Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

Abstract

-The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03-70.20 for RM and 1.03-60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition. Index terms:Bos taurus x Bos indicus, animal breeding, beef cattle, correlation matrix, crossbreeding, variance inflation factor. Grau de multicolinearidade e variáveis envolvidas na dependência linear em modelos aditivo-dominantesResumo -O objetivo deste trabalho foi avaliar o grau de multicolinearidade e identificar as variáveis envolvidas na dependência linear em modelos aditivo-dominantes. Foram utilizados dados de peso ao nascimento (n=141.567), peso ao ano (n=58.124) e perímetro escrotal (n=20.371) de bovinos de corte compostos Montana Tropical. O diagnóstico de multicolinearidade foi baseado no fator de inflação de variância (VIF) e no exame dos índices de condição e dos autovalores da matriz de correlações entre as variáveis explanatórias. O primeiro modelo estudado (RM) incluiu o efeito fixo de classe de idade da mãe ao parto e as covariáveis associadas aos efeitos aditivos e não aditivos diretos e maternos. O segundo modelo (R) incluiu todos os efeitos do RM, exceto os efeitos aditivos maternos. Detectou-se multicolinearidade em ambos os modelos para todas as características consideradas, com valores de VIF de 1,03-70,20, para RM, e de 1,03-60,70, para R. As colinearidades aumentaram com o aumento de variáveis no modelo e com a redução no volume de observações, e foram classificadas como fracas, com valores de índice de condição entre 10,00 e 26,77. Em geral, as variáveis associadas aos efeitos aditivos e não aditivos estiveram envolvidas em multicolinearidade, parcialmente em razão da ligação natural entre essas covariáveis como frações dos tipos biológicos na composição racial.Termos para indexação: Bos taurus x Bos indicus, melhoramento animal, bovino de...

Factors Related to Behavioral Functioning in Mothers of Children with Type 1 Diabetes: Application of Transactional Model of Stress and Coping

“…Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and in our data set, with condition index values between 1 and 15.52 the collinearity was classified as weak (16).…”

Genetic Architecture of Carcass and Meat Quality Traits in Montana Tropical® Composite Beef Cattle

“…Coefficients for biological types (N, A, B, and C) were equal to the proportion of each biological type in the breed composition (as recorded by the producers/technicians or calculated based on pedigree relationship between animals), and it was assumed that the sum of all proportions of biological types in one animal were equal to one. To avoid multicollinearity, direct additive effects of the biological type N were excluded from the statistical models, i.e., the effects for A, B, and C were estimated as deviations of the additive effects of N (Dias et al, 2011;Petrini et al, 2012). Genetic correlations.…”

Factors Affecting Vocational College Instructors’ Usage of LMS in the Post-Pandemic Normal

“…The results in Table 4 show that the independent variables' tolerance value is more significant than 0.20, the VIF value is less than 10, and the CI value is less than 30. This finding indicates that these variables are not multicollinear (Petrini et al, 2012;Robinson & Schumacker, 2009). The IBM SPSS Statistics 22 package software was used to conduct the analysis.…”