Study Scenario: Two groups of participants (A and B) in my study viewed 4 scenes (1, 2, 3, and 4) and had to provide a verbal response after viewing the images. Each scene forms an individual trial. There is no restriction of time for each image here. Each image was divided into 3 areas of interest (X, Y & Z) and I examined what these participants fixate upon when making their decisions. Thus I tabulated the no. of fixations on each of these 3 areas of interests (X, Y and Z) and expressed in as a percentage of the total no. of fixations for each trial. I analysed percentage data for X, Y & Z separately with linear mixed model as I've got asymmetrical participant group size.
I've analysed my data with the following fixed factors as it was the most parsimonious model.Fixed Factors:
(1) Group,
(2) Scenes (repeated measures),
(3) Visual Acuity, and
(4) Group x Scenes
Technically, the estimated marginal means (EMM) should only be between 0% and 100%. When analysing the proportions of X, the model predicted that for Group B Scene 4, the EMM [Confidence Interval] was at 105% [97%, 113%]. For proportions of Y, the model predicted that for Group B Scene 4, the EMM [Confidence Interval] was at -4% [-12%, 4%]. I do have EMM that are well within range, however, the Confidence range overshoots or undershoots the 0-100% If the maximum range of the data can only be between 0 and 100%, can I ask if such data overshoot or undershoot acceptable (& why)? Logically speaking, it seems awkward if the EMM > 100% or < 0%. If it's not acceptable, how can I deal with this issue?
Statistically I do have a reason not to drop fixed effect (3) Visual Acuity from my model based on the likelihood ratio test, I was wondering if I should keep to the following simpler model below just to fit my data within (0-100% range)
(1) Group,
(2) Scenes (repeated measures), and
(3) Group x Scenes
FYI: majority of the raw data for the proportions of X in Group B Scene 4 is in the high 90s range or 100, while majority of the raw data for the proportions of Y in Group B Scene 4 is close to 0 or zero.If anyone can enlighten me, that will be great. Many thanks in advance.
Have you checked your assumptions including collinearity?. What do the residual plots show?. I assume you are building a predictive model so why not try model building with lasso. This approach is much better suited to predictive model building than is the approach you seemed to use. I am attaching papers that should help. The most detailed involves lasso for logistic regression but it is easy to switch to your models.
Programs for your models are given here:
https://www.amazon.com/Everyone-Advanced-Analytics-Graphics-Addison-Wesley/dp/013454692X/ref=sr_1_1?s=books&ie=UTF8&qid=1524161971&sr=1-1&keywords=lander+Jared+R+everyone
Programs and examples are given in the references. Contact me if I can help. Best wishes, David
For proportions, you can try a generalized mixed model with beta distribution and a logit link function.
Thanks all for your suggestions!!
What I'm trying to find out is whether there were differences in the types of visual cues used between the two groups of participant across the 4 scenes. I've added visual acuity as a fixed factor to account for the differences in VA. Based on the data, the participants tend to fixate on X and Y visual cues. Z is literally negligible.
Couple of reasons why I've used linear mixed model and why I've converted the fixation frequency counts in percentage of the total number of fixations for each trial instead of just tabulating the frequency counts.
(1) Timing of each trial was not standardised (plus I'm not interested in time as a variable, I'm only interested in what they fixate on prior to arriving at a decision).
(2) Non independence of observations (unavoidable with any given eye tracking data)
(3) Asymmetrical participants grouping size
My uni's statistician suggested that I could consider a transformation of data or make the data conform to a binomial distribution to ensure that the EMMs within the appropriate range. I've tried a transformation e.g arcsine (for proportions)- E.g arcsin(100%) = 1.57, but the EMM for Group B Scene 4 is at 1.61 from the Linear mixed model which mean the data would be > 100% still - thus transformation didn't do anything literally. I think Binomial would be appropriate if I disregard Z and consider only X & Y visual cue. As I expressed the proportions of fixations on each AOI as a percentage of the no. of fixations within the trial - I would think that Binomial distribution would be inappropriate.
Also, I'm limited to SPSS at the moment and the residuals (unfortunately) from the linear mixed model are not normally distributed. Are there any other ways I could resolve my issues within my limitations?
Well you aren't limited to SPSS. R is open source freeware available for download from the CRAN website. I've attached a beginning R book with download instructions. The Lander book I gave you a link for in my first post has a lot of research ready to go R programs. Very helpful. As far as transformations go you might try the Box-Cox family. R has a great package for this, here is a link. Mehmet's suggestion is very good.
https://www.google.com/search?q=box+cox+r+package&ie=utf-8&oe=utf-8&client=firefox-b-1
Best wishes, David
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