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Results tagged with mixed-model
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user 9162
Mixed (aka multilevel or hierarchical) models are linear models that include both fixed effects and random effects. They are used to model longitudinal or nested data.
3
votes
1
answer
236
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Why does this mixed model produce discrepant output in SPSS and R?
I've been working with an example from the Heck et al (2013) textbook, which gives the following model:
$Y_{ij} = \gamma_{00} + \gamma_{01}\text{ses_mean}_j + \gamma_{02}\text{pro4yrc}_j + \gamma_{03} …
3
votes
2
answers
155
views
What's an example of a situation in which it makes sense to assume random slopes but a fixed...
I'm referring to multilevel modelling. Field (2013) writes:
It’s worth noting that it would be unusual in reality to assume random
slopes without also assuming random intercepts, because variab …
2
votes
0
answers
38
views
Mixed models: Why are deviations of each level of the grouping factor's value from the popul...
Bolker (2015) talks of a research scenario in which site is the grouping factor. He writes on p.312 that
Treating site as a random effect compromises between the extremes of pooling and estimating …
2
votes
1
answer
629
views
In multilevel modelling, what's the interpretation of $\gamma_{00}$?
I am thinking of a null model (also known as a random-effects ANOVA, or intercept-only model)
$$ y_{ij} = \gamma_{00} + u_j + e_{ij} $$
where $u_j$ are the level-2 residuals and $e_{ij}$ are the lev …
2
votes
0
answers
522
views
Mixed models: When can adding a predictor increase the residual variance?
I saw that Andrew Gelman had discussed this issue in one of his books, and a relevant excerpt is presented here. He also very briefly discusses this issue in his blog post here.
In the book excerpt G …
1
vote
0
answers
27
views
Principles for deciding to model a variable as both random and fixed in the same analysis
There are quite a lot of questions which touch on this issue, but there does not seem to be any that sets out any general principles for deciding when it would be a good idea (or a bad idea, or a poin …
2
votes
1
answer
1k
views
Multilevel modeling: Why aren’t level-1 predictors allowed in level-2 equations?
I’m reading a presentation by Preacher, who gives the following level-1 and level-2 equations
Level 1
$y_{ij} = \beta_{0j} + \beta_{1j}x_{1ij} + \epsilon_{ij}$
Level 2
$\beta_{0j} = \gamma_{00} + \ga …
2
votes
1
answer
360
views
Why did removing the between-subjects factor from a two-way mixed ANOVA change the SSwithin?
I have been playing with this SPSS data file, which is a class example from a university I am not enrolled in.
In the original file there are 10 men and 10 women. I did a two-way mixed ANOVA with gen …
1
vote
1
answer
82
views
Longitudinal multilevel models: deleting the baseline timepoint
I'm reading a paper which reports a multilevel model with random intercepts and slopes in which individual people's score on a scale of anxiety is assessed at five different timepoints. So the timepoi …
3
votes
1
answer
759
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Why does this 3-level multilevel logistic regression fail to converge?
I'm running a multilevel logistic regression in which I estimate the probability the authors of scientific papers will make a particular sort of error in reporting a null hypothesis significance test …
0
votes
0
answers
66
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When will a cross-level interaction increase the slope variance?
Heck et al (2012) give the following model
$Y_{ij} = \gamma_{00} + \gamma_{01}\text{ses_mean}_j + \gamma_{02}\text{pro4yrc}_j + \gamma_{03}\text{public}_j + \gamma_{10}\text{ses}_{ij} + u_{0j} + u_{1j …
1
vote
1
answer
1k
views
What kind of linear mixed model is most appropriate for this data?
I previously wrote about this data here, and was advised that a linear mixed model applied to the raw data would provide "more precision and power" than the originally suggested approach of a regressi …
3
votes
0
answers
2k
views
Is this a complete list of the assumptions of linear mixed-effects models?
Crawley (2012) p682 writes:
There are five fundamental assumptions of linear mixed-effects models:
Within-group errors are independent with mean zero and variance $σ^2$.
Within-group er …
15
votes
2
answers
915
views
ICC as expected correlation between two randomly drawn units that are in the same group
In multilevel modelling the intraclass correlation often gets calculated from a random-effects ANOVA
$$ y_{ij} = \gamma_{00} + u_j + e_{ij} $$
where $u_j$ are the level-2 residuals and $e_{ij}$ are th …
7
votes
1
answer
4k
views
How is repeated-measures ANOVA a special case of linear mixed models?
In this comment @gung mentions that
On a different note, I think it's fair to think of RM ANOVA as a
special case of linear mixed models.
and a subsequent comment concurs with this.
I under …