# General Linear Models (GLM)

### Variables and their many names

January 12, 2018

Many of the statistical procedures used by marketing researchers are based on “general linear models” (GLM). These can be categorised into univariate, multivariate, and repeated measures models.  The underlying statistical formula is Y = Xb + e where Y is generally referred to as the “dependent variable”, X as the “independent variable”, b is the “parameters” to be estimated, and e is the “error” or noise which is present in all models (also generally referred to as the statistical error, error terms, or residuals). Note that both [READ MORE]

### Repeated Measures ANOVA versus Linear Mixed Models.

March 9, 2017

You want to measure performance of the same individual measured over a period of time (repeated observations) on an interval scale dependant variable, but, which procedure to use?  So we are looking for an equivalent of the paired samples t-test, but we want to allow for two or more levels of the categorical variable i.e. pre, during, post. The Repeated Measures ANOVA [SPSS: ANALYZE / GENERAL LINEAR MODEL / REPEATED MEASURES] is simpler to use but sadly its often not as accurate and flexible as using Linear Mixed Models (SPSS: ANALYZE / MIXED MODELS / LINEAR). Reminder that the Linear [READ MORE]

### Outlier cases – bivariate and multivariate outliers

August 14, 2016

In follow-up to the post about univariate outliers, there are a few ways we can identify the extent of bivariate and multivariate outliers:   First, do the univariate outlier checks and with those findings in mind (and with no immediate remedial action), follow some, or all of these bivariate or multivariate outlier identifications depending on the type of analysis you are planning.  _____________________________________________________ BIVARIATE OUTLIERS: For one-way ANOVA, we can use the GLM (univariate) procedure to save standardised or studentized residuals. Then do a normal [READ MORE]

### Variables – three key types

February 10, 2016

Now here’s an easy one: What is a variable? It is simply something that varies – either its value or its characteristic. In fact, it must vary. If it does not vary then we can’t call it a VARiable, so we call it a “constant” such as the regression constant (the y-intercept).    In the equation of a straight line (linear relationship) Y = a + bX, where:    Y=dependent variable    X=independent variable    a=constant (the Y-axes intercept, or the value of Y when X=0)    b=coefficient (slope of the line, in other words the amount that Y increases [or [READ MORE]

### So many regression procedures. Confused?

September 11, 2015

Regression is the work-horse  of research analytics. It has been around for a long time and it probably will be around for a long time to come. Whether we always realise it or not, most of our analytical tools are in some way or another based on the concept of correlation and regression.   Lets look at a few regression based procedures in the researchers’ toolbox:   1. Simple and multiple linear regression: Applicable if both the single dependent variable (outcome or response variable) and one or many independent variables (predictors) are measured on an interval scale. If we [READ MORE]

### Analysis of Covariance (ANCOVA)

May 13, 2015

BRIEF DESCRIPTION The Analysis of Covariance (ANCOVA) follows the same procedures as the ANOVA except for the addition of an exogenous variable (referred to as a covariate) as an independent variable. The ANCOVA procedure is quite straightforward: It uses regression to determine if the covariate can predict the dependent variable and then does a test of differences (ANOVA) of the residuals among the groups. If there remains a significant difference among the groups, it signifies a significant difference between the dependent variable and the predictors after the effect of the [READ MORE]

### When the regression work-horse looks sick

June 19, 2013

Regression, in particular simple bivariate and multiple regression (and to a much lesser extent multivariate regression which is a “multivariate general linear model” procedure) is the work-horse of many researchers. For some, it is a horse exploited to the bone when other statistical (or even non-statistical) procedures would have done a better job!  Also, many statistical procedures are based on linear regression models (often without us realising it such as the fact that the ANOVA can be explained as a simple regression model).    At the core of many statistical analytics is [READ MORE]