Showing papers on "Mixed model published in 1975"
TL;DR: The T2 test is shown to be asymptotically equivalent to the analysis of variance F test in the balanced case and some investigation is made of the distribution of the test statistic by applying the method of Box (1954).
Abstract: SUMMARY The analysis of data from multiclinic experiments is put in the framework of a mixed model in which the treatment effects are assumed to be fixed, and clinic and clinic by treatment effects are assumed to be random. The analysis in the unbalanced case is developed under the usual mixed model assumptions. The maximum likelihood estimates and likelihood ratio tests of the parameters are derived following the approach of Hemmerle and Hartley [1973]. The T2 test is shown to be asymptotically equivalent to the analysis of variance F test in the balanced case. The distribution of the test statistic in the case of proportional cell frequencies is also discutssed. Some investigation is made of the distribution of the test statistic by applying the method of Box [1954]. Clinical studies in which several clinics participate in the evaluation of therapies using a common protocol have become relatively common. Each clinic contributes patients in proportion to the size of the population it serves that is eligible for the study. The number of clinics is often relatively large, of order 10-20, and the number of patients contributed by each clinic may be relatively small. The evaluation of the efficacy of treatments may not be the same in every clinic due to random variation among the clinics and small sample sizes. The objective of the investigation reported here is to develop a method of global evaluation in the circumstances described above. We shall assume an experimental design in which the clinics participating in a study are presumed to be a random sample from the population of clinics which might conceivably use the treatments under investigation and that patients are allocated at random within each clinic. We assume further that the clinics use identical criteria for selection of patients and for their management and evaluation. The design described and the assumptions made are identical to those of a randomized blocks design in which block effects (clinic effects) and clinic by treatment interactions are random. In most applications to medical research, we have the added complication of unequal sample sizes. Thus an appropriate model for this situation is a two-way classified mixed effects model with unequal cell frequencies, generally called unbalanced data. In case of balanced data (i.e. when cell frequencies are equal) the inference problems of this model have been studied by several authors (Eisenhart [1947], Scheffe [1959], Graybill [1961] among others). By considering cell means Scheffe constructed Hotelling's T2-test for testing the hypothesis of equality of fixed effects, while by imposing symmetric condition on covariance matrix, Graybill considered analysis of variance F-test. Since analysis of variance (A.O.V.) estimates of variance components may sometimes be negative, the maximum likelihood (ML) procedure may not lead to this A.O.V. F-test even in the balanced
22 citations
TL;DR: In this paper, a paired compositions scaling model was adapted to provide a linear model for round-robin experiments, which was applied to illustrative data from the field of physiological psychology.
Abstract: Investigation of the effects of a series of treatment conditions upon some social behaviors may require observation of a set of subjects which have been mutually paired, in round-robin fashion. Data arising from such experiments are difficult to analyze, partly because they do not fit neatly into standard designs. A paired compositions scaling model due to Bechtel is adapted to provide a linear model for such round-robin experiments. Both fixed and mixed versions of the model are considered and some results of a Monte Carlo study of the mixed model are reported. The model is applied to illustrative data from the field of physiological psychology.
12 citations
TL;DR: In this article, the authors consider analysis of several models, where the structure of the covariance matrix is intermediate between that of intra-class correlation form and completely arbitrary, in terms of likelihood ratio tests.
Abstract: In this paper we consider analysis of several models, where the structure of the covariance matrix is intermediate between that of intra-class correlation form and completely arbitrary. The designs considered are incomplete blocks and split-plot. Some of these models arise in studies of growth-curves, learning processes and other areas. Analysis is generally in terms of likelihood ratio tests.
8 citations
TL;DR: Some misconceptions concerning the application of Griffing's fixed effects model I and mixed effects model B are discussed.
Abstract: Some misconceptions concerning the application of Griffing's fixed effects model I and mixed effects model B are discussed.
2 citations