Generalizability Theory: The Software Problem

1985 ◽  
Vol 10 (1) ◽  
pp. 19-29 ◽  
Author(s):  
John F. Bell
Keyword(s):  
Analysis Of Variance ◽  
Variance Components ◽  
Generalizability Theory ◽  
Estimation Of Variance

This paper outlines the problems associated with the estimation of variance components in generalizability analyses using analysis of variance software, and discusses the most useful software currently available for this specialist application: the MIVQUE method of the SAS procedure VARCOMP.

An Alternative Method for Estimating Variance Components in Generalizability Theory

1990 ◽  
Vol 66 (2) ◽  
pp. 379-386 ◽  
Author(s):  
George A. Marcoulides
Keyword(s):  
Maximum Likelihood ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Generalizability Theory ◽  
Simulated Data ◽  
Restricted Maximum Likelihood ◽  
Alternative Method ◽  
Sample Data

This study compares, using simulated data, two methods for estimating variance components in generalizability (G) studies. Traditionally variance components are estimated from an analysis of variance of sample data. The alternative method for estimating variance components is restricted maximum likelihood (REML). The results indicate that REML provides estimates for the components in the various designs that are closer to the true parameters than the estimates from analysis of variance.

Correct and incorrect estimation of within-day and between-day variation.

1986 ◽  
Vol 32 (9) ◽  
pp. 1734-1737 ◽  
Author(s):  
M J Bookbinder ◽  
K J Panosian
Keyword(s):  
Statistical Theory ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Total Population ◽  
Total Variance ◽  
Population Variance ◽  
Biased Estimators ◽  
The Impact ◽  
Estimation Of Variance

Abstract Between-day variance is an ambiguous term representing either total variance or pure between-day variance. In either case, it is often incorrectly calculated even though analysis of variance (ANOVA) and other excellent methods of estimation are available. We used statistical theory to predict the magnitude of error expected from using several intuitive approaches to estimation of variance components. We also evaluated the impact of estimating the total population variance instead of pure between-day variance and the impact of using biased estimators. We found that estimates of variance components could be systematically biased by several hundred percent. On the basis of these results, we make recommendations to remove these biases and to standardize precision estimates.

Handling Missing Observations in the Two-way Analysis of Variance with Interaction

1978 ◽  
Vol 14 (4) ◽  
pp. 381-388
Author(s):  
H. A. Abou-El-Fittouh ◽  
E. O. Taha
Keyword(s):  
Analysis Of Variance ◽  
Variance Components ◽  
Missing Values ◽  
Missing Observations ◽  
Missing Value ◽  
Tests Of Significance ◽  
Estimation Of Variance

SUMMARYThree procedures for handling missing values in randomized block experiments with more than one observation per plot are examined, and their effects on the resulting expectations of mean squares in the analysis of variance studied. Using the average of the available observations in the plot in which the missing value occurs has the least effect on the validity of the tests of significance and on the estimation of variance components.

Estimating Variance Components from Mean Squares for Random and Mixed Effects Analysis of Variance Models

1966 ◽  
Vol 22 (2) ◽  
pp. 559-570 ◽  
Author(s):  
Norman S. Endler
Keyword(s):  
Total Variation ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Null Hypothesis ◽  
Theoretical Models ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Relative Contribution ◽  
Using Data ◽  
Estimation Of Variance

The analysis of variance can be used for: (a) F tests of the null hypothesis; (b) investigating theoretical models; and (c) estimating, from mean squares, the relative contributions of variance components. The methods of estimation of variance components enable the researcher not only to test significance but to attribute the relative contribution (percentage of variance) of each source to the total variation (sum of variance components). Discussion concerns the advantages, disadvantages and limitations of random and mixed effects models. The study concludes that each researcher must logically choose the model which best describes his experiment. Three-way random and mixed effects models with one observation per cell are compared and illustrated using data from a multidimensional personality inventory.

The Estimation of Variance Components in Generalizability Studies: A Resampling Approach

1989 ◽  
Vol 65 (3) ◽  
pp. 883-889 ◽  
Author(s):  
George A. Marcoulides
Keyword(s):  
Variance Components ◽  
Generalizability Theory ◽  
Measurement Procedure ◽  
Small Samples ◽  
Accurate Estimation ◽  
Nonnormal Data ◽  
Nonnormal Distributions ◽  
Unbalanced Designs ◽  
Resampling Procedure ◽  
Estimation Of Variance

The accurate estimation of variance components is essential for studying the reliability of a measurement procedure in generalizability theory. Previous research has shown that errors in estimation of variance components lead to erroneous interpretations. This is particularly true with small samples, nonnormal data, and unbalanced designs. This study explores a resampling procedure for obtaining estimates of variance components. The results suggest that the proposed method is useful when most needed—with small samples, nonnormal distributions, and unbalanced designs.

Estimation of variance components in normal linear mixed models with additivity

2015 ◽  
Author(s):  
Dário Ferreira ◽  
Sandra S. Ferreira ◽  
Célia Nunes ◽  
João T. Mexia
Keyword(s):  
Mixed Models ◽  
Variance Components ◽  
Linear Mixed Models ◽  
Estimation Of Variance
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