Testing of multivariate repeated measures data with block exchangeable covariance structure

Test ◽  
2017 ◽  
Vol 27 (2) ◽  
pp. 360-378 ◽  
Author(s):  
Ivan Žežula ◽  
Daniel Klein ◽  
Anuradha Roy
Keyword(s):  
Repeated Measures ◽  
Covariance Structure ◽  
Repeated Measures Data

The use of MIXED models in the analysis of animal experiments with repeated measures data

2004 ◽  
Vol 84 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Z. Wang and L. A. Goonewardene
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Repeated Measures ◽  
Mixed Model ◽  
Covariance Structure ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
General Linear ◽  
Repeated Measures Data ◽  
Split Plot

The analysis of data containing repeated observations measured on animals (experimental unit) allocated to different treatments over time is a common design in animal science. Conventionally, repeated measures data were either analyzed as a univariate (split-plot in time) or a multivariate ANOVA (analysis of contrasts), both being handled by the General Linear Model procedure of SAS. In recent times, the mixed model has become more appealing for analyzing repeated data. The objective of this paper is to provide a background understanding of mixed model methodology in a repeated measures analysis and to use balanced steer data from a growth study to illustrate the use of PROC MIXED in the SAS system using five covariance structures. The split-plot in time approach assumes a constant variance and equal correlations (covariance) between repeated measures or compound symmetry, regardless of their proximity in time, and often these assumptions are not true. Recognizing this limitation, the analysis of contrasts was proposed. If there are missing measurements, or some of the data are measured at different times, such data were excluded resulting in inadequate data for a meaningful analysis. The mixed model uses the generalized least squares method, which is generally better than the ordinary least squares used by GLM, if the appropriate covariance structure is adopted. The presence of unequally spaced and/or missing data does not pose a problem for the mixed model. In the example analyzed, the first order ante dependence [ANTE(1)] covariance model had the lowest value for the Akaike and Schwarz’s Bayesian information criteria fit statistics and is therefore the model that provided the best fit to our data. Hence, F values, least square estimates and standard errors based on the ANTE (1) were considered the most appropriate from among the five models demonstrated. It is recommended that the mixed model be used for the analysis of repeated measures designs in animal studies. Key words: Repeated measures, General Linear Model, Mixed Model, split-plot, covariance structure

Estimation of genotypic correlation and heritability of apricot traits, using restricted maximum likelihood in repeated measures data

2016 ◽  
Vol 96 (3) ◽  
pp. 439-447 ◽  
Author(s):  
Ahmad Ismaili ◽  
Farhad Karami ◽  
Omidali Akbarpour ◽  
Abdolhossein Rezaei Nejad
Keyword(s):  
Maximum Likelihood ◽  
Repeated Measures ◽  
Mixed Model ◽  
Covariance Structure ◽  
Restricted Maximum Likelihood ◽  
Environment Interaction ◽  
Genotypic Correlation ◽  
Model Based ◽  
Repeated Measures Data ◽  
Heritability Estimation

In estimation of genetic parameters in perennial tree species on the basis of analysis of variance (ANOVA), heterogeneity of years and genotype × environment interaction for data sets during the juvenility to maturity life period is ignored. Therefore, a linear mixed model based on restricted maximum likelihood (REML) approximation for modeling of covariance structure of longitudinal data can improve our ability to analyze repeated measures data. In the present research, a modeling of variance-covariance structure by mixed model based on the REML approach has been used for characteristics of 26 apricot genotypes recorded during three years. Fitting unstructured covariance (UN) models for all traits indicated a great heterogeneity of variances among repeated years and the trends of response variables in the genotypes (except for RWC) was due to imperfect correlation of subjects measured in different years. Based on the same structure, positive correlations were estimated among fruit set, potassium content, and yield of pistil in repetitive years, and most traits showed high heritability estimation. To our knowledge, this is the first report in plant that genotypic correlation and heritability and their standard errors are estimated in a repeated measures data over years using REML approximation.

Probability-Based and Measurement-Related Hypotheses With Full Restriction for Investigations by Means of Confirmatory Factor Analysis

Methodology ◽  
2011 ◽  
Vol 7 (4) ◽  
pp. 157-164
Author(s):  
Karl Schweizer
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Cognitive Processing ◽  
Latent Variables ◽  
Repeated Measures ◽  
Latent Variable ◽  
Model Fit ◽  
Repeated Measures Data ◽  
Confirmatory Factor ◽  
And Performance

Probability-based and measurement-related hypotheses for confirmatory factor analysis of repeated-measures data are investigated. Such hypotheses comprise precise assumptions concerning the relationships among the true components associated with the levels of the design or the items of the measure. Measurement-related hypotheses concentrate on the assumed processes, as, for example, transformation and memory processes, and represent treatment-dependent differences in processing. In contrast, probability-based hypotheses provide the opportunity to consider probabilities as outcome predictions that summarize the effects of various influences. The prediction of performance guided by inexact cues serves as an example. In the empirical part of this paper probability-based and measurement-related hypotheses are applied to working-memory data. Latent variables according to both hypotheses contribute to a good model fit. The best model fit is achieved for the model including latent variables that represented serial cognitive processing and performance according to inexact cues in combination with a latent variable for subsidiary processes.

Power of Modified Brown-Forsythe and Mixed-Model Approaches in Split-Plot Designs

Methodology ◽  
2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Pablo Livacic-Rojas ◽  
Guillermo Vallejo ◽  
Paula Fernández ◽  
Ellián Tuero-Herrero
Keyword(s):  
Repeated Measures ◽  
Statistical Power ◽  
Mixed Model ◽  
Covariance Structure ◽  
Simulation Method ◽  
Future Research ◽  
Repeated Measures Design ◽  
Fixed And Random Effects ◽  
Split Plot ◽  
High Level

Abstract. Low precision of the inferences of data analyzed with univariate or multivariate models of the Analysis of Variance (ANOVA) in repeated-measures design is associated to the absence of normality distribution of data, nonspherical covariance structures and free variation of the variance and covariance, the lack of knowledge of the error structure underlying the data, and the wrong choice of covariance structure from different selectors. In this study, levels of statistical power presented the Modified Brown Forsythe (MBF) and two procedures with the Mixed-Model Approaches (the Akaike’s Criterion, the Correctly Identified Model [CIM]) are compared. The data were analyzed using Monte Carlo simulation method with the statistical package SAS 9.2, a split-plot design, and considering six manipulated variables. The results show that the procedures exhibit high statistical power levels for within and interactional effects, and moderate and low levels for the between-groups effects under the different conditions analyzed. For the latter, only the Modified Brown Forsythe shows high level of power mainly for groups with 30 cases and Unstructured (UN) and Autoregressive Heterogeneity (ARH) matrices. For this reason, we recommend using this procedure since it exhibits higher levels of power for all effects and does not require a matrix type that underlies the structure of the data. Future research needs to be done in order to compare the power with corrected selectors using single-level and multilevel designs for fixed and random effects.

scholarly journals Evaluation of a novel threonine source for nursery pig diets

2020 ◽  
Vol 4 (4) ◽  
Author(s):  
Dalton Humphrey ◽  
Spenser Becker ◽  
Jason Lee ◽  
Keith Haydon ◽  
Laura Greiner
Keyword(s):  
Repeated Measures ◽  
Fixed Effects ◽  
Average Daily Gain ◽  
Covariance Structure ◽  
Treatment Phase ◽  
Positive Control ◽  
Negative Control ◽  
Feed Ratio ◽  
Experimental Unit ◽  
Nursery Pigs

Abstract Four hundred and eighty (PIC 337 X 1050, PIC Genus, Hendersonville, TN) pigs were used to evaluate a novel threonine source (ThrPro, CJ America Bio, Fort Dodge, IA) for nursery pigs from approximately 7 to 20 kg body weight (BW). After weaning, pigs were sorted by sex and fed a common diet for 1 wk. Upon completion of the first week, pigs were sorted into randomized complete blocks, equalized by weight, within 16 replications. Pigs were allocated to one of three dietary treatments: positive control (POS)—standard ileal digestible threonine-to-lysine ratio (SID; Thr:Lys) 0.60, negative control (NEG)—SID Thr:Lys ≤0.46, and alternative Thr source (TEST)—SID Thr:Lys 0.60. The alternative Thr source included fermentative biomass and was assumed to contain 75% Thr and a digestibility coefficient of 100% based on the manufacturer’s specifications. All other nutrients met or exceeded the NRC recommendations. Growth and intake data were analyzed as repeated measures with a compound symmetry covariance structure using the MIXED procedure in SAS 9.4 (SAS Institute Inc., Cary, NC) with pen as the experimental unit. Treatment, phase, the interaction between treatment and phase, and block were included as fixed effects in the model. Differences in total removals were tested using Fisher’s Exact Test of PROC FREQ. Results were considered significant at P ≤ 0.05 and considered a trend at P > 0.05 and P ≤ 0.10. During the first 14 d, pigs fed TEST had decreased gain-to-feed ratio (G:F; 0.77 vs. 0.80, P = 0.022) compared to POS and increased G:F (0.77 vs. 0.73, P < 0.001) compared to NEG. Over days 14–28, pigs fed TEST had similar G:F (0.71 vs. 0.70, P = 0.112) compared to POS and increased G:F (0.71 vs. 0.63, P < 0.001) compared to NEG. Overall (days 0–28), pigs fed TEST had similar average daily gain (ADG; 0.47 vs. 0.47 kg/d, P = 0.982) and G:F (0.76 vs. 0.74, P = 0.395) compared to POS and increased ADG (0.47 vs. 0.43 kg/d, P < 0.001) and G:F (0.76 vs. 0.67, P < 0.001) compared to NEG. The average daily feed intake was not significantly different across treatments for the entirety of the study. In conclusion, the replacement of crystalline L-Thr with a novel Thr source resulted in similar growth performance in nursery pigs from approximately 7 to 20 kg.

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