Latent variable model for suicide risk in relation to social capital and socio-economic status

Abstract

Background

There is little evidence on the association between suicide outcomes (ideation, attempts, self-harm) and social capital. This paper investigates such associations using a structural equation model based on health survey data, and allowing for both individual and contextual risk factors.

Methods

Social capital and other major risk factors for suicide, namely socioeconomic status and social isolation, are modelled as latent variables that are proxied (or measured) by observed indicators or question responses for survey subjects. These latent scales predict suicide risk in the structural component of the model. Also relevant to explaining suicide risk are contextual variables, such as area deprivation and region of residence, as well as the subject's demographic status. The analysis is based on the 2007 Adult Psychiatric Morbidity Survey and includes 7,403 English subjects. A Bayesian modelling strategy is used.

Results

Models with and without social capital as a predictor of suicide risk are applied. A benefit to statistical fit is demonstrated when social capital is added as a predictor. Social capital varies significantly by geographic context variables (neighbourhood deprivation, region), and this impacts on the direct effects of these contextual variables on suicide risk. In particular, area deprivation is not confirmed as a distinct significant influence. The model develops a suicidality risk score incorporating social capital, and the success of this risk score in predicting actual suicide events is demonstrated.

Conclusions

Social capital as reflected in neighbourhood perceptions is a significant factor affecting risks of different types of self-harm and may mediate the effects of other contextual variables such as area deprivation.

Appendix 1: model specification

Consider the model form without indexing by gender, for simplicity. Under model 1 the measurement model for the latent suicide risk scores S _i is

$$ Y_{ki}\sim \hbox{Bern}(\rho _{ki}),\quad k=1,\ldots,3, $$

$$ \hbox{logit} (\rho _{ki})=\kappa _{1k}+\kappa _{2k}S_{i}, $$

$$ S_{i}\sim N(S.P_{i},1), $$

where Bern(ρ) denotes a Bernoulli variable with probability ρ. The structural component in model 1 specifies dependence of the predicted risk S.P _i on the latent scales {SES, ISOL} and on demographic and contextual variables:

$$ S.P_{i}=\beta _{1}\hbox{SES}_{i}+\beta _{2}\hbox{ISOL}_{i}+\beta _{3}\hbox{WHITE}_{i}+\beta _{4}\hbox{AGE}_{i}+\beta _{5}\hbox{ADEP}_{i}+u_{\hbox{REG}_{i}}, $$

$$ u_{l}\sim N(0,\tau _{\hbox{REG}}^{2}),\quad l=1,\ldots,9. $$

where region effects are random, and τ ²_REG is their variance. The measurement model for SES involves the continuous indicator income, and four binary indicators, so that

$$ W_{1i}\sim N(\gamma _{11}+\lambda _{11}\hbox{SES}_{i}+\delta _{1}\hbox{ADEP}_{i},\sigma _{1}^{2}), $$

$$ W_{ri}\sim \hbox{Bern}(\pi _{ri})\quad r=2,\ldots,5, $$

$$ \hbox{logit}(\pi _{ri})=\gamma _{1r}+\lambda _{1r}SES_{i}+\delta _{r}\hbox{ADEP}_{i}, $$

$$ \hbox{SES}_{i}\sim N(0,1). $$

The measurement model for ISOL involves three binary indicators, so that

$$ Z_{qi}\sim \hbox{Bern}(\eta _{qi}),\quad q=1,..3, $$

$$ \hbox{logit}(\eta _{qi})=\gamma _{2q}+\lambda _{2q}\hbox{ISOL}_{i}, $$

$$\hbox{ISOL}_{i}\sim N(0,1). $$

In model 2 the structural component is expanded to include the effect of social capital (SCAP):

$$ S.P_{i}=\beta _{1}\hbox{SES}_{i}+\beta _{2}\hbox{ISOL}_{i}+\beta _{3}\hbox{SCAP}_{i}+\beta _{4}\hbox{WHITE}_{i}+\beta _{5}\hbox{AGE}_{i}+\beta _{6}\hbox{ADEP}_{i}+u_{\hbox{REG}_{i}}. $$

SES and ISOL are measured as for model 1, while for SCAP there are P = 18 binary indicators. Hence

$$ X_{pi}\sim \hbox{Bern}(\omega _{pi})\quad p=1,\ldots,18, $$

$$ \hbox{logit}(\omega _{pi})=\gamma _{3p}+\lambda _{3p}\hbox{SCAP}_{i}, $$

$$\hbox{SCAP}_{i}\sim N(0,1). $$

In model 3, a differential intercept and construct effects are included according to psychiatric illness present (D _i  = 2) or absent (D _i  = 1), with the structural model becoming

$$ S.P_{i}=\beta _{0}I(D=2)+\beta _{1,D_{i}}SES+\beta _{2,D_{i}}ISOL+\beta _{3,D_{i}}SCAP+\beta _{4}WHITE_{i}+\beta _{5}AGE_{i}+\beta _{6}ADEP_{i}+u_{REG_{i}}. $$

Because the latent scales {S, SES, ISOL, SCAP} have a preset variance of 1, the item loadings {κ _2k , λ _1r , δ _r , λ _2q , λ _3p } in the above models are all unknowns. To ensure consistent construct labelling, the initial loadings for each construct are constrained to be positive via gamma priors: $\kappa _{21}\sim Ga(1,1),\lambda _{11}\sim Ga(1,1),\lambda _{21}\sim Ga(1,1),$ and $\lambda_{31}\sim Ga(1,1).$ Remaining loadings are assigned N(0,10) priors. N(0,100) priors are adopted for β coefficients in the structural model, for the δ coefficients in the SES measurement model, and for the intercepts {κ _1k , γ _1r , γ _2q , γ _3p }. The precisions 1/τ ²_REG and 1/σ ²₁ are assigned Ga(1,0.001) priors.

Let x _j generically denote one of the latent constructs SCAP, SES, or ISOL, or one of the observed predictors AGE, WHITE or ADEP. Then standardised coefficients (in Tables 4, 5) express change in suicidality S (in standard deviations) in response to a standard deviation change in x _j :

$$ \beta _{j}^{^{\prime }}=\beta _{j}\hbox{sd}(x_{ji})/\hbox{sd}(S_{i}). $$

Comparable standardised effects of region are obtained as

$$ u_{l}^{\prime }=u_{l}\tau _{\hbox{REG}}/\hbox{sd}(S_{i}). $$