[R-sig-ME] First post: binomial model for omission of items of questionnaire, and advice on reading

[Chris Evans]

Huge thanks to both Steven and Dimitris for these inputs. I managed to scan read pertinent parts of Dimitris's lecture notes this morning and that was already hugely helpful (and your shiny app looked great Dimitris), these too look great pointers. 

Can I be cheeky as I realise a committed a fundamental error in my post by asking two rather different questions. Would any comment on the first part of the question about whether what I was doing looked right, Dimitris's lecture notes suggested to me that it wasn't necessarily wrong and helped me understand that the question could also be tackled using a GEE approach which is really new to me but I got the impression that my glmer was on the right lines but I'm still keen to have reassurance or corrections/improvements or just any comments. 

TIA, 

Chris 

> From: "Pierce, Steven" <pierces1 using msu.edu>
> To: "Chris Evans" <chrishold using psyctc.org>
> Sent: Friday, 10 May, 2019 14:22:52
> Subject: RE: [R-sig-ME] First post: binomial model for omission of items of
> questionnaire, and advice on reading

> Chris,

> Here are some reading suggestions that may help you learn more about using mixed
> effects models. I could provide more (mixed models is a huge topic area), but
> these are a good start. Best of luck in your continuing journey to learn how to
> use mixed models.

> Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis:
> Modeling change and event occurrence . New York, NY: Oxford University Press.

> · First half of the book is a very reader-friendly intro to mixed effect models,
> second half focuses on discrete-time survival analysis.

> Gelman, A., & Hill, J. (2007). Data analysis using regression and
> multilevel/hierarchical models . New York, NY: Cambridge University Press.

> · Shows the connection between basic regression and mixed effects models. Good
> foundational resource.

> Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel analysis: An introduction
> to basic and advanced multilevel modeling (2nd ed.). London, UK: Sage.

> · Good foundational resource.

> West, B. T., Welch, K. B., Gałecki, A. T., & Gillespie, B. W. (2015). Linear
> mixed models: A practical guide using statistical software. Retrieved from [
> http://www.crcnetbase.com/isbn/978-1-4665-6102-1 |
> http://www.crcnetbase.com/isbn/978-1-4665-6102-1 ]

> Enders, C. K., & Tofighi, D. (2007). Centering predictor variables in
> cross-sectional multilevel models: A new look at an old issue. Psychological
> Methods, 12(2), 121-138. doi:10.1037/1082-989X.12.2.121

> · Centering affects how one interprets the coefficients in models. This is an
> excellent paper for getting a handle on that issue.

> Steven J. Pierce, Ph.D.

> Acting Director; Associate Director

> Center for Statistical Training & Consulting (CSTAT)

> Michigan State University

> Giltner Hall

> 293 Farm Lane, Room 100A

> East Lansing, MI 48824

> Office Phone & Fax: (517) 353-1051

> E-mail: pierces1 using msu or Steve.Pierce using cstat.msu.edu

> Web: https://cstat.msu.edu

> -----Original Message-----
> From: Chris Evans <chrishold using psyctc.org>
> Sent: Thursday, May 9, 2019 2:26 PM
> To: r-sig-mixed-models using r-project.org
> Subject: [R-sig-ME] First post: binomial model for omission of items of
> questionnaire, and advice on reading

> I've followed this list for some years now and learned much about analyses of
> mixed models from it but I'm pretty sure this is my first post and I suspect
> it's embarrassingly obvious and that leads to its second part: advice on
> reading.

> The immediate question is about testing whether participants omitting an item of
> a questionnaire relates to the cueing, negative or positive of the item. The
> data look like this:

> > head(longDat[,c(7,3,4,6)])

> ID itemN positive missed

> 1 1 1 FALSE 1

> 2 2 1 FALSE 0

> 3 3 1 FALSE 0

> 4 4 1 FALSE 0

> 5 5 1 FALSE 1

> 6 6 1 FALSE 0

> "itemN" is a factor as at the moment I'm not testing any order effect through
> completion of the questionnaire. The variable "positive" is the cueing and
> "missed" is whether the item was omitted by the participant or not.

> I think a reasonable model is that people vary in a general willingness to omit
> items and that there might in addition to that random variance, be an effect of
> cueing, probably that negatively cued items are less likely to be omitted but I
> wouldn't want a directional test. As it happens in this questionnaire there are
> 10 items, three positively cued and seven negatively cued. I've simulated data
> so the ten items have rather different omission rates and the cueing has an
> effect on top of those.

> I analysed my data with:

> > res3 <- glmer(missed ~ positive + (1 | ID), family = binomial, data = longDat)

> > res3

> Generalized linear mixed model fit by maximum likelihood (Laplace Approximation)
> ['glmerMod']

> Family: binomial ( logit )

> Formula: missed ~ positive + (1 | ID)

> Data: longDat

> AIC BIC logLik deviance df.resid

> 12597.534 12619.165 -6295.767 12591.534 9997

> Random effects:

> Groups Name Std.Dev.

> ID (Intercept) 1.056

> Number of obs: 10000, groups: ID, 1000

> Fixed Effects:

> (Intercept) positiveTRUE

> 0.6102 -0.7833

> > se <- sqrt(diag(vcov(res1)))

>> (tab <- cbind(Est = fixef(res3), LL = fixef(res3) - 1.96 * se, UL = fixef(res3)
> > + 1.96 * se))

> Est LL UL

> (Intercept) 0.6101525 0.5330314 0.6872737

> positiveTRUE -0.7832788 -0.8603999 -0.7061576



> That all seems fine and to fit with the parameters that I'd put into simulating
> the data but I'm sufficiently new to this to want to check with people more
> experienced than I am if that does seem the right approach. I may have some
> follow up work where there are more ways to classify the ten items (including
> order).

> My tangential question is about recommended reading for someone who comes out of
> medicine through psychotherapy so doesn't really have algebra, let alone matrix
> algebra and Bayesian theory say, running in my veins. I have many
> peer-reviewed, empirical, quantitative papers from the last three decades,
> almost all based on my having to do my own statistical analyses as I've rarely
> worked anywhere where I've had either money to pay for statistical help or a
> resident statistician. However, I'm fairly new to multilevel models (as you can
> see!) but I'm increasingly seeing them as vital to the sorts of data I analyse.
> Where should I start?!

> TIA,

> Chris

> --

> Chris Evans < [ mailto:chris using psyctc.org | chris using psyctc.org ] > Skype:
> chris-psyctc

> Visiting Professor, University of Sheffield < [
> mailto:chris.evans using sheffield.ac.uk | chris.evans using sheffield.ac.uk ] >

> I do some consultation work for the University of Roehampton < [
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-- 
Chris Evans <chris using psyctc.org> Skype: chris-psyctc 
Visiting Professor, University of Sheffield <chris.evans using sheffield.ac.uk> 
I do some consultation work for the University of Roehampton <chris.evans using roehampton.ac.uk> and other places but this <chris using psyctc.org> remains my main Email address. 
I have "semigrated" to France, see: https://www.psyctc.org/pelerinage2016/semigrating-to-france/ if you want to book to talk, I am trying to keep that to Thursdays and my diary is now available at: https://www.psyctc.org/pelerinage2016/ecwd_calendar/calendar/ 
Beware: French time, generally an hour ahead of UK. That page will also take you to my blog which started with earlier joys in France and Spain! 

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