SUMMARY
Kernel smoothing is studied in partial linear models, i.e. semiparametric models of the form yi=ξi‱β+f(ti)+εi(1≤i≤n), where the ξi are fixed known p vectors, β is an unknown vector parameter and f is a smooth but unknown function. Two methods of estimating β and f are considered, one related to partial smoothing splines and the other motivated by partial residual analysis. Under suitable assumptions, the asymptotic bias and variance are obtained for both methods, and it is shown that estimating β by partial residuals results in improved bias with no asymptotic loss in variance. Application to analysis of covariance is made, and several examples are presented.
We present a statistical model for inference with response time (RT) distributions. The model has the following features. First, it provides a means of estimating the shape, scale, and location (shift) of RT distributions. Second, it is hierarchical and models between-subjects and within-subjects variability simultaneously. Third, inference with the model is Bayesian and provides a principled and efficient means of pooling information across disparate data from different individuals. Because the model efficiently pools information across individuals, it is particularly well suited for those common cases in which the researcher collects a limited number of observations from several participants. Monte Carlo simulations reveal that the hierarchical Bayesian model provides more accurate estimates than several popular competitors do. We illustrate the model by providing an analysis of the symbolic distance effect in which participants can more quickly ascertain the relationship between nonadjacent digits than that between adjacent digits.
THEORETICAL AND REVIEW ARTICLES
In fitting the process-dissociation model (L. L. Jacoby, 1991) to observed data, researchers aggregate outcomes across participant, items, or both. T. Curran and D. L. Hintzman (1995) demonstrated how biases from aggregation may lead to artifactual support for the model. The authors develop a hierarchical process-dissociation model that does not require aggregation for analysis. Most importantly, the Curran and Hintzman critique does not hold for this model. Model analysis provides for support of process dissociation--selective influence holds, and there is a dissociation in correlation patterns among participants and items. Items that are better recollected also elicit higher automatic activation. There is no correlation, however, across participants; that is, participants with higher recollection have no increased tendency toward automatic activation. The critique of aggregation is not limited to process dissociation. Aggregation distorts analysis in many nonlinear models, including signal detection, multinomial processing tree models, and strength models. Hierarchical modeling serves as a general solution for accurately fitting these psychological-processing models to data.
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