## Multivariate Regression

This page will allow users to examine the relative importance of predictors in multivariate multiple regression using relative weight analysis (LeBreton & Tonidandel, 2008). Numerous capabilities are built in that allow users to:

- Produce raw relative weight values (epsilons) as well as rescaled weights (scaled as a percentage of predictable variance) for every predictor in the model. Rescaled weights are presented as a function of P squared – see LeBreton & Tonidandel (2008) for an overview.
- Produce the confidence interval around each relative weight with coverage probability specified by the user. The approach used here mirrors that described by Johnson (2004) with the notable exception of computing the confidence interval around the raw weights using the bias corrected accelerated method for generating the bootstrapped confidence intervals as recommended by Tonidandel, LeBreton, and Johnson (2009).
- Evaluate the statistical significance of the relative weights using the approach outlined by Tonidandel, LeBreton, and Johnson (2009). A weight is considered to be statistically significant if the confidence interval produced here does not contain zero (this confidence interval is different from the confidence interval described in the previous bullet point – see Tonidandel et. al. 2009 for clarification)
- Test whether the relative weights from two predictors are significantly different from one another using the approach suggested by Johnson (2004) with the updates recommended by Tonidandel, LeBreton, and Johnson (2009). Two relative weights are considered to be significantly different from one another if the confidence interval produced here does not contain zero.
- Test whether a predictor's relative weight differs significantly across two groups. As before, a description of the original approach can be found in Johnson (2004) with additional recommendations in Tonidandel, LeBreton, and Johnson (2009). The relative weight of a predictor is considered to be significantly different between two groups if the confidence interval produced here does not contain zero.

Two options are available to users wishing to perform any of the above procedures.

- Users can supply the necessary input parameters and choose to download the generated R code. Users can then run this code locally on their own personal computer (R can be freely downloaded at: http://cran.r-project.org/ )
- Users can supply the necessary input parameters and execute the generated R code on the R web server by choosing this option and pressing the submit button. Users will then recieve the results in an email with a copy of the R-code that was executed and the results. The calculations for confidence intervals and tests of significance require running multiple boostrapped replications. As a result, it can take some time (5 to 10 minutes or more) before a result is returned. Please be patient.

__User Input__

**Before beginning, please note that R is case sensitive. Failure to use the correct case when specifying variable names, file names, or file paths will result in an error message.**

- Choose to download code to run locally or send the code directly to the R server.
- Specify the location of the data file. The data format should be a .csv file with variable names in the first row. A valid variable name consists of letters, numbers and the dot or underline characters (other special characters including spaces are not permitted) and starts with a letter or the dot (not a number). If you start a variable name with a dot, it may not be followed by a number (e.g. names such as '".2way"' are not valid). There are also some reserved names that are not valid variable names. The list of reserved names is quite short and can be found here: http://stat.ethz.ch/R-manual/R-devel/library/base/html/Reserved.html
- Specify the format of the input file (either correlation matrix or raw data). The input file can be either raw data or a correlation matrix. Please note that all of the confidence intervals/tests of significance described above require bootstrapping raw data so that output will not be available if your input data file is a correlation matrix. Also, if your input file is a correlation matrix, the criterion variables must be the first variables in the matrix and in the order listed in the criterion variables box below. Similarly, the predictor variables that follow must also appear in the order listed in the predictors box below. Example input data files of each type can be found here - http://academics.davidson.edu/psychology/Tonidandel/TonidandelExampleDataSets.htm
- Choose a missing data option. If the input file is raw data, one must indicate how missing data should be handled if it is encountered.
- Enter the variable names of the criterion variables. Each variable should be entered on a new line (R is case sensitive).
- Enter the variable names of the predictors in the model. Each predictor should be entered on a new line (R is case sensitive).
- Select the number of iterations to use for the boostrapping procedures. We recommend at least 10,000.
- Specify the alpha value used to compute confidence intervals/test for statistical significance.
- Select variables to evaluate statistical significance. If one wishes to test whether the relative weight of a predictor is significantly different from the relative weight of another predictor, one must enter the variable name of one of the predictors here (R is case sensitive). The variable listed here will be tested against all of the other predictors in your data set.
- Identify the groups to be compared. If one wishes to test whether a predictor's relative weight differs significantly across two groups, one must enter the name of the grouping variable (R is case sensitive) as well as the values for the two levels to be compared. All the predictors in the model will be tested across the two groups.