Unbalanced Repeated-Measures Models with Structured Covariance Matrices

Jennrich, Robert I.; Schluchter, Mark D.

doi:10.2307/2530695

Cited by 1,140 publications

(585 citation statements)

References 26 publications

Supporting

Mentioning

573

Contrasting

Unclassified

Order By: Relevance

“…Little and Rubin (1987) catalogued EM algorithms for any missing-data problems. EM has also been applied to many situations that are not necessarily thought of as missing-data problems but can be formulated as such: multilevel linear models for unbalanced repeated measures data, where not all participants are measured at all time points (Jennrich & Schluchter, 1986;Laird & Ware, 1982); latent class analysis (Clogg & Goodman, 1984) and other finitemixture models (Titterington, Smith, & Makov, 1985); and factor analysis (Rubin & Thayer, 1983). For some of these problems, non-EM methods are also available.…”

Section: Computing ML Estimatesmentioning

confidence: 99%

Missing data: Our view of the state of the art.

Schafer¹,

Graham²

2002

Psychological Methods

9,430

7,570

View full text Add to dashboard Cite

Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR.Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.

show abstract

Section: Computing ML Estimatesmentioning

confidence: 99%

Missing data: Our view of the state of the art.

Schafer¹,

Graham²

2002

Psychological Methods

9,430

7,570

View full text Add to dashboard Cite

show abstract

“…To account for the likely correlation between outcomes observed at subsequent assessments of the same subject, we relied on generalized estimating equations (GEE) extension of conventional multiple linear regression for longitudinal data (39). In GEE analyses, we assumed the autoregressive order 1 structure of the covariance matrix of the residuals, which implies that correlations between observations that are closer in time are stronger than for observations several months apart, a standard assumption in longitudinal studies (40).…”

Section: Statistical Analysesmentioning

confidence: 99%

Maintenance of exercise in women with fibromyalgia

Dobkin¹,

Abrahamowicz²,

Fitzcharles³

et al. 2005

Arthritis & Rheumatism

View full text Add to dashboard Cite

Objective. To identify predictors of maintenance of exercise for women with fibromyalgia (FM).Methods. Women with FM who had been randomized to the exercise arm of a clinical trial were studied prospectively during and 3 months following treatment. Subjects completed exercise logs weekly and returned the data via postal mail. Outcome variables were duration of aerobic and stretching exercises. Two separate multivariate models for longitudinal data were built with adjustment for in-treatment adherence and time. Pretreatment characteristics (self efficacy, pain, disability, stress, exercise barriers and benefits, and age) and changes during treatment (pain, disability, stress, and exercise barriers and benefits) were considered potential predictors of exercise maintenance. Results. Stretching significantly decreased in the 3 months following treatment. High stress at baseline and increases in stress during treatment were associated with poor maintenance of stretching. Disability at baseline (measured with the Fibromyalgia Impact Questionnaire), an increase in barriers to exercise during treatment, and increases in upper-body pain during treatment were associated with worse maintenance of aerobic exercise in the 3 months following treatment. Conclusion. The maintenance of an exercise program in women with FM appears to be contingent on being able to deal with stress, pain, barriers to exercise, and disability.

show abstract

“…But this type of matrix is too complex, since all variances and covariances are different and too large matrices would then have to be calculated. According to Jennrich and Schluchter (1986), the number of estimatable parameters is q 5 (T*(T 1 1))/2, where T is the length of the time series. With a maximum length of time series in our dataset of about 225 measures (lactation day 6 to 230), the number of parameters to estimate would arise to q 5 25 425.…”

Section: Model I (Fr)mentioning

confidence: 99%

Analysis of water intake, dry matter intake and daily milk yield using different error covariance structures

Kramer

Stamer²,

Spilke

et al. 2008

Animal

View full text Add to dashboard Cite

The aim of the present study was to investigate the daily measured traits milk yield, water intake and dry matter intake with fixed and random regression models added with different error covariance structures. It was analysed whether these models deliver better model fitting in contrast to conventional fixed and random regression models. Furthermore, possible autocorrelation between repeated measures was investigated. The effect of model choice on statistical inference was also tested. Data recording was performed on the Futterkamp dairy research farm of the Chamber of Agriculture of SchleswigHolstein. A dataset of about 21 000 observations from 178 Holstein cows was used. Average milk yield, water intake and dry matter intake were 34.9, 82.4 and 19.8 kg, respectively. Statistical analysis was performed using different linear mixed models. Lactation number, test day and the parameters to model the function of lactation day were included as fixed effects. Different structures were tested for the residuals; they were compared for their ability to fit the model using the likelihood ratio test, and Akaike's and Bayesian's information criteria. Different autocorrelation patterns were found. Adjacent repeated measures of daily milk yield were highest correlated (p 1 5 0.32) in contrast to measures further apart, while for water intake and dry matter intake, the measurements with a lag of two units had the highest correlations with p 2 5 0.11 and 0.12. The covariance structure of TOEPLITZ was most suitable to indicate the dependencies of the repeated measures for all traits. Generally, the most complex model, random regression with the additional covariance structure TOEPLITZ(4), provided the lowest information criteria. Furthermore, the model choice influenced the significance values of one fixed effect and therefore the general inference of the data analysis. Thus, the random regression 1 TOEPLITZ(4) model is recommended for use for the analysis of equally spaced datasets of milk yield, water intake and dry matter intake.

show abstract

Unbalanced Repeated-Measures Models with Structured Covariance Matrices

Cited by 1,140 publications

References 26 publications

Missing data: Our view of the state of the art.

Missing data: Our view of the state of the art.

Maintenance of exercise in women with fibromyalgia

Analysis of water intake, dry matter intake and daily milk yield using different error covariance structures

Contact Info

Product

Resources

About