
^{§}
2.31
0.93
1
5
Eating Habits
1812
^{§}
10.63
8.85
0
62
Relatives with Depression
1512
^{§}
1.76
3.02
0
55
§ the number is different from the total of 12376 because of missing values
Of great importance in SEM is the extent to which the hypothesized model fits the dataset. Using SEM technique, Model 1 (see Figure 1) had values less than the minimum acceptable level and the goodnessoffit indices proved not to be a good fit to the dataset. In particular, it showed that Genes is not a good construct of gender and relatives with depression.
In an effort to improve the model the variable relatives with depression was eliminated due to large numbers of missing data and the connection between gender and depression was dropped due to its nonsignificant path (Model 2). However, these changes did not improve the model satisfactorily. Consequently the resulting third model had one latent variable, Environ, with gender connected to it directly. The model contained 6 observed variables: physical activity, SES, stress management, gender, BMI and depression and one latent variable, Environ. In this third model it was hypothesized that BMI is directly affected by physical activity and depression is directly influenced by stress, as previously reported in the literature 33.
For this model the estimated RMSEA is 0.047 with the 90% confidence interval of (0.040, 0.054) and the pvalue for the test of closeness of fit of 0.776. The interpretation of the confidence interval indicates that with 90% confidence the true RMSEA value in the population falls within the bounds of 0.040 and 0.054, and therefore represents a good degree of precision. Given that the upper bound of the 90% confidence interval is less than the suggested value of 0.06 34, and the probability value associated with this test of close fit is > 0.50 (i.e. 0.776), it can be concluded that the hypothesized model fits the data well. In addition, the CFI value is 0.898 which indicates an acceptable level for model fitting. Also, the factor loadings and path coefficients for this model are significantly different from zero and there is no nearzero standard errors for the factor loadings and path coefficients (Table 2). Of great interest in the analysis are the path coefficients that constitute the structural portion of the model. The path coefficients for the path from BMI to depression, from depression to BMI, from Environ to BMI and Environ to depression are all significant. In addition, AMOS estimates a stability index for each model. An index value between 1 and 1 indicates a stable model 26. For Model 3 a stability index of 0.042 indicates that the system is indeed stable.
<p>Table 2</p>
Regression coefficients for Model 3
Estimate
SE
CR*
P
Phys.Activ ← Environ
1.053
0.101
10.387
< 0.001
Stress M ← Environ
0.548
0.044
12.420
< 0.001
BMI ← Environ
1.738
0.256
6.781
< 0.001
Depression ← Environ
0.963
0.141
6.821
< 0.001
BMI ← Phys.Activ
0.252
0.021
11.859
< 0.001
Depression ← Stress M
0.274
0.034
8.091
< 0.001
SES ← Environ
1.000
Gender ← Environ
0.600
0.048
12.385
< 0.001
BMI ← Depression
0.282
0.116
2.439
0.015
Depression ← BMI
0.150
0.045
3.359
< 0.001
* Critical ratio (the estimate divided by its standard error)
Subgroup analysis
Model 3 indicates that there is a relationship between BMI and depression and the effect of gender on this relationship is accounted for through the latent variable of Environ (see Table 2). This result indicates that relation between depression and obesity may be gender dependent. Therefore, we used SEM to assess the relation between BMI and depression separately for males and females. From the total sample of 12,376 respondents there were 5,660 males and 6,716 females. In subgroup analysis, Model 3 fit very well to the male group (Figure 2) with the goodness of fit indices of RMSEA = 0.056 and CFI = 0.890. However, the same model was not appropriate for the female participants.
<p>Figure 2</p>
SEM model for male participants (Stress M = Stress Management)
SEM model for male participants (Stress M = Stress Management).
In searching for a suitable model for females we dropped the connection between stress management and depression and the arrow from BMI to depression because they were not statistically significant. In this final model (Figure 3) all estimates were indeed significant and the goodnessof fit indices were at acceptable level; RMSEA = 0.038 with 90% CI= (0.028, 0.048) and CFI = 0.879.
<p>Figure 3</p>
SEM model for female participants (Stress M = Stress Management)
SEM model for female participants (Stress M = Stress Management).
Discussion
This work is based on a crosssectional dataset and we had no information about history of obesity and depression in the family, history of debilitating diseases in the family and household, and adverse childhood experiences. Therefore, any statistically significant relation between variables cannot necessarily indicate causality. In addition, while SEM may produce a well fitting model, it may not be unique and there can be other reasonable models for the same dataset. Limitations with the AMOS software did not allow for the use of appropriate sampling weights for estimations and modeling. Nevertheless, this modeling has generated some useful conclusions which may be used to inform future studies.
Although BMI is not a direct measure of body fat or lean tissue, it is the most widely investigated indicator of health problems associated with underweight and overweight statuses. However, BMI as an indicator of risk may have limitations for individuals or populations who are very tall or very short or who have very long or short limb lengths in relation to trunk measurement 35.
Results of this analysis indicate that BMI and depression are associated and that this relation is gender dependent which is supported by some other studies 3637. In general, it can be concluded that higher BMI may result in more severe forms of depression (see Table 2) which is consistent with some other recent findings 1112. On the other hand, the same conclusion may not be drawn for the effect of depression on BMI, therefore, a more severe form of depression may not result in more weight gain. The subgroup analysis based on gender showed that in males the higher BMI is related to the more severe form of depression, and the higher is the level of depression the lower is the BMI. These seemingly contradictory results about the relation between BMI and depression are in accordance with studies conducted by Palinkas et al. 13 and Stewart and Brook 14 and show the ability of the SEM method to differentiate directions of effects in a complicated modeling procedure. A possible explanation might be that new medications used to treat patients with depression have reduced/no weight gain side effect when compared to previous treatment options. However this is only a hypothesis as information regarding the treatment of these respondents was not available.
Another important result is the negative relationship between physical activity and BMI, which translates into "more physical activity – less weight problems". Model 3 also indicated that stress management had a direct relation with depression. The high score on the stress management means less ability to handle stress, indicating that individuals with reduced ability to handle stress suffer more from depression. The same relation was seen when males were analysed separately from females.
Among females stress management did not indicate a direct relation with depression and the path from obesity to depression was not statistically significant. In addition, the analysis did not show any relation between eating habits and relatives with depression and the outcome variables of BMI and depression. This lack of relationship may be explained by the large numbers of missing values in the variables of eating habits and relatives with depression.
In conclusion, this work shows that SEM can be used as an appropriate method to disentangle the complexity of the relation between obesity and depression. Further research is needed to better understand the structure of such complexity. Interestingly, this work showed that obesity and depression are associated but the form of the relation is different among males and females.
Competing interests
The author(s) declare that they have no competing interests.
Authors' contributions
Both authors contributed equally in designing the study and drafting the manuscript. The analysis was carried out by AD.