Lecture 9.1 Introduction to Mixed Effects Models

so we've just looked at generalized linear models or GLM's as generalizations of linear models which are typical ANOVA's but two responses that are not normal and that allow us to handle response distributions like Poisson or multinomial or ordinal responses so as we've said the linear model generalizes to the generalized linear model but this generalized linear model as we said can only handle between subjects data now we're going to introduce what are called mixed models and there is a linear mixed model much like the linear model but now a mixed model and we'll say what that means in a moment and then after that we'll look at its generalization the generalized linear mixed model and both of these analyses can handle both between and within subjects data allowing us to handle data with repeated measures which an interaction design and HCI studies repeated-measures come up all the time so these are very powerful models let's set our scenario and then we'll describe more what it means to be a mixed model our scenario is that we'll return to our data for our mobile text entry study where we had people using two different keyboards in three different postures sitting standing and walking you might recall we had 24 subjects they were in two conditions of keyboard the iPhone and the galaxy they were in three postures sit stand and walk keyboard was between subjects postures was within subjects or repeated measures and they entered twenty phrases which we might call a trial which is a general term meaning a sort of single a single data point that we're gonna capture from a subject before we averaged their words per minute and their error rate across their 20 phrases within each posture and keyboard but now we're going to keep all 20 phrases and thus bring us to fourteen hundred and forty data points for this data table that we can analyze so we're keeping all of the individual phrases that we measure and not averaging over them anymore so that's our scenario and we'll return to analyze that data shortly but to do that we're gonna have to introduce the concept of random effects and what we've been working with all along but haven't called them this yet are fixed effects when you have both of these in a statistical model you have the mixed term for mixed model which is their generalized linear mixed model and linear mixed model we're mixing fixed and random effects so what are these fixed effects are the factors of interest that we manipulate in a study they've been the kinds of variables the independent variables we've looked at all along keyboard and posture our fixed effects they're the factors in our study random effects we haven't considered yet random effects have a very special meaning and allow us to use linear mixed and generalized linear mixed models random effects are factors whose levels were sampled randomly from a larger population about which we wish to generalize but whose specific level values we actually don't care about so in interaction design and HCI studies subject is a classic random effect the subjects are sampled from a population of subjects we wish to generalize about and we don't care about the specific levels of the subject factor they're coded one two three and so on for however many subjects we may have actually we had 24 subjects in this particular study so we'll go with 24 but we don't care about the specific levels we just care that we have a pool of subjects they are a classic random effect and by making them a random effect in our models with otherwise fixed effects we have linear mixed models and if we need them generalized linear mixed models for different kinds of responses subject included in the model allows us to correlate measures across the same subjects across different rows in our data table and that's how we can handle within subjects designs using mixed models mixed models have a number of advantages and they're very powerful indeed they can have some missing data cells if you drop data you can still use a mixed model approach to analyze that data and it doesn't fort your study to have some empty cells in your data table you can also better handle unbalanced designs where you have different amounts of data in different conditions there's also no longer a mock Lee's ferocity test needed anymore we don't worry about the sphericity property we just model the covariance in the data directly remember that spher isset e is the situation where the variances of the differences between all combinations of levels of a within subjects factor are equal or or close to equal now we care about that but we can model severe city however form it takes whatever form it takes directly what are the disadvantages of using mixed models I just cited three advantages but what are the disadvantages well really they're just computationally more intensive sometimes they can take longer to run they also retain larger denominator degrees of freedom what we've seen is the DF residuals or DF denominator in the F report we have our numerator here let's say - and our denominator goes here and for a lot of data and a mixed model that number may stay fairly large it may be something for this data like 1200 we'll see the exact number later this is a fairly large number and for some people unfamiliar with mixed models who are used to traditional fixed effects models only which have much smaller degrees of freedom this can sometimes alarm them make them think perhaps you didn't do the right analysis but don't be dissuaded this in fact is how mixed models should be working now to do this kind of analysis where we have trial we have each of our 20 trials there's one more item that we have to consider and this comes up a lot with mixed models and that is the idea of nesting in particular the idea of nested effects and it's a practical matter to consider when using mixed models so what's a nested effect well nesting comes into play when the levels of a factor shouldn't be pooled just by their label when you're doing an any kind of ANOVA analysis the levels of a factor are are grouped together and the calculations are made for example for all the set data stand data walk data all the iPhone data or galaxy data in the case of trial as a factor you'll see in our data table we'll in kirb trial just as a number for the 20 trials within each of the sit stand walk levels in each of the phone and galaxy combinations there so trial takes on values of 1 to 20 throughout the table but we don't have any special meaning to pooling all of the the data for variance calculations for all the trials numbered one or number two or number three those levels aren't that important and we don't want a pool across all levels 1 all levels 2 in all levels 3 because trial number 1 well sitting using an iPhone is very different than trial number 1 while standing using galaxy so we nest trial within posture and keyboard if they're used to dot notation from certain programming languages like Java you can think of it as a kind of keyboard dot posture dot trial where trial is kind of nested here so we would pool values for example across say iphone while sitting and pool all of those trial ones and twos and so forth but within iphone and sitting in general when you have a factor like a trial where you you it's not meaningful to consider them in isolation trial one by itself doesn't mean very much you might be in a situation where you want to nest and that will allow you to get a more accurate response in your results let's go now to our our terminal and we'll carry out linear mixed models on words per minute and we'll carry out a generalized linear mixed model on error rate and we'll see nesting happen in the process we'll do that now

Channel: IxD Online: UCSD & Coursera

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Keywords: interaction design, mixed effects models, experiments

Id: QeCJ9ON0WDc

Length: 11min 13sec (673 seconds)

Published: Sat Jun 08 2019