Average Predictive Comparisons for Models with Nonlinearity, Interactions, and Variance Components

Datos Bibliográficos

ID8019784
AutoresAndrew Gelman (0000-0002-6975-2601, Columbia University), Iain Pardoe (University of Oregon, Eugene)
Año2007
Volumen37
Número1
Páginas23-51
Fecha de publicación2007-05-18
Peer ReviewedSí
Open AccessSí
TipoARTICLE
RevistaSociological Methodology (JOURNAL)
Identificadores de la revistaISSN: 0081-1750 • E-ISSN: 1467-9531
EditorialSAGE Publishing (PUBLISHER • US)
DOI10.1111/j.1467-9531.2007.00181.x
OpenAlexW2062423635
IdiomaEN
Citas recibidas34
Referencias citadas32

In a predictive model, what is the expected difference in the outcome associated with a unit difference in one of the inputs? In a linear regression model without interactions, this average predictive comparison is simply a regression coefficient (with associated uncertainty). In a model with nonlinearity or interactions, however, the average predictive comparison in general depends on the values of the predictors. We consider various definitions based on averages over a population distribution of the predictors, and we compute standard errors based on uncertainty in model parameters. We illustrate with a study of criminal justice data for urban counties in the United States. The outcome of interest measures whether a convicted felon received a prison sentence rather than a jail or non-custodial sentence, with predictors available at both individual and county levels. We fit three models: (1) a hierarchical logistic regression with varying coefficients for the within-county intercepts as well as for each individual predictor; (2) a hierarchical model with varying intercepts only; and (3) a nonhierarchical model that ignores the multilevel nature of the data. The regression coefficients have different interpretations for the different models; in contrast, the models can be compared directly using predictive comparisons. Furthermore, predictive comparisons clarify the interplay between the individual and county predictors for the hierarchical models and also illustrate the relative size of varying county effects

Contrast (vision · Data mining · Econometrics · Economics · Explained variation · Hierarchical database model · Linear regression · Logistic regression · Multilevel model · Population · Regression · Regression analysis · Statistics · Variance (accounting · Advanced Causal Inference Techniques · Artificial Intelligence · Computer Science · Demography · Mathematics · Statistical Methods and Bayesian Inference · Statistical Methods and Inference