GZLM... including GEE

Generalized Linear Modelling A family of significance tests... Something we don’t see mentioned much in articles yet... but will hear more of Maybe we should be using it!

Often we have RQs and RHs that require us to compare groups and/or conditions. E.g. – Do student attitudes vary depending on year of study and on which of two types of speaking instruction they received? – Does word length and word frequency affect how well learners remember the word? – Do speakers differ in their pronunciation of a sound depending on gender and formality of situation? – Do students trained to use online dictionaries improve in writing more than those who are not?

Well known statistical significance tests for these comparisons are the GLM family General Linear Model GLM includes: – t tests – ANOVA – Pearson correlation – Linear regression

But GLM is picky... comes with prerequisite requirements 1. the DV scale – Can’t deal with data that is not scores... –...that are ‘equal interval’ and –...on a supposedly open ended scale – Counts have to be treated as scores – Rating scales possibly, but... are they ‘equal interval’ – Not binary data such as pass/fail or yes/no responses

2. Further features of the score data (in the population) e.g. – Normality of distribution shape of scores – Similarity of spread of scores in different groups (aka homoscedasticity or homogeneity of variance) – Similarity of variance of differences between pairs of repeated measures (aka sphericity)

Previous ways of dealing with data that fails the prerequisites – Use GLM anyway, claiming it is ‘robust’ even when prerequisites are missing Or just use GLM and don’t check/mention the problems – For normality, transform the data to be more ‘normal’ in shape (Example) But results are then hard to talk about – Use an alternative test (nonparametric, weaker) But such tests are only available for simple comparisons

Since the 80s, but only recently available in popular packages like SPSS... GZLM, including GEE, covers most of the ground of the GLM family, and more, and deals with most of the problems Generalized Linear Model itself for comparing groups only (GZLM) An extension of GZLM called Generalized Estimating Equations (GEE) for comparing repeated measures (and groups if necessary)

An example comparing groups We see the issue of choosing the right analysis for the distribution shape Marin’s data, DV6 – DV: Six point rating scale response for how often learners use vocab strategies – EV: Two genders – EV: Five years of study in university

An example with repeated measures We see how to turn the data into ‘long’ form which GEE requires Issariya’s data – DV: Percent correct scores for learning vocab wordlists – EV: Pretest versus posttest – EV: Experimental group (with vocab learning strategy instruction) and control group (with extra practice)

An example with Poisson distribution We see computational limitations Nushoor’s data – DV: Counts of how often people used types of modifier expression with requests – EV: Types of modifier – EV: Four groups (2 NS, 2 NNS) – EVs: Types of request situation in terms of social variables such as power, and seriousness

An example with binary data Vineeta’s r data – DV: Numbers of r produced versus other variants – EVs: Various features of the word – EVs: Various features of the people – EV: Formality of situation This analysis is I think more or less equivalent to what traditional Varbrul analysis does....BUT – The output is in a different form – In fact this sort of analysis is not really statistically acceptable anyway (see _200043_en.pdf) _200043_en.pdf

To analyse data like Vineeta’s properly we need either the latest version of Varbrul called Rbrul, or GZLM Mixed... the latest bit of GZLM added to SPSS Watch this space....