Multivariate Multiple Regression

Multivariate multiple regression regresses two or more outcome variables on the same set of predictors and tests each predictor's joint effect on all outcomes with multivariate statistics such as Pillai's trace and Wilks' lambda.

다변량 다중회귀는 여러 결과변수를 같은 설명변수로 함께 회귀하고 Pillai 흔적·Wilks 람다로 설명변수의 결과 전체에 대한 효과를 검정하는 방법입니다.

I have several correlated outcome scores and the same predictors for each; how do I test whether a predictor affects the outcomes as a set?

같은 설명변수로 여러 결과 점수를 볼 때, 한 설명변수가 결과들 전체에 영향을 주는지 어떻게 검정하나요?

Multivariate multiple regression estimates one coefficient per predictor for each outcome, identical to separate regressions, and adds multivariate tests that consider all outcomes together. Pillai's trace and Wilks' lambda test whether a predictor is related to the set of outcomes while accounting for their correlations.

When to use Multivariate Multiple Regression

• Several continuous outcomes are analysed with the same predictors
• You want one test per predictor across all outcomes to control error rates
• Outcomes are moderately correlated

When to use something else

• Equations need different predictors; use seemingly unrelated regression instead
• Predictors are only group indicators; use MANOVA instead

Assumptions and requirements

• Outcomes are linearly related to the predictors
• Residuals follow a multivariate normal distribution
• Residual covariance matrix is constant across observations
• Observations are independent

What the analysis reports

• Coefficients, standard errors and tests for each outcome
• Pillai's trace and Wilks' lambda for each predictor with F approximations
• Degrees of freedom and p values
• Residual normality check for each outcome

How to report it

In a multivariate multiple regression, [predictor] was jointly related to [outcomes], Pillai's trace = [value], F([df1], [df2]) = [value], p = [value]; its effect on [outcome 1] was b = [value], p = [value].

Related methods

• Seemingly Unrelated Regression (SUR)
• MANOVA
• Multiple Linear Regression

Run Multivariate Multiple Regression on Quorant