BrainVoyager QX v2.8

# Multi-Subject RFX GLM

## Introduction

For second-level random effects (RFX) analyses, statistical maps containing estimated effects (beta values) separately for each subject are required as input. These beta values can be computed with the RFX-GLM function, which is an optimized version of a standard "separate-subject predictors" GLM. While a standard multi-subject GLM can also be used to prepare RFX analyses, the RFX-GLM routine operates substantially faster and requires much less working memory by running internally a series of individual single-subject GLMs instead of one monolithic GLM (for details, see below). In order to use the RFX-GLM, the RFX GLM option must be checked in the General Linear Model: Multi-Study, Multi-Subject dialog. The multi-subject design matrix (MDM) is specified as usual by adding funtional runs (VTCs or MTCs) and associated single-run (RTC) design matrix files.

## Detailed Description

Random effects analysis can be performed in BrainVoyager QX by running a multi-subject GLM with predictors separated for each included subject. For the resulting GLM the random effects option can be turned on to test effects across subjects using the summary statistics approach. In this approach, the same contrast is specified for each subject and the resulting mean value across the subjects is tested against zero using a t-test. In a similar way, two groups can be compared by computing the mean of the summary statistic (contrast) for each group followed by a t-test to compare the group means. While statistically valid (and identical to the ANOVA analysis), this "old" approach to RFX analysis is limited to simple models. A more flexible RFX analysis approach is provided by the ANCOVA dialog allowing to specify multi-factorial designs with both within and between factors.

### Why RFX-GLM?

A limiting factor for all random effects analyses is that the standard separate-subject predictor GLM does not scale well to cases with a large number (e.g. more than 50) subjects. This property of the standard multi-subject GLM rests in the used approach to construct an overall design matrix for all included studies of all subjects. The resulting huge matrix is then further processed to estimate simultaneously all beta values for all subjects. While this approach constitutes the most powerful approach (allowing to formulate subject x condition intractions), the possibilities of a monolithic design matrix are not needed for random effects analyses. For RFX analyses the monolithic design matrix approach is inefficient since the created overall design matrix contains mostly zero values: Only diagonal sections where time courses and subject predictors are crossed are filled in the design matrix. In order to speed up the computation of random effects analyses, the new RFX-GLM has been introduced in version 1.3 of BrainVoyager QX. The major difference to the standard multi-subject GLM is that an overall design matrix is not created. Instead, the beta values are estimated individually for each included study and the results from the studies belonging to the same subject are pooled. This approach results in the same beta values as the standard multi-subject GLM approach but the computations are obtained much faster with a substantially reduced memory load. This approach internally runs a series of single-study GLMs resulting in linear scaling behavior with respect to both memory requirements and computation time. While running a RFX-GLM, the Log tab presents information about each conducted single-study GLM. The resulting GLM file can not be used to test fixed effects contrasts since the standard errors of the estimated betas are not computed. It can be used, however, both for the summary statistics random effects analysis as well as for the ANCOVA random effects analysis. Because of its advantages, it is recommended to use the RFX-GLM for random effects analyses. Since the RFX-GLM estimates beta values as input for a second level random effects analysis, it is also not necessary to turn on the "correct for serial correlations" option since the estimate of betas is unbiased even in the case of serial correlations and the fixed-effects first-level standard error values are not used in the second level analysis. The RFX-GLM uses as default the percent signal change time course normalization option, which is recommended for random effects analyses because it appears to reflect differences in effect size between subjects better than z normalization. Note also that at present only RFX-GLMs (besides fixed-effects GLMs) show estimated beta values of all subjects in the Voxel Beta Plot window while moving the mouse cursor over individual voxels.

Copyright © 2014 Rainer Goebel. All rights reserved.