The October 27, 2017 Workshop on Quantitative Methods in Education, Health, and the Social Sciences (QMeHSS) will take place from 10:30am - 12:00pm in the Social Science Research Building Conference room 302. Yongyun Shin from Virginia Commonwealth University will be leading this workshop. The Social Science Research Building is located at 1226 East 59th Street , Chicago, IL.
Sources of Variance in a Random Coefficients Model Given Data MAR
Department of Biostatistics
Virginia Commonwealth University
Abstract: In a random coefficients model (RCM) where log household income (Income) has randomly varying effects on the reading achievement of children across schools, of interest is the impact of school mean Income, as well as other school characteristics, on the random coefficients. With Income observed at the child level, a pervasive approach is to analyze the sample school mean Income as a regressor. This approach, however, produces biased estimation. Furthermore, missing values in the outcome and covariates make it difficult to estimate the RCM efficiently. To correct the bias while analyzing all observed data, we express the RCM given the unobservable true school mean Income. The key idea is to view partially observed variables and their random coefficients, including the school mean Income, as complete data (CD); estimate a CD joint distribution given known covariates with data assumed missing at random (MAR) by the EM algorithm; and transform the estimated joint model to the RCM. With Income MAR, however, the joint model yields the likelihood based on a nonstandard distribution to make the E step difficult. We estimate the joint model by maximum likelihood via adaptive Gauss Hermite quadrature, evaluate this approach by simulation, and analyze a national sample of children estimating the RCM.