Likelihood Ratio Type Statistics for Repeated Measures Designs with Heterogeneous Covariance Matrices

2013 ◽  
Vol 42 (6) ◽  
pp. 1070-1086
Author(s):  
A. Stavropoulos ◽  
M. G. Akritas ◽  
C. Caroni
Keyword(s):  
Likelihood Ratio ◽  
Repeated Measures ◽  
Covariance Matrices ◽  
Repeated Measures Designs ◽  
Ratio Type Statistics

Nonparametric Tests for Analyzing Interactions Among Intra-Block Ranks in Multiple Group Repeated Measures Designs

2000 ◽  
Vol 25 (1) ◽  
pp. 20-59 ◽  
Author(s):  
T. Mark Beasley
Keyword(s):  
Repeated Measures ◽  
Profile Analysis ◽  
Nonparametric Tests ◽  
Covariance Matrices ◽  
Statistical Properties ◽  
Multivariate Approach ◽  
Omnibus Test ◽  
Multiple Group ◽  
Multiple Groups ◽  
Repeated Measures Designs

This study developed an extension of the Hollander and Sethuraman (1978) statistic (B2 ) for testing discordance among intra-block rankings of K elements for multiple groups (J ≥ 2) of raters. B2 was demonstrated to be equivalent to the Pillai-Bartlett trace (V ) from a multivariate profile analysis performed on the ranks such that B2 = V (N - 1) Results confirmed the utility of B2 as an omnibus test of interaction (i.e., discordance) among intra-block ranks and demonstrated that it was more powerful than the multivariate approach to ranked data suggested by Serlin and Marascuilo (1983) . An extension of the Friedman (1937) two-way ANOVA for intra-block ranks was also developed. The adequacy of these procedures for testing interactions in multiple group repeated measures designs was investigated. The Friedman model demonstrated adequate statistical properties only when covariance matrices were spherical. Results also demonstrated that the Hollander-Sethuraman model was useful in testing interaction contrasts.

Power Comparisons of Eight Tests for Sphericity in Repeated Measures Designs

1992 ◽  
Vol 17 (3) ◽  
pp. 233-249 ◽  
Author(s):  
John E. Cornell ◽  
Dean M. Young ◽  
Samuel L. Seaman ◽  
Roger E. Kirk
Keyword(s):  
Repeated Measures ◽  
Covariance Matrices ◽  
Block Designs ◽  
Sample Covariance Matrices ◽  
Large Samples ◽  
Sample Covariance ◽  
Invariant Test ◽  
Power Comparisons ◽  
Repeated Measures Designs ◽  
Randomized Block Designs

A Monte Carlo simulation was conducted to investigate the relative power of eight tests for sphericity in randomized block designs. Box’s (1954) epsilon values º = .35, .55, .75, .80, .85, .90, .95, and 1.00 were used to quantify departures from sphericity for rank-1 population covariance matrices of dimension p = 3, 5, 7, and 9. Sample covariance matrices were generated for samples of size n = 10, 15, 20, and 30. The locally best invariant test demonstrated substantial power to detect departures from sphericity—regardless of p— for both small and large samples for rank-1 alternatives. Recommendations are made regarding the use of preliminary tests.

Increasing Precision without Altering Treatment Effects: Repeated Measures Designs in Survey Experiments

2021 ◽  
pp. 1-18
Author(s):  
SCOTT CLIFFORD ◽  
GEOFFREY SHEAGLEY ◽  
SPENCER PISTON
Keyword(s):  
Treatment Effect ◽  
Repeated Measures ◽  
Treatment Effects ◽  
Repeated Measurements ◽  
Experimental Designs ◽  
Treatment Effect Size ◽  
Standard Design ◽  
Survey Experiments ◽  
Repeated Measures Designs ◽  
Alternative Designs

The use of survey experiments has surged in political science. The most common design is the between-subjects design in which the outcome is only measured posttreatment. This design relies heavily on recruiting a large number of subjects to precisely estimate treatment effects. Alternative designs that involve repeated measurements of the dependent variable promise greater precision, but they are rarely used out of fears that these designs will yield different results than a standard design (e.g., due to consistency pressures). Across six studies, we assess this conventional wisdom by testing experimental designs against each other. Contrary to common fears, repeated measures designs tend to yield the same results as more common designs while substantially increasing precision. These designs also offer new insights into treatment effect size and heterogeneity. We conclude by encouraging researchers to adopt repeated measures designs and providing guidelines for when and how to use them.

Classification Based on Multivariate Repeated Measures with Time Effect on Mean Vector and an AR (1) Correlation Structure on the Repeated Measures

2005 ◽  
Vol 57 (1-2) ◽  
pp. 49-66 ◽  
Author(s):  
Anuradba Roy ◽  
Ravindra Khattree
Keyword(s):  
Maximum Likelihood ◽  
Repeated Measures ◽  
Likelihood Estimation ◽  
Covariance Matrices ◽  
Time Effect ◽  
Population Parameters ◽  
Time Effects ◽  
Mean Vectors ◽  
Mean Vector ◽  
Over Time

In repeated measures studies how observations change over time is often of prime interest. Modelling this time effect in the context of discrimination, is the objective of this article. We study the problem of classification with multiple q-variate observations with time effect on each individual. The covariance matrices as well as mean vectors are mordelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects. Computation schemes for maximum likelihood estimation of required population parameters are provided.

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