Showing papers on "Mixed model published in 1971"

Statistical Inference in Random Coefficient Regression Models

Abstract: I -- Introduction.- 1.1 Purpose and Outline of the Study.- 1.2 Review of the Literature on Regression Models with Random and Fixed Coefficients.- 1.3 Conclusions.- II -- Efficient Methods of Estimating a Regression Equation with Equicorrelated Disturbances.- 2.1 Introduction.- 2.2 Some Useful Lemmas.- 2.3 A Regression Model with Equicorrelated Disturbances.- 2.4 Analysis of Time Series of Cross-Sections.- 2.5 Estimation When the Variance-Covariance Matrix of Disturbances is Singular.- 2.6 Estimation When the Remaining Effects are Heteroskedastic.- 2.7 Conclusions.- III -- Efficient Methods of Estimating the Error Components Regression Models.- 3.1 Introduction.- 3.2 Some Matrix Results.- 3.3 Covariance Estimators.- 3.4 Estimation of Error Components Models.- 3.5 A Class of Asymptotically Efficient Estimators.- 3.6 Small Sample Properties of the Pooled Estimator.- 3.7 A Comparison of the Efficiencies of Pooled and OLS Estimators.- 3.8 A Comparison of the Efficiency of Pooled Estimator with Those of its Components.- 3.9 Alternative Estimators of Slope Coefficients and the Regression on Lagged Values of the Dependent Variables.- 3.10 Analysis of an Error Components Model Under Alternative Assumptions.- 3.11 Maximum Likelihood Method of Estimating Error Components Model.- 3.12 Departures from the Basic Assumptions Underlying the Error Components Model.- 3.13 Conclusions.- IV -- Statistical Inference in Random Coefficient Regression Models Using Panel Data.- 4.1 Introduction.- 4.2 Setting the Problem.- 4.3 Efficient Methods of Estimating the Parameters of RCR Models.- 4.4 Estimation of Parameters in RCR Models when Disturbances are Serially Correlated.- 4.5 Problems Associated with the Estimation of RCR Models Using Aggregate Data.- 4.6 Forecasting with RCR Models.- 4.7 Relaxation of Assumptions Underlying RCR Models.- 4.8 Similarities Between RCR and Bayesian Assumptions.- 4.9 Empirical CES Production Function Free of Management Bias.- 4.10 Analysis of Mixed Models.- 4.11 Conclusions.- V -- A Random Coefficient Investment Model.- 5.1 Introduction.- 5.2 Grunfeld's Hypothesis of Micro Investment Behavior.- 5.3 Estimation and Testing of Random Coefficient Investment Model.- 5.4 Aggregate Investment Function.- 5.5 Comparison of Random Coefficient Model with Fixed Coefficient Macro Model.- 5.6 Comparison of Random Coefficient Model with Fixed Coefficient Micro Model.- 5.7 Conclusions.- VI -- Aggregate Consumption Function with Coefficients Random Across Countries.- 6.1 Introduction.- 6.2 Aggregate Consumption Model.- 6.3 Source and Nature of Data.- 6.4 Fixed Coefficient Approach.- 6.5 Random Coefficient Approach.- 6.6 Conclusions.- VII -- Miscellaneous Topics.- 7.1 Introduction.- 7.2 Identification.- 7.3 Incorporation of Prior Information in the Estimation of RCR Models.- 7.4 Conclusions.

The analysis of categorical data from mixed models

Abstract: This paper is concerned with contingency tables which are analogous to the well-known mixed model in analysis of variance. The corresponding experimental situation involves exposing each of n subjects to each of the d levels of a given factor and classifying the d responses into one of r categories. The resulting data are represented in an r X r X ... X r contingency table of d dimensions. The hypothesis of priincipal interest is equality of the one-dimensioinal marginal distributions. Alternatively, if the r categories may be quantitatively scaled, then attention is directed at the hypothesis of equality of the mean scores over the d first order marginals. Test statistics are developed in terms of minimum Neyman X2 or equivalently weighted least squares analysis of underlying linear models. As such, they bear a strong resemblance to the Hotelling T2 procedures used with continuous data in mixed models. Several numerical examples are given to illustrate the use of the various methods discussed.

lARGE SAMPLE VARIANCES OF MAXIMUM LIKELIHOOD ESTIMATORS OF VARIANCE COMPONENTS IN THE 3-WAY NESTED ClASSIFICATION, RANDOM MODEL, WITH UNBAlANCED DATA

Abstract: Summary Explicit expressions are presented for the elements of the information matrix of the variance components in a 3-way nested classification, random model, with normality and unbalanced data. 1. Introduction and Model ~ Searle [1970] developed a general method for obtaining, under normality conditions, the elements of the information matrix of the variance components of mixed models, with unbalanced data; in particular he displayed the results for the 2-way nested classification. This paper presents analogous results for the 3-way nested classification, random model, for the general case of unbalanced data. The linear model for an observation is taken to be