Neighborhood Sociodemographic Predictors of Serious Emotional Disturbance (SED) in Schools: Demonstrating a Small Area Estimation Method in the National Comorbidity Survey (NCS-A) Adolescent Supplement

Abstract

We evaluate the precision of a model estimating school prevalence of SED using a small area estimation method based on readily-available predictors from area-level census block data and school principal questionnaires. Adolescents at 314 schools participated in the National Comorbidity Supplement, a national survey of DSM-IV disorders among adolescents. A multilevel model indicated that predictors accounted for under half of the variance in school-level SED and even less when considering block-group predictors or principal report alone. While Census measures and principal questionnaires are significant predictors of individual-level SED, associations are too weak to generate precise school-level predictions of SED prevalence.

Appendices

Appendices

Appendix 1

See Table 3.

Appendix 2: Technical Appendix

In our multilevel logistic model, the linear predictor including the random effect is logit P(SED) = x′β + δ, where δ ~ N(0,σ²) and σ² is the random-effects variance. We assume that the distribution of the fixed-effects linear predictor across schools is approximately normal, x′β = z ~ N(μ, S ² _x ), where S ² _x is the variance across schools of the mean linear predictor x′β, estimated by the sample variance of the school means. An estimate of the squared correlation between predicted and population prevalence on the logit scale was calculated from model parameter estimates as R ² = S ² _x /(S ² _x  + σ²), the fraction of SED variance among schools explained by the model.

A school at the q quantile of the predictor distribution has x′β = z ₀ = μ + S _x Φ⁻¹(q). The predictive distribution of the linear predictor including the random effect δ is then x′β + δ ~ N(z ₀, σ²) with (1 − p)-level prediction interval (z ₀ − Φ⁻¹(1 − p/2)σ, z ₀ + Φ⁻¹(1 − p/2)σ); these bounds can then be transformed to probabilities through the inverse logit transformation.To estimate probabilities of exceeding the p quantile of prevalence for the population of schools at or above the q quantile of predicted prevalence, we note that this is a conditional probability ${\text{P}}(z + \delta > \mu + \Phi^{-1} (p)\surd ({S^2_x + \sigma^2})\mid z > \mu + \Phi^{-1} (q)S_x)$where z and δ have the unconditional normal distributions given above. The denominator is 1 − q and the numerator can be expressed as the probability of a quadrant of a bivariate normal distribution.