Posted by
Mike on
Dec 15, 2016; 7:07pm
URL: http://spssx-discussion.165.s1.nabble.com/Interactions-binary-logistic-regression-tp5733602p5733616.html
On Thursday, December 15, 2016 12:45 PM, "PhD student" wrote:
[snip]
> Assuming that you have random assignment to the two "Treatment"
> groups, your independent variable is a two level between-subjects
> factor. If not randomly assignment, it is some form of
> quasi-independent
> variable. *It is a form of quasi-independent variable. I propose my
> experiment to patients and I match controls on age, IQ, sex...*
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.
> 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.
> So, this is where the within-subject design is described:
> (1) a factor which we'll call "Gain-Loss" (2 levels: gain vs loss)
> *Yes*
> (2) a factor which we'll call "Riskiness" (2 levels: low vs high)
> *Yes*
> (3) a facotr which we'll call "Repitition" (2 levels: 1st trial vs 2nd
> trial) *I have only two factors, but as each level of risk includes 2
> percentages I have 8 different trials*
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.
It is possible to maintain the 3 within subject factors by using
the following design:
(1a) Gain-loss (2 levels)
(2a) Low Risk (2 levels: 20% vs 40%)
(3a) High Risk (2 levels: 60% vs 80%)
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%. 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%).
> 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?
> 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?
> 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?
-Mike Palij
New York University
[hidden email]
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