Re: Interactions binary logistic regression
Posted by PhD student on Dec 15, 2016; 8:48pm
URL: http://spssx-discussion.165.s1.nabble.com/Interactions-binary-logistic-regression-tp5733602p5733619.html
You should be clearer that you are using a quasi-independent variable,
which variables you are matching on and why you are/are not using
propensity scoring. In this experiment focusing on individuals with Anxiety Disorders I match participants on age, sex, IQ and each subject completed an assessment of Anxiety symptoms on a scale (score to this scale has to be above the cut-off for patients with Anxiety disorders and below for control participants)
> So each subject/participant is repeatedly measures 8 times but
> these represent a factorial (?) combination of three independent
> variables/factors. *Yes each participant was confronted to 8 choices.
> Choices were derived from the combination of two independant
> variables:
> Formulation (Gain vs Loss) and Level of risk (Low, 20% 40% vs High 60%
> 80%)*
This is where the confusion starts: You have a 2x4 design even
though you use the terms "low" and "High" for risk. It is unclear
whether you use the original response at each of 4 levels or
average the two levels of low and the two level of high, converting
this into a 2x2 design. I would assume that you use the original
data (i.e., 2x4 design) but for other reasons (e.g., "standard
practices in the area") average the two values at low and
high risk.
I don't understand your descrition. Yes, you have two factors,
the original (1) but (2) and (3) are now a single factor of
level of risk, that is, 20% 40%, 60% 80%. You keep making
the distinction of low vs high but you have 4 levels of risk.
For clarity of expression you really need to be clear about
whether you are using data from the four levels or averaged
the 2 low levels and 2 high levels. Yes, even if I have a 2x4 design, I though to label 20% and 40% as low and 60% and 80% as high in order to treat my data as a 2x2 design, as it is commonly done in litterature
It is unclear why you have two levels for low risk and high risk
since the way you describe Riskiness, you focus on only two
levels (low vs high). On an a priori basis, it seems that you
are assuming that there is no difference between 20% vs 40%
and 60% vs 80%. Authors included 4 levels of risk because it allows to have more trials. It was initially used for psychophysiological method, which requires many trials, but it was kept even in behavioral studies because participants are less aware of the proximity between trials
If so, why have 2 levels? Note that
looking at a graph of mean response to the 4 levels, you
assume that you would see a "step function" (horizontal
for 20% and 40%, up or down to a horizontal line for 60%
and 80%). Yes, exactly
> Assuming a factorial design, this gives one a 2x2x2 combination of
> conditions which produces the 8 trials that each subject/participant
> responds to, right? In what you originally posted you only went up
> to a 3-way interaction while my design implies the presence of a
> 4-way interaction. You've done something that is not obvious. *Yes I
> have a
> 3-way interaction: Group X Formulation X Level of risk*
You understand that this take precedence in interpretation relative to
all lower interactions, right? Yes of course, I mentionned the 2-way interaction for purposes of clarity.
> If by "Formulation" you are referring to what I call "Gain-Loss", then
> you appear to be referring to a 2x2 result, with each group having two
> values for "Gain-Loss". Do you have a table or a figure for this
> result?
> If so, please reproduce it so people can better see what you mean
> by "influence of formulation within each group". *Here is an
> hypothetic
> example of my data set*
>
> Subject Group Formulation Level of risk Choice
> 1 1 Gain Low 1
> 1 1 Gain Low 0
> 1 1 Gain High 0
> 1 1 Gain High 0
> 1 1 Loss Low 1
> 1 1 Loss Low 0
> 1 1 Loss High 1
> 1 1 Loss High 1
So, you don't distinguish the 4 levels of risk but, as Eugene
Maguin mentions in another post, you have a 4th design factor
which is identified as (3) in my list above and used in my
listing of effects below. You seem to be assuming that
there are no main effects for repitition and does not interact
with any other factor. Why? I am not sure to understand the repitition factor. In fact, participants were not confronted to the same trial twice ?
> For completeness sake, it appears that you have the following design
> and set of results. The 2-way interaction Gx1 seems to be of interest
> to
> you but I have to ask: are any of the higher interactions significant?
> *Yes,
> my Group X Formulation X Level of risk was also significant but I gave
> an
> example that I though easier to understand*
>
> 4 main effects: G (for groups), 1 (for gain-loss), 2 (for riskiness) &
> 3
> (for repetition)
>
> 6 two-way interactions:
> Gx!, Gx2, Gx3, !x2, 1x3, 2x3
>
> 4 three-way interactions:
> Gx1x2, Gx1x3, Gx2x3, 1x2x3
>
> 1 four-way interaction:
> Gx1x2x3 *Except repetition, it is exactly my design*
But if replication has an effect, how would you know? I understand, but the average was done in order to situate in the range of previous publication. If I do not average the low and high level of risk I have 3 main effects: Group, formulation (gain-loss) and riskiness(20% 40% 60% 80%) and thus 3 two-way interactions and 1 three way interaction.
But maybe I don't understand what you refer to as Repitition factor ?