The choice of algorithm in multivariate regression can indeed influence the results, particularly the estimation of standard errors becuase of their methods of computing as described below:
- CWLS (Component-Wise Least Squares) approach estimates the regression coefficients for each response variable separately, which can lead to smaller standard errors if the responses are not highly correlated. It does not account for the covariance between response variables in the error terms, potentially underestimating standard errors if there is significant correlation.
- MVN (Multivariate Normal): Assumes a multivariate normal distribution for the errors and estimates the coefficients considering the covariance structure between responses This method generally provides more robust standard error estimates when responses are correlated, as it accounts for the covariance.
Some basic suggestions for choosing the right algorithm:
- Correlation Between Responses: If your response variables are correlated, mvn is usually more appropriate as it accounts for this correlation in the estimation process.
- Model Assumptions: Consider the assumptions of each method. mvn assumes multivariate normality of errors, which might not hold in all cases.
- Data Characteristics: If you have a large dataset with complex covariance structures, mvn might be better suited. For simpler cases or when computational efficiency is a concern, cwls might suffice.
