# Random-effects models for longitudinal data.

@article{Laird1982RandomeffectsMF, title={Random-effects models for longitudinal data.}, author={Nan M. Laird and James Harold Ware}, journal={Biometrics}, year={1982}, volume={38 4}, pages={ 963-74 } }

Models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit. Multivariate models with general covariance structure are often difficult to apply to highly unbalanced data, whereas two-stage random-effects models can be used easily. In two-stage models, the probability distributions for the response vectors of different individuals belong to a single family, but some random-effects parameters vary across individuals, with a…

## 8,219 Citations

Models for Longitudinal Data with Random Effects and AR(1) Errors

- Mathematics
- 1989

Abstract For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test…

Linear Mixed Effects Models for Longitudinal Data

- Economics
- 2014

This paper describes a general LME model for longitudinal Gaussian data, presenting the model definition and its underlying assumptions, as well as asymptotic inference methods.

Analysis of Longitudinal Data by Models with Random Effects and Ar(1) Errors

- Mathematics
- 1990

For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for…

Random Effects Models for Longitudinal Data

- Biology
- 2010

This chapter gives an overview of frequently used mixed models for continuous as well as discrete longitudinal data, with emphasis on model formulation and parameter interpretation.

Models for longitudinal data: a generalized estimating equation approach.

- MathematicsBiometrics
- 1988

This article discusses extensions of generalized linear models for the analysis of longitudinal data in which heterogeneity in regression parameters is explicitly modelled and uses a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes.

Generalized Linear Mixed Models for Longitudinal Data

- Mathematics
- 2012

The study of longitudinal data plays a significant role in medicine, epidemiology and social sciences. Typically, the interest is in the dependence of an outcome variable on the covariates. The…

Random coeffcient models for complex longitudinal data

- Mathematics
- 2014

Longitudinal data are common in biological research. However real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This…

Random-effects models for serial observations with binary response.

- MathematicsBiometrics
- 1984

This paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants. Each subject's serial responses are assumed to arise from a…

Marginal and dynamic regression models for longitudinal data

- PsychologyStatistics in medicine
- 2001

This paper discusses the use of dynamic models in which a lagged response serves as a predictor and compares these to marginal models, exploring models explored through analysis of data from the Childhood Respiratory Study.

A Random-Effects Model for Multiple Characteristics with Possibly Missing Data

- Mathematics
- 1997

Abstract The use of random-effects models for the analysis of longitudinal data with missing responses has been discussed by several authors. This article extends the random-effects model for a…

## References

SHOWING 1-10 OF 26 REFERENCES

Analysis of growth and dose response curves.

- MathematicsBiometrics
- 1969

The method yields results identical to those obtained by weighting inversely by the sample covariance matrix, but has the additional feature of allowing flexibility in weighting by choosing subsets of covariates that have special properties.

Estimation in Covariance Components Models

- Mathematics
- 1981

Abstract Estimation techniques for linear covariance components models are developed and illustrated with special emphasis on explaining computational processes. The estimation of fixed and random…

Missing Values in Multivariate Analysis

- Mathematics
- 1975

SUMMARY This paper presents computational results for some alternative methods of analysing multivariate data with missing values. We recommend an algorithm due to Orchard and Woodbury (1972), which…

Linear regression with randomly dispersed parameters

- Mathematics
- 1973

SUMMARY Consider a collection of individual linear regression models, in which each individual parameter vector is independently drawn from a common multivariate normal distribution and is fixed over…

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

- MathematicsBiometrika
- 1965

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.

A Bayesian approach to growth curves

- Mathematics
- 1975

SUMMARY Recent work on the analysis of growth curves has concentrated on the generalized growth model put forward by Potthoff & Roy (1964), the model being studied from a Bayesian viewpoint by…

Simultaneous estimation of parameters in different linear models and applications to biometric problems.

- MathematicsBiometrics
- 1975

Empirical Bayes procedure is employed in simultaneous estimation of vector parameters from a number of Gauss-Markoff linear models. It is shown that with respect to quadratic loss function, empirical…

Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

- Mathematics
- 1977

Abstract Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a…

Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper

- Engineering
- 1977

Vibratory power unit for vibrating conveyers and screens comprising an asynchronous polyphase motor, at least one pair of associated unbalanced masses disposed on the shaft of said motor, with the…

Growth Curves

- Materials ScienceNature
- 1946

IN NATURE of January 19, 1946, there is a short communication by Prof. W. G. Burgers on “‘Stimulation Crystals’ and Twin-formation in Recrystallized Aluminium”. As indicated in ref. 1 to this…