The paper explores some issues related to endogeneity in multilevel models, focusing on the case where the random effects are correlated with a level 1 covariate in a linear random intercept model. We consider two basic specifications, without and with the sample cluster mean. It is generally acknowledged that the omission of the cluster mean may cause omitted-variable bias. However, it is often neglected that the inclusion of the sample cluster mean in place of the population cluster mean entails a measurement error that yields biased estimators for both the slopes and the variance components. In particular, the contextual effect is attenuated, while the level 2 variance is inflated. We derive explicit formulae for measurement error biases that allow us to implement simple post-estimation corrections based on the reliability of the covariate. In the first part of the paper, the issue is tackled in a standard framework where the population cluster mean is treated as a latent variable. Later we consider a different framework arising when sampling from clusters of finite size, where the latent variable methods may have a poor performance, and we show how to effectively modify the measurement error correction. The theoretical analysis is supplemented with a simulation study and a discussion of the implications for effectiveness evaluation.

The role of sample cluster means in multilevel models: a view on endogeneity and measurement error issues / L.Grilli; C.Rampichini. - In: METHODOLOGY. - ISSN 1614-1881. - STAMPA. - 7:(2011), pp. 121-133. [10.1027/1614-2241/a000030]

The role of sample cluster means in multilevel models: a view on endogeneity and measurement error issues

GRILLI, LEONARDO;RAMPICHINI, CARLA
2011

Abstract

The paper explores some issues related to endogeneity in multilevel models, focusing on the case where the random effects are correlated with a level 1 covariate in a linear random intercept model. We consider two basic specifications, without and with the sample cluster mean. It is generally acknowledged that the omission of the cluster mean may cause omitted-variable bias. However, it is often neglected that the inclusion of the sample cluster mean in place of the population cluster mean entails a measurement error that yields biased estimators for both the slopes and the variance components. In particular, the contextual effect is attenuated, while the level 2 variance is inflated. We derive explicit formulae for measurement error biases that allow us to implement simple post-estimation corrections based on the reliability of the covariate. In the first part of the paper, the issue is tackled in a standard framework where the population cluster mean is treated as a latent variable. Later we consider a different framework arising when sampling from clusters of finite size, where the latent variable methods may have a poor performance, and we show how to effectively modify the measurement error correction. The theoretical analysis is supplemented with a simulation study and a discussion of the implications for effectiveness evaluation.
2011
7
121
133
L.Grilli; C.Rampichini
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/403165
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