Multilevel mixed linear model analysis using iterative generalized least squares

  title={Multilevel mixed linear model analysis using iterative generalized least squares},
  author={Harvey Goldstein},
SUMMARY Models for the analysis of hierarchically structured data are discussed. An iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case. There is a discussion of applications to complex surveys, longitudinal data, and estimation in multivariate models with missing responses. An example is given using educational data. 

Tables from this paper

Multilevel analysis of structural equation models

SUMMARY This paper considers the multilevel analysis of structural equation models with unbalanced sampling designs. The analysis is based on the maximum likelihood and the generalized least squares

A general model for two-level data with responses missing at random

A general model for two-level multivariate data, with responses possibly missing at random, is described. The model combines regressions on fixed explanatory variables with structured residual

Variance Components as a Method for Routine Regression Analysis of Survey Data

We discuss a general modelling framework for variance component analysis of data from hierarchical structures. Areas of application include large scale surveys, small area statistics, longitudinal

Random Coefficient Models for Multilevel Analysis

A random coefficient regression model is proposed for both contextual analysis and slopes as outcomes analysis in multilevel analysis and its statistical properties are investigated in some detail.

Restricted unbiased iterative generalized least-squares estimation

SUMMARY It is shown that the iterative least-squares procedure for estimating the parameters in a general multilevel random coefficients linear model can be modified to produce unbiased estimates of


We discuss several issues arising in applications of variance component analysis for data with multilevel structure, with specific reference to the Fisher scoring algorithm of Longford (1987). An

Consistent Parameter Estimation for Lagged Multilevel Models

Simulations are used to demonstrate their success in obtaining consistent parameter estimated for this formulation of the multilevel model and first and second difference instrument methods for consistent estimation are developed.

Multilevel modelling of medical data

An overview of multilevel or hierarchical data modelling and its applications in medicine is presented and it is shown how this can be extended to fit flexible models for repeated measures data and more complex structures involving cross‐classifications and multiple membership patterns within the software package MLwiN.

An Investigation of Methods for Missing Data in Hierarchical Models for Discrete Data

The proposed method provides an alternative to standard selection and pattern-mixture modeling frameworks when data are not missing at random and is applied to data from the third Waterloo Smoking Project, a seven-year smoking prevention study having substantial non-response due to loss-to-following.



Transformations for Estimation of Linear Models with Nested-Error Structure

Abstract Two linear models with error structure of the nested type are considered. Transformations are presented by which uncorrelated errors with constant variances are obtained. The transformed

Large Sample Variances of Maximum Likelihood Estimators of Variance Components

Summary A general expression is obcained for the elements of the information matrix of the maximum likelihood estimators of variance components derived from unbalanced data of any mixed model. This

Least Squares Estimation When the Covariance Matrix and Parameter Vector are Functionally Related

Abstract Estimation for the linear model y = Xβ + e with unknown diagonal covariance matrix G is considered. The diagonal elements of G are assumed to be known functions of the explanatory variables

Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution

Regression Estimation after Correcting for Attenuation

Abstract The limiting distribution of the regression coefficients calculated from a correlation matrix that has been corrected for attenuation is obtained. Methods of estimating the covariance matrix

Regression Analysis of Data from Complex Surveys

SUMMARY Three methods of carrying out a regression analysis of data collected by means of a survey of complex design are investigated. Least squares methods which ignore population structure such as

Best Linear Unbiased Estimators for Repeated Surveys

SUMMARY Recent work on the problem of obtaining best linear unbiased estimators from a sample survey which is repeated on several occasions has centred on the effects of extending the model

Advances in factor analysis and structural equation models

The methods in this book do not provide final answers to the question of model specification but offer the researcher the flexibility to formulate and test a variety of causal models and to guide the analysis toward more adequate explanations of the relationships embedded in data.

The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves.

In the present paper, a class of problems where the dispersion matrix has a known structure is considered and the appropriate statistical methods are discussed.

Generalized Least Squares Estimators in the Analysis of Covariance Structures.

SUMMARY Let S represent the usual unbiased estimator of a covariance matrix, Σ0, whose elements are functions of a parameter vector . A generalized least squares (G.L.S) estimate, of may be