GZLM

1. GZLM ... including GEE

2. 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!

3. 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?

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

5. 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

6. 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)

7. 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

8. 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)

9. 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

10. 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)

11. An example with Poisson distribution • We see computational limitations • Nushoor’sdata • 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

12. An example with binary data • Vineeta’sr 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 http://www.scottishhistorysociety.org/media/media_200043_en.pdf)

13. 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....