I have data with both between and withinsubjects Independent Variables (IV) and a multiple binary Dependent Variable (DV).
In order to determine the extent to which the IV influenced the DV, I performed a hierarchical binary logical regression with main effects as step 1, twoway interactions as step 2 and the three way interaction as step 3. However, as my results revealed significant interactions, I want to compare specific proportions of my DV according to some IV (as planned ttest after a significant ANOVA). I found that some authors used chisquares to do that but I know that chisquares are not suitable for withinsubjects design. Is there a specific analysis ? If no, is it possible to split my regression according to some IV? Thank you in advance for your help! 
I'm confused by what you are doingor, maybe, it's just your description. So let's say you are using the logistic regression command and your syntax is something like this (I assume iv1 iv2 iv3 are all dichotomous and coded 0,1):
Logistic regression variables=dv with iv1 iv2 iv3 iv1 by iv2 iv1 by iv3 iv2 by iv3 iv1 by iv2 by iv3/enter iv1 iv2 iv3/ Enter iv1 by iv2 iv1 by iv3 iv2 by iv3/enter iv1 by iv2 by iv3. I suggest you look at the GenLin command. It sounds like you are interested in planned comparisons. GenLin will give those to you if you specify the EMMeans command. The genlin syntax is very different and, frankly, confusing until you have some experience with it. Unfortunately, no examples that you can copy are given. Gene Maguin Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of PhD student Sent: Thursday, December 15, 2016 8:30 AM To: [hidden email] Subject: Interactions binary logistic regression I have data with both between and withinsubjects Independent Variables (IV) and a multiple binary Dependent Variable (DV). In order to determine the extent to which the IV influenced the DV, I performed a hierarchical binary logical regression with main effects as step 1, twoway interactions as step 2 and the three way interaction as step 3. However, as my results revealed significant interactions, I want to compare specific proportions of my DV according to some IV (as planned ttest after a significant ANOVA). I found that some authors used chisquares to do that but I know that chisquares are not suitable for withinsubjects design. Is there a specific analysis ? If no, is it possible to split my regression according to some IV? Thank you in advance for your help!  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/Interactionsbinarylogisticregressiontp5733602.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
In reply to this post by PhD student
Please describe your DV in more detail.
What labels do your variables have? What does "multiple binary Dependent Variable" mean? Do you have categorical variable with several values that you are representing with a set of dichotomies? Or Do you have a set of variables the are separate dichotomous variables? Or Do you have continuous variables that have been coarsened to dichotomies?
Art Kendall
Social Research Consultants 
In reply to this post by Maguin, Eugene
I'm not familiar with these procedures but I will look carefully the GenLin command, which seems to be an appropriate technique.
Thank you very much for your help! 
In reply to this post by Art Kendall
In my experiment, 2 independent groups (patient vs. control) carried out 8 trials in which they had to chose between 2 options, one safe and one risky. 4 trials were formulated in terms of gain (2 with a low risk and 2 with a high risk) and 4 trials were formulated in terms of loss (2 with a low risk and two with a high risk).
All my IV, Group (patient vs control), formulation (gain vs loss) and level of risk (low vs high) are dichotoumous. For example, I have a significant Group X Formulation interaction, but I am not sure how I can precisely observe the influence of the formulation within each group. 
Some things are still not clear to me.
1) Two groups (got that) and each participant completed all 8 trials? Or something else? This element is important! 2) In each trial participants selected either a risky option or a safe option. The dichotomous DV. 3) A trial was formulated as a gain or as a loss and as low risk or high risk. Four combinations. 4) Each combination was replicated twice. If each participant did all eight trials, you have a repeated measures design. Just suppose the DV were continuous, how would you set up the analysis? If each participant did only one trial, you have a between groups+conditions design. Again, how would you set this up if the DV were continuous? Gene Maguin Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of PhD student Sent: Thursday, December 15, 2016 10:35 AM To: [hidden email] Subject: Re: Interactions binary logistic regression In my experiment, 2 independent groups (patient vs. control) carried out 8 trials in which they had to chose between 2 options, one safe and one risky. 4 trials were formulated in terms of gain (2 with a low risk and 2 with a high risk) and 4 trials were formulated in terms of loss (2 with a low risk and two with a high risk). All my IV, Group (patient vs control), formulation (gain vs loss) and level of risk (low vs high) are dichotoumous. For example, I have a significant Group X Formulation interaction, but I am not sure how I can precisely observe the influence of the formulation within each group.  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/Interactionsbinarylogisticregressiontp5733602p5733606.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
In reply to this post by PhD student
On Thursday, December 15, 2016 10:35 AM, "PhD student" wrote:
It may just be me but the way you describe your design is a little odd/confusing. It sound like you have a 4way mixed design (old school mixed) or a 2x2x2x2 design with a dichotomous dependent variable.. > In my experiment, 2 independent groups (patient vs. control) Assuming that you have random assignment to the two "Treatment" groups, your independent variable is a two level betweensubjects factor. If not randomly assignment, it is some form of quasiindependent variable. Next are the Withinsubject factors which is where the confusion arise. >carried out 8 trials So each subject/participant is repeatedly measures 8 times but these represent a factorial (?) combination of three independent variables/factors. >in which they had to chose between 2 options, one safe and one risky. Now, this seens to be your dependent variable, right? But it is unclear what the response actually is (e.g., "Yes" vs "No", or "Accept" vs "Refuse", etc.) which apparently you coded as 0,1 or 1,2 or whatever, which is why you are doing a binary logistic regression  the fact that you independent variables/factors are dichotomous is besides the point. > 4 trials were formulated in terms of gain (2 with a low risk and 2 > with a > high risk) and 4 trials were formulated in terms of loss (2 with a low > risk > and two with a high risk). So, this is where the withinsubject design is described: (1) a factor which we'll call "GainLoss" (2 levels: gain vs loss) (2) a factor which we'll call "Riskiness" (2 levels: low vs high) (3) a facotr which we'll call "Repitition" (2 levels: 1st trial vs 2nd trial) 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 3way interaction while my design implies the presence of a 4way interaction. You've done something that is not obvious. > All my IV, Group (patient vs control), formulation (gain vs loss) and > level > of risk (low vs high) are dichotoumous. I really don't understand what you are saying here. The critical point is whether your dependent variable is dichotomous or not. If it is, then binary logistic regression may be the appropriate analysis. If not, then you're not providing full information. > For example, I have a significant Group X Formulation interaction, but > I am > not sure how I can precisely observe the influence of the formulation > within > each group. If by "Formulation" you are referring to what I call "GainLoss", then you appear to be referring to a 2x2 result, with each group having two values for "GainLoss". 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". For completeness sake, it appears that you have the following design and set of results. The 2way interaction Gx1 seems to be of interest to you but I have to ask: are any of the higher interactions significant? 4 main effects: G (for groups), 1 (for gainloss), 2 (for riskiness) & 3 (for repetition) 6 twoway interactions: Gx!, Gx2, Gx3, !x2, 1x3, 2x3 4 threeway interactions: Gx1x2, Gx1x3, Gx2x3, 1x2x3 1 fourway interaction: Gx1x2x3 Mike Palij New York University [hidden email] ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
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In reply to this post by Maguin, Eugene
1) Two groups (got that) and each participant completed all 8 trials? Or something else? This element is important! Yes, exactly
2) In each trial participants selected either a risky option or a safe option. The dichotomous DV. Yes 3) A trial was formulated as a gain or as a loss and as low risk or high risk. Four combinations. I was not clear enought, the level of risk was 20% chances of winning, 40% 60% and 80%, but authors recommend to categorize 20 and 40% as low and 60 and 80% as high 4) Each combination was replicated twice. Therefore, each combination was presented once. If each participant did all eight trials, you have a repeated measures design. Just suppose the DV were continuous, how would you set up the analysis? If my DV was continuous, I would use ANOVA. In my speciality, data are classically treated with ANOVA, but I am not sure that is the most appropriate technique due to the dichotomous DV 
In reply to this post by Mike
It may just be me but the way you describe your design is a little
odd/confusing. It sound like you have a 4way mixed design (old school mixed) or a 2x2x2x2 design with a dichotomous dependent variable.. I apologize my presentation was not clear. My design was 2 (Group: patients vs control) X 2 (Formulation: Gain vs Loss) X 2 (Level of Risk: High vs Low) with Group a between subjects factor and Formulation + Level of risk withinsubjects factors. Assuming that you have random assignment to the two "Treatment" groups, your independent variable is a two level betweensubjects factor. If not randomly assignment, it is some form of quasiindependent variable. It is a form of quasiindependent variable. I propose my experiment to patients and I match controls on age, IQ, sex... 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%) >in which they had to chose between 2 options, one safe and one risky. Now, this seens to be your dependent variable, right? But it is unclear what the response actually is (e.g., "Yes" vs "No", or "Accept" vs "Refuse", etc.) which apparently you coded as 0,1 or 1,2 or whatever, which is why you are doing a binary logistic regression  the fact that you independent variables/factors are dichotomous is besides the point. Yes my dependent variable was dichotomous. Choice of the sure option was coded 0 and choice of the risky option was coded 1 > 4 trials were formulated in terms of gain (2 with a low risk and 2 > with a > high risk) and 4 trials were formulated in terms of loss (2 with a low > risk > and two with a high risk). So, this is where the withinsubject design is described: (1) a factor which we'll call "GainLoss" (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 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 3way interaction while my design implies the presence of a 4way interaction. You've done something that is not obvious. Yes I have a 3way interaction: Group X Formulation X Level of risk > All my IV, Group (patient vs control), formulation (gain vs loss) and > level > of risk (low vs high) are dichotoumous. I really don't understand what you are saying here. The critical point is whether your dependent variable is dichotomous or not. If it is, then binary logistic regression may be the appropriate analysis. If not, then you're not providing full information. Exactly, my DV is dichotomous, which led to the choice of binary logistic regression > For example, I have a significant Group X Formulation interaction, but > I am > not sure how I can precisely observe the influence of the formulation > within > each group. If by "Formulation" you are referring to what I call "GainLoss", then you appear to be referring to a 2x2 result, with each group having two values for "GainLoss". 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 For completeness sake, it appears that you have the following design and set of results. The 2way 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 gainloss), 2 (for riskiness) & 3 (for repetition) 6 twoway interactions: Gx!, Gx2, Gx3, !x2, 1x3, 2x3 4 threeway interactions: Gx1x2, Gx1x3, Gx2x3, 1x2x3 1 fourway interaction: Gx1x2x3 Except repetition, it is exactly my design 
In reply to this post by PhD student
This is kind of grueling but it is still not clear. Your response to Mike included this example data
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 Choice is your DV. Each person sees each combination of formulation and risk level twice. Thus, replication is another level in your experimental design. If you were doing this in anova, you'd describe the analysis as one between, three within: GLM yf0l0r1 yf0l0r2 yf0l1r1 yf0l1r2 yf1l0r1 yf1l0r2 yf1l1r1 yf1l1r2 by group/Wsfactor form 2 level 2 rep 2/ wsdesign form level rep form*level form*rep level*rep form*level*rep. * f=formulation, l=level of risk, r=replication. I know there are list members who are more knowledgeable and experienced than I am with both genlin and genlinmixed and can give you better help. Gene Maguin Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of PhD student Sent: Thursday, December 15, 2016 12:23 PM To: [hidden email] Subject: Re: Interactions binary logistic regression 1) Two groups (got that) and each participant completed all 8 trials? Or something else? This element is important! *Yes, exactly* 2) In each trial participants selected either a risky option or a safe option. The dichotomous DV. *Yes* 3) A trial was formulated as a gain or as a loss and as low risk or high risk. Four combinations. *I was not clear enought, the level of risk was 20% chances of winning, 40% 60% and 80%. Classically, but authors recommend to categorize 20 and 40% as low and 60 and 80% as high* 4) Each combination was replicated twice. *Therefore, each combination was presented once.* If each participant did all eight trials, you have a repeated measures design. Just suppose the DV were continuous, how would you set up the analysis? *If my DV was continuous, I would use ANOVA. In my speciality, data are classically treated with ANOVA, but I am not sure that is the most appropriate technique due to the dichotomous DV*  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/Interactionsbinarylogisticregressiontp5733602p5733611.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
Without the regroupment suggested by some authors that I mention before, my data are exactly under this form. No trial was presented twice.
Subject Group Formulation Level of risk Choice 1 1 Gain 20% 1 1 1 Gain 40% 0 1 1 Gain 60% 0 1 1 Gain 80% 0 1 1 Loss 20% 1 1 1 Loss 40% 0 1 1 Loss 60% 1 1 1 Loss 80% 1 Thank you very much for your help 
In reply to this post by PhD student
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 betweensubjects > factor. If not randomly assignment, it is some form of > quasiindependent > variable. *It is a form of quasiindependent variable. I propose my > experiment to patients and I match controls on age, IQ, sex...* You should be clearer that you are using a quasiindependent 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 withinsubject design is described: > (1) a factor which we'll call "GainLoss" (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) Gainloss (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 3way interaction while my design implies the presence of a > 4way interaction. You've done something that is not obvious. *Yes I > have a > 3way 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 "GainLoss", then > you appear to be referring to a 2x2 result, with each group having two > values for "GainLoss". 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 2way 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 gainloss), 2 (for riskiness) & > 3 > (for repetition) > > 6 twoway interactions: > Gx!, Gx2, Gx3, !x2, 1x3, 2x3 > > 4 threeway interactions: > Gx1x2, Gx1x3, Gx2x3, 1x2x3 > > 1 fourway 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] ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
In reply to this post by Maguin, Eugene
IF
the level of risk were not coarsened you might have additional info. Am I correct that you only coarsened the risk level to have "repeats"? If risk were not coarsened the most complex interaction would not be estimable but all lower order interactions would be. What do other list members think of trying an analysis without coarsening the risk variable?
Art Kendall
Social Research Consultants 
This makes sense to me. However, based on Phd Student's note, it seems that although experiments are/may be designed with multiple risk levels (20, 40, 60, 80, in this case), customary practice is to collapse design levels into "low" and "high" for analysis and reporting. Gene Maguin
Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Art Kendall Sent: Thursday, December 15, 2016 2:12 PM To: [hidden email] Subject: Re: Interactions binary logistic regression *IF* the level of risk were not coarsened you might have additional info. Am I correct that you only coarsened the risk level to have "repeats"? If risk were not coarsened the most complex interaction would not be estimable but all lower order interactions would be. What do other list members think of trying an analysis without coarsening the risk variable?  Art Kendall Social Research Consultants  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/Interactionsbinarylogisticregressiontp5733602p5733617.html Sent from the SPSSX Discussion mailing list archive at Nabble.com. ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
In reply to this post by Mike
You should be clearer that you are using a quasiindependent 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 cutoff 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 3way interaction while my design implies the presence of a > 4way interaction. You've done something that is not obvious. *Yes I > have a > 3way 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 2way interaction for purposes of clarity. > If by "Formulation" you are referring to what I call "GainLoss", then > you appear to be referring to a 2x2 result, with each group having two > values for "GainLoss". 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 2way 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 gainloss), 2 (for riskiness) & > 3 > (for repetition) > > 6 twoway interactions: > Gx!, Gx2, Gx3, !x2, 1x3, 2x3 > > 4 threeway interactions: > Gx1x2, Gx1x3, Gx2x3, 1x2x3 > > 1 fourway 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 (gainloss) and riskiness(20% 40% 60% 80%) and thus 3 twoway interactions and 1 three way interaction. But maybe I don't understand what you refer to as Repitition factor ? 
In reply to this post by Maguin, Eugene
It is a few years since I was up to date in math psych, but I am not sure how "customary" it is to coarsen that way.
Not coarsening might give useful insight
Art Kendall
Social Research Consultants 
Yes, I totally agree but as I am not familiar with interactions in logistic regression (and as I though that splitting the level of risk and recomputing the regression for each modality could be a solution to interpret significant interactions) I thought that having a dichotomous Level of risk also has the advantage to be easier to interpret. I am going to take a look to the GenLin procedure suggested by Mr Maguin, it might give me useful insight to interpret this significant interaction without coarsening the Level of risk.

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From the IBM Knowledge Center (re GENLIN with GEE):
Using Generalized Estimating Equations to Fit a Repeated Measures Logistic Regression http://www.ibm.com/support/knowledgecenter/SSLVMB_24.0.0/spss/tutorials/gee_wheeze_intro.html Rather than using GENLIN with generalized estimating equations (GEE), you could use GENLINMIXED, with the repeated measures clustered within subjects. One or two of the examples on the following page may be close enough to give you the general idea. (E.g., the second example has repeated measures; but you would have to use logit link and binomial error distribution rather than log link and Poisson error distribution.) http://www.ibm.com/support/knowledgecenter/SSLVMB_20.0.0/com.ibm.spss.statistics.help/idh_glmm.htm HTH.

Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." NOTE: My Hotmail account is not monitored regularly. To send me an email, please use the address shown above. 
Genlimixed seems to be exactly the procedure that I need. Now, I have to understand how to perform it (which does not seem to be the easiest part!...).
Thank you very much for all your help and support 
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The 2012 book by Heck, Thomas & Tabata might be helpful to you (2nd link below).
http://www2.hawaii.edu/~ltabata/mlm/HTT2013.html http://www2.hawaii.edu/~ltabata/mlm/HTT2012.html HTH.

Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." NOTE: My Hotmail account is not monitored regularly. To send me an email, please use the address shown above. 
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