Interactions binary logistic regression

[PhD student]

After the reading of this very helpful book (Heck, Thomas & Tabata, 2010), it would appear that GEE are particularly appropriate for my data. However I still have a little question in how to explain my significant 3 way interaction.

Just as a reminder, my participants (Anxiety Disorders vs. Control) carried out 8 trials resulting from the combination of a 2 (Formulation : Gain vs Loss) and a 4 (Level of risk : 20% vs 40% vs 60% vs 80%) within subject factors. In each trial, they had to choose between a safe and a risky option.

As I know that it is easy to make mistakes with these “recent” analyses (I did not find any well-written example in my field and any of my supervisors/colleagues know much about this analysis), I will briefly explain how I proceed.

First, I chose a logit link and a binomial error distribution. Then, in order to select the most appropriate working correlation structure, I ran 3 different models using either the independent, autoregressive or exchangeable correlation structure. I found that QIC for the independent, autoregressive and exchangeable were in the same range (i.e., vary less than 2 points between these 3 structures). As complete independence between trials within the same individual is not credible and as any of my participants report changing his strategy across trials, I selected an exchangeable working correlation structure.

Second, I ran a full factorial model (including 3 main effects: Group, Formulation and Level of Risk; three 2-way interaction: Group X Formulation, Group X Level of Risk and Formulation X Level of Risk; one 3 way interaction: Group X Formulation X Level of Risk). The 3-way interaction was significant, thus I did not interpret main effects or 2-way interaction and I focused only on the significant 3-way interaction. In order to explain this significant 3-way interaction, I ran pairwise comparison corrected with the bonferonni procedure and I described comparisons that answered my hypotheses.
What do you think about this analysis ?


Here is my syntax :
* Generalized Estimating Equations.
GENLIN choice (REFERENCE=LAST) BY Group Formulation Risk (ORDER=ASCENDING)

/MODEL GROUP FORMULATION RISK GROUP*FORMULATION GROUP*RISK FORMULATION*RISK        GROUP*FORMULATION*RISK INTERCEPT=YES
DISTRIBUTION=BINOMIAL LINK=LOGIT
  /CRITERIA METHOD=FISHER(1) SCALE=1 MAXITERATIONS=100 MAXSTEPHALVING=5 PCONVERGE=1E-006(ABSOLUTE)
SINGULAR=1E-012 ANALYSISTYPE=3(WALD) CILEVEL=95 LIKELIHOOD=FULL
  /EMMEANS TABLES=GROUP*FORMULATION*RISK SCALE=ORIGINAL COMPARE=GROUP*FORMULATION*RISK CONTRAST=PAIRWISE PADJUST=BONFERRONI
  /REPEATED SUBJECT=ID WITHINSUBJECT=Trial SORT=YES CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES COVB=MODEL MAXITERATIONS=100 PCONVERGE=1e-006(ABSOLUTE) UPDATECORR=1
  /MISSING CLASSMISSING=EXCLUDE


Thank you again for your amazing support!

[Rich Ulrich]

I think that I would have to modify this procedure, a couple of ways.

    "The 3-way interaction was
    significant, thus I did not interpret main effects or 2-way interaction and
    I focused only on the significant 3-way interaction. In order to explain
    this significant 3-way interaction, I ran pairwise comparison corrected with
    the bonferonni procedure and I described comparisons that answered my
    hypotheses."

1) How big are the various effects?  If the N is big enough, it is easy for trivial effects to

be magnified to "significance" at the arbitrary level.  "Be cautious" about interpreting

effects is a more cautious way of giving the conventional warning.  You may hear

"do not interpret" from people who are looking at your analysis if they see that the high-

order interaction is about as big as the others, but they are skipping the statement of the

assumption, that these are all the same size. (Professors who have not done much data

analysis can also be guilty of this oversight.)

2) Before worrying about followup tests, look at the means.  Is there an obvious story

there?  Do you have "basement" or "ceiling" effects which would introduce interactions?

 - those are the sort that are easiest to ignore, as potential artifacts of scaling.  (Dichotomies

created from continuous scales introduce additional potential for artifact, but, like analyzing

ranks, these are apt to be too small to show up unless the N is very large.)

Paired tests are the right sort to run for follow-up, but I don't see that they should deliver

a good "answer" for your hypotheses, because interactions disrupt the narrative of the main

effects.  I think it is awkward if your design puts the hypothesis into the interaction.  What an

unexpected and strong interaction sometimes shows you is that your whole model should be

constructed differently.  -- I learned that from a Usenet newsgroup poster, 15 or 20 years ago.

--

Rich Ulrich

---

From: SPSSX(r) Discussion <[hidden email]> on behalf of PhD student <[hidden email]>
Sent: Monday, January 23, 2017 4:47:05 AM
To: [hidden email]
Subject: Re: Interactions binary logistic regression

 

After the reading of this very helpful book (Heck, Thomas & Tabata, 2010), it
would appear that GEE are particularly appropriate for my data. However I
still have a little question in how to explain my significant 3 way
interaction.

Just as a reminder, my participants (Anxiety Disorders vs. Control) carried
out 8 trials resulting from the combination of a 2 (Formulation : Gain vs
Loss) and a 4 (Level of risk : 20% vs 40% vs 60% vs 80%) within subject
factors. In each trial, they had to choose between a safe and a risky
option.

As I know that it is easy to make mistakes with these “recent” analyses (I
did not find any well-written example in my field and any of my
supervisors/colleagues know much about this analysis), I will briefly
explain how I proceed.

First, I chose a logit link and a binomial error distribution. Then, in
order to select the most appropriate working correlation structure, I ran 3
different models using either the independent, autoregressive or
exchangeable correlation structure. I found that QIC for the independent,
autoregressive and exchangeable were in the same range (i.e., vary less than
2 points between these 3 structures). As complete independence between
trials within the same individual is not credible and as any of my
participants report changing his strategy across trials, I selected an
exchangeable working correlation structure.

Second, I ran a full factorial model (including 3 main effects: Group,
Formulation and Level of Risk; three 2-way interaction: Group X Formulation,
Group X Level of Risk and Formulation X Level of Risk; one 3 way
interaction: Group X Formulation X Level of Risk). The 3-way interaction was
significant, thus I did not interpret main effects or 2-way interaction and
I focused only on the significant 3-way interaction. In order to explain
this significant 3-way interaction, I ran pairwise comparison corrected with
the bonferonni procedure and I described comparisons that answered my
hypotheses.
What do you think about this analysis ?


Here is my syntax :
* Generalized Estimating Equations.
GENLIN choice (REFERENCE=LAST) BY Group Formulation Risk (ORDER=ASCENDING)

/MODEL GROUP FORMULATION RISK GROUP*FORMULATION GROUP*RISK FORMULATION*RISK      
GROUP*FORMULATION*RISK INTERCEPT=YES
DISTRIBUTION=BINOMIAL LINK=LOGIT
  /CRITERIA METHOD=FISHER(1) SCALE=1 MAXITERATIONS=100 MAXSTEPHALVING=5
PCONVERGE=1E-006(ABSOLUTE)
SINGULAR=1E-012 ANALYSISTYPE=3(WALD) CILEVEL=95 LIKELIHOOD=FULL
  /EMMEANS TABLES=GROUP*FORMULATION*RISK SCALE=ORIGINAL
COMPARE=GROUP*FORMULATION*RISK CONTRAST=PAIRWISE PADJUST=BONFERRONI
  /REPEATED SUBJECT=ID WITHINSUBJECT=Trial SORT=YES CORRTYPE=EXCHANGEABLE
ADJUSTCORR=YES COVB=MODEL MAXITERATIONS=100 PCONVERGE=1e-006(ABSOLUTE)
UPDATECORR=1
  /MISSING CLASSMISSING=EXCLUDE


Thank you again for your amazing support!




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[PhD student]

1) As I do not have many trials per participants, although I have an “important” sample compared to others psychological studies with patients, my N = 648 (which is quite low I think).
All my significant effects (2/3 main effects; 1/3 two-way interactions; 1/1 three-way interaction) have a beta ranging from 1.3 (for the 3-way interaction) to 1.9, with an associated wald test ranging from 4 to 12.

2) In fact, although we can fear a basement effect due to the risk-aversion of individuals with Anxiety Disorders, overall means revealed that they chose the gamble option for 40% of trials vs. ~50% for control. When specifying all the conditions, the lowest value of gambling for the patients is 25%.
Looking at means, the three-way interaction is easily explained by the fact that both patients and controls are affected by the formulation in the low risk condition whereas only controls were still affected by the formulation in the high risk condition.

3) The main hypothesis of this study was that contrary to controls, individuals with AD would be susceptible to the formulation only in the high risk condition (which corresponds to the 3-way interaction).

However, we also had less specific hypothesis, such as both AD and controls would be affected, overall, by the formulation or AD would do overall less risky choices than controls but as my model included the 3-way interaction, I could not conclude on these hypotheses. Maybe an option could be to run 3 different models one including only main effect, one with main effects and two-way interactions and the third with the full factorial design, but I have never seen an example of this procedure for GEE.