Robust Optimium Invariant Tests of Covariance Structures Useful in Linear Models.

Multivariate mixed models (MMM) are generalized linear models with both fixed and random effect having multiple response variables. MMM allow partitioning of total (phenotypic) (co)variances for multiple traits into (co)variances on hierarchically lower levels. We outline why ecologists and evolutionary biologists should be interested in such partitioning as well as the levels of analyses that arise when making inferences on multi-level covariance structures. We consider biological levels of interest to be genes (e.g. GWAS, genomic selection), genotypes (genetic (co)variances), individual or other subject (e.g. between-individual (co)variances) and phylogenetic taxa (phylogenetic (co)variances). All of these biological levels can be modelled in a MMM and we distinguish several demand levels of using MMM of increasing complexity. We present an overview of current open-access software implementations of MMM in the open software R with respect to these demand levels, and present example scripts aimed at getting started with MMM on all biological levels. We describe four freely available R packages for MMM, two using Bayesian (Monte Carlo and Hamiltonian Markov Chains) and two using a likelihood framework. Depending on the need of the analyst, there are a number of freely available R-based MMM implementations of relevance to the field of ecology and evolution.

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Similar tests for covariance structures in multivariate linear models

Journal of Multivariate Analysis ◽

10.1016/j.jmva.2004.04.001 ◽

2005 ◽

Vol 93 (2) ◽

pp. 223-237

Author(s):

G. Forchini

Keyword(s):

Linear Models ◽

Covariance Structures ◽

Multivariate Linear Models

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Covariance Structures of Linear Models

Pakistan Journal of Statistics and Operation Research ◽

10.18187/pjsor.v7i2-sp.298 ◽

2011 ◽

Vol 7 (2-Sp) ◽

Author(s):

Arjun K. Gupta ◽

D. G. Kabe

Keyword(s):

Linear Models ◽

Covariance Structures

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Applied Linear Models with SAS

10.1017/cbo9780511778643 ◽

2009 ◽

Cited By ~ 4

Author(s):

Daniel Zelterman

Keyword(s):

Linear Models

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Improved inference in linear models with additional information

Optimization ◽

10.1080/02331937508842298 ◽

1975 ◽

Vol 6 (5) ◽

pp. 817-829

Author(s):

O. Bunke

Keyword(s):

Linear Models ◽

Additional Information

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A Note on Effects of Digital Approximation in Linear Models

Communications in Statistics - Simulation and Computation ◽

10.1080/03610917408548483 ◽

1974 ◽

Vol 3 (9) ◽

pp. 893-897

Author(s):

Gerald McWilliams ◽

James Poirot†

Keyword(s):

Linear Models

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Effects of Momentary Affect on Satisfaction Judgments

Journal of Individual Differences ◽

10.1027/1614-0001/a000304 ◽

2020 ◽

Vol 41 (2) ◽

pp. 61-67

Author(s):

Marko Tončić ◽

Petra Anić

Keyword(s):

Linear Models ◽

Time Frame ◽

Hierarchical Linear Models ◽

Curvilinear Relationship ◽

Positive And Negative Affect ◽

Transient Events ◽

Time Frames ◽

Events Data ◽

Level Satisfaction ◽

Source Of Information

Abstract. This study aims to examine the effect of affect on satisfaction, both at the between- and the within-person level for momentary assessments. Affect is regarded as an important source of information for life satisfaction judgments. This affective effect on satisfaction is well established at the dispositional level, while at the within-person level it is heavily under-researched. This is true especially for momentary assessments. In this experience sampling study both mood and satisfaction scales were administered five times a day for 7 days via hand-held devices ( N = 74 with 2,122 assessments). Several hierarchical linear models were fitted to the data. Even though the amount of between-person variance was relatively low, both positive and negative affect had substantial effects on momentary satisfaction on the between- and the within-person level as well. The within-person effects of affect on satisfaction appear to be more pronounced than the between-person ones. At the momentary level, the amount of between-person variance is lower than in studies with longer time-frames. The affect-related effects on satisfaction possibly have a curvilinear relationship with the time-frame used, increasing in intensity up to a point and then decreasing again. Such a relationship suggests that, at the momentary level, satisfaction might behave in a more stochastic manner, allowing for transient events/data which are not necessarily affect-related to affect it.

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