Lecture06_GLMGroupMultipleCompare

Lecture06_GLMGroupMultipleCompare - Extending the GLM So...

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1 Extending the GLM • So far, we have considered the GLM for one run in one subject • The same logic can be applied to multiple runs and multiple subjects GLM Stats For any given region, we can evaluate the GLM stats total length of sequence = 4 runs * 155 volumes = 620 volumes blue: original time course green: best fitting model red: residuals = + Outline • Mixed effects motivation • Evaluating mixed effects methods • Three methods – Summary statistic approach (HF) (SPM96,99,2) – SPM2 –FSL3 • Conclusions Overview • Mixed effects motivation • Evaluating mixed effects methods • Three methods – Summary statistic approach (HF) (SPM96,99,2) – SPM2 • Conclusions Lexicon Hierarchical Models • Mixed Effects Models • Random Effects (RFX) Models • Components of Variance ... all the same ... all alluding to multiple sources of variation (in contrast to fixed effects)
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2 Subject1 Subject2 Subject3 Random Effects Illustration • Standard linear model assumes only one source of iid random variation • Consider this RT data • Here, two sources – Within subject var. – Between subject var. – Causes dependence in Subject1 Subject2 Subject3 3 Ss, 5 replicated RT’s Residuals X Y x Subj. 1 Subj. 2 Subj. 3 Subj. 4 Subj. 5 Subj. 6 0 Fixed vs. Random Effects in fMRI • Fixed Effects –In t ra -sub jec t variation suggests all these subjects different from zero • Random Effects – Intersubject variation suggests population not very different from zero Distribution of each subject’s estimated effect Distribution of population effect 2 FFX 2 RFX Fixed Effects • Only variation (over subjects/sessions) is measurement error • True Response magnitude is fixed Random/Mixed Effects • Two sources of variation – Measurement error – Response magnitude • Response magnitude is random – Each subject/session has random magnitude Random/Mixed Effects • Two sources of variation – Measurement error – Response magnitude • Response magnitude is random – Each subject/session has random magnitude – But note, population mean magnitude is fixed Fixed vs. Random • Fixed isn’t “wrong,” just usually isn’t of interest • Fixed Effects Inference – “I can see this effect in this cohort” • Random Effects Inference – “If I were to sample a new cohort from the population I would get the same result”
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3 Two Different Fixed Effects Approaches • Grand GLM approach – Model all subjects at once – Good: Mondo DF – Good: Can simplify modeling – Bad: Assumes common variance over subjects at each voxel – Bad: Huge amount of data Two Different Fixed Effects Approaches • Meta Analysis approach – Model each subject individually – Combine set of T statistics • mean(T) n~ N(0,1) • sum(-logP) ~ 2 n – Good: Doesn’t assume common variance – Bad: Not implemented in software Hard to interrogate statistic maps Overview • Mixed effects motivation • Evaluating mixed effects methods • Three methods – Summary statistic approach (HF) (SPM96,99,2)
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Lecture06_GLMGroupMultipleCompare - Extending the GLM So...

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