Graphical methods for multivariate linear models in psychological research: An R tutorial

Abstract

This paper is designed as a tutorial to highlight some recent developments for visualizing the relationships among response and predictor variables in multivariate linear models (MLMs), and implemented in convenient packages for R. These models include multivariate multiple regression analysis (MMRA), multivariate analysis of variance (MANOVA) and multivariate analysis of covariance (MANCOVA). The methods we describe go well beyond what can be understood and explained from simple univariate graphical methods for the separate response variables. We describe extensions of these methods for the case of more than just a few response variables, where the important relationships can be readily seen in the low-dimensional (2D) space that accounts for most of the relevant information. As befits the tutorial nature of this paper, we analyze some sample psychological research studies utilizing these multivariate designs, showing examples in R. In the process, we also take up several practical problems related to the assumptions of MLMs, and how these can be dealt with using graphical methods. Finally, we provide guidelines to aid researchers in conducting multivariate research, pertaining to the analysis, visualization, and reporting of such designs. The graphical and statistical methods described here are all freely available and implemented in the R packages candisc, car, heplots, and mvinfluence.

Selection of popcorn genotypes tolerant toSpodoptera frugiperdaand key traits related to the identification of tolerance

“…The high cophenetic correlation coefficient (CCC = 0.93) indicated an optimal fit between the original data and the dissimilarity matrix and high accuracy of the experimental results. The dendrogram shows two main groups, making the discrimination of the tolerance and/or susceptibility of each genotype group possible [1, 5, 23].…”

“…The groups were established according to the methodology proposed by [22]. Then, canonical variable analysis was carried out with clustering by the Tocher method, factor analysis and later canonical correspondence analysis [23].…”

“…The high cophenetic correlation coefficient (CCC = 0.93) indicated an optimal fit between the original data and the dissimilarity matrix and high accuracy of the experimental results. The dendrogram shows two main groups, making the discrimination of the tolerance and/or susceptibility of each genotype group possible[1,5,23].The first group contained the variety Zapalote Chico, considered by several authors as tolerant to S. frugiperda[7,13,17], and variety Arachida. The varieties Composto Gaúcho, UEM J1 and Composto Márcia were grouped in the second(Figure 1).…”

Yield related key traits in the selection of super sweetcorn hybrids

“…The canonical correspondence analysis was carried out according to Ter Braak (1986). The means were subjected to the Hotelling T2 test at 5% probability, in order to associate the results obtained with the other analyses (Friendly and Sigal 2017). The analyses were carried out using the statistical software Genes (Cruz 2016) and SAS (SAS Institute 2011).…”

Making Meaning out of MANOVA: The Need for Multivariate Post Hoc Testing in Gifted Education Research

“…However, visualization is again strongly recommended to further evaluate the extent of the heterogeneity between the groups. Friendly and Sigal (2017, 2018) provide explanation and code for several visualizations of multivariate linear models. Figure 2 depicts one of these, a plot of the log determinants with surrounding asymptotic confidence intervals (see Cai, Liang, & Zhou, 2015) for each group matrix and the pooled covariance matrix.…”