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

scholarly journals Least Squares Estimations for the General Linear Model Parameters with Epsilon Skew Normal Error Term

2020 ◽  
pp. 636-645
Author(s):  
Hussain Karim Nashoor ◽  
Ebtisam Karim Abdulah
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Skewed Distribution ◽  
General Linear ◽  
Average Error ◽  
Model Parameters ◽  
Skew Normal

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model. 

scholarly journals Sensitivity analysis in linear models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Shuangzhe Liu ◽  
Tiefeng Ma ◽  
Yonghui Liu
Keyword(s):  
Sensitivity Analysis ◽  
Least Squares ◽  
Linear Model ◽  
Linear Models ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
The Other ◽  
Regression Coefficients ◽  
General Linear ◽  
Least Squares Estimators

AbstractIn this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coefficients and variance. We propose a newly unified set of definitions for local sensitivity for both situations, one for the estimators of the regression coefficients, and the other for the estimators of the variance. Based on these definitions, we present the estimators’ sensitivity results.We include brief remarks on possible links of these definitions and sensitivity results to local influence and other existing results.

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 Linear models for diallel crosses: a review with R functions

2020 ◽  
Author(s):  
Andrea Onofri ◽  
Niccolò Terzaroli ◽  
Luigi Russi
Keyword(s):  
Linear Model ◽  
Combining Ability ◽  
Linear Models ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
General Purpose ◽  
General Linear ◽  
Mixed Effect ◽  
Typical Process ◽  
R Functions

Abstract Key message A new R-software procedure for fixed/random Diallel models was developed. We eased the diallel schemes approach by considering them as specific cases with different parameterisations of a general linear model. Abstract Diallel experiments are based on a set of possible crosses between some homozygous (inbred) lines. For these experiments, six main diallel models are available in literature, to quantify genetic effects, such as general combining ability (GCA), specific combining ability (SCA), reciprocal (maternal) effects and heterosis. Those models tend to be presented as separate entities, to be fitted by using specialised software. In this manuscript, we reinforce the idea that diallel models should be better regarded as specific cases (different parameterisations) of a general linear model and might be fitted with general purpose software facilities, as used for all other types of linear models. We start from the estimation of fixed genetical effects within the R environment and try to bridge the gap between diallel models, linear models and ordinary least squares estimation (OLS). First, we review the main diallel models in literature. Second, we build a set of tools to enable geneticists, plant/animal breeders and students to fit diallel models by using the most widely known R functions for OLS fitting, i.e. the ‘lm()’ function and related methods. Here, we give three examples to show how diallel models can be built by using the typical process of GLMs and fitted, inspected and processed as all other types of linear models in R. Finally, we give a fourth example to show how our tools can be also used to fit random/mixed effect diallel models in the Bayesian framework.

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