The analyses involve two independent variables with two conditions each (call them IV1 and IV2), and two dependent variables (call them DV1 and DV2). Both DV1 and DV2 are dichotomous, but are mainly analyzed through averages across blocks of data, and hence could be treated as continuous. All data is withinsubjects.
My main hypothesis is that when looking only at data from Condition 1 of IV1, there is no statistically significant relationship between [the extent to which IV2 impacts DV1] and [DV2], whereas in Condition 2 of IV1, as [the extent to which IV2 impacts DV1] increases, [DV2] decreases, and vice versa. I would like to determine if this is true. Moreover, it would be extremely helpful if there was some numerical measure of significance to quantify the impact of [IV1] on [the interaction between [the extent to which IV2 impacts DV1] and [DV2]], as opposed to simply running two separate analyses for the different conditions of IV1 and finding one significant and the other not. The second analysis is more difficult to describe. The experiment involves three independent variables  each with two conditions each. Every subject experiences eight blocks  one for each configuration of the independent variables. Within each block, DV2 is measured six times. My hypothesis is that in Condition 2 of IV1, subjects will show significantly greater preference toward one value of DV2 over another, than in Condition 1 of IV1. I do not claim to know which value the subject prefers, or even that this preference is consistent across blocks  merely that in Condition 2 blocks, there is a significantly greater directional orientation than in Condition 1 blocks. Any help on how to run these analyses would be appreciated! I am running them in SPSS. 
Your study description is confusing. Are both questions about the same experiment? Is this an accurate, succinct statement of the study design: Two DVs, both dichotomous. Two between factors, three within factors, all factors dichotomous. Each participant sees eight within conditions. Each within condition is presented six times to each participant.
Main hypothesis. I understand what you are describing as an interaction. Ignore the dichotomous nature of the DVs. For DV1 you're proposing (a) that for IV1=0, DV1 at IV2=0 is not significantly different from DV1 at IV2=1 and (b) that IV1=1, DV1 at IV2=0 is significantly different greater than DV1 at IV2=1. You're averaging DV1 across replications (and conditions?) so, this is not a mixed analysis. Use GLM with Emmeans. Basically: GLM DV1 by IV1 IV2/emmeans tables(IV1*IV2) compare(IV2). Repeat for DV2. Gene Maguin Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of sphericity Sent: Wednesday, February 08, 2017 11:32 AM To: [hidden email] Subject: How would I run the following mixedmodel analyses in SPSS? The analyses involve two independent variables with two conditions each (call them IV1 and IV2), and two dependent variables (call them DV1 and DV2). Both DV1 and DV2 are dichotomous, but are mainly analyzed through averages across blocks of data, and hence could be treated as continuous. All data is withinsubjects. My main hypothesis is that when looking only at data from Condition 1 of IV1, there is no statistically significant relationship between [the extent to which IV2 impacts DV1] and [DV2], whereas in Condition 2 of IV1, as [the extent to which IV2 impacts DV1] increases, [DV2] decreases, and vice versa. I would like to determine if this is true. Moreover, it would be extremely helpful if there was some numerical measure of significance to quantify the impact of [IV1] on [the interaction between [the extent to which IV2 impacts DV1] and [DV2]], as opposed to simply running two separate analyses for the different conditions of IV1 and finding one significant and the other not. The second analysis is more difficult to describe. The experiment involves three independent variables  each with two conditions each. Every subject experiences eight blocks  one for each configuration of the independent variables. Within each block, DV2 is measured six times. My hypothesis is that in Condition 2 of IV1, subjects will show significantly greater preference toward one value of DV2 over another, than in Condition 1 of IV1. I do not claim to know which value the subject prefers, or even that this preference is consistent across blocks  merely that in Condition 2 blocks, there is a significantly greater directional orientation than in Condition 1 blocks. Any help on how to run these analyses would be appreciated! I am running them in SPSS.  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/HowwouldIrunthefollowingmixedmodelanalysesinSPSStp5733793.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 
Thank you very much for your response. Both questions are about the same experiment. If you are referring to the DVs as between factors, then that is an accurate description of the study design. I will restate the hypotheses in clearer, more precise terms.
HYPOTHESIS #1: At IV1=0, there is no correlation between [DV2] and [the effect of IV2 on DV1]. At IV1=1, the greater [DV2] is, the weaker [the effect of IV2 on DV1], and the smaller [DV2] is, the stronger [the effect of IV2 on DV1]. If there were some way to simply measure the significance of the effect of [IV1] on [the correlation between [DV2] and [the effect of IV2 on DV1]], that would be ideal, but not necessary. HYPOTHESIS #2: Within a given IV condition, DV2 is measured six times. At IV1=1, there is significantly less variation in these six measurements of DV2 than at IV1=0. Please let me know if I can provide additional clarification. I apologize for the confusion. 
Would you please give us a succinct and precise description of your experimental design. Your design is clear to you because you designed it; it is not clear to me and may not be clear to others.
I ask for this because in your main hypothesis question in your original message you named IV1, IV2, DV1 and DV2. In the absence of more information I assumed IV1 and IV2 were between subjects factors. I understood DV1 and DV2 to be your dependent variables. I also assumed that each participant contributed one data value for each DValthough this text was confusing: "... averages across blocks of data". I can go on. Please start over by describing your design. Gene Maguin Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of sphericity Sent: Wednesday, February 08, 2017 8:57 PM To: [hidden email] Subject: Re: How would I run the following mixedmodel analyses in SPSS? Thank you very much for your response. Both questions are about the same experiment. If you are referring to the DVs as between factors, then that is an accurate description of the study design. I will restate the hypotheses in clearer, more precise terms. *HYPOTHESIS #1:* At IV1=0, there is no correlation between [DV2] and [the effect of IV2 on DV1]. At IV1=1, the greater [DV2] is, the weaker [the effect of IV2 on DV1], and the smaller [DV2] is, the stronger [the effect of IV2 on DV1]. If there were some way to simply measure the significance of the effect of [IV1] on [the correlation between [DV2] and [the effect of IV2 on DV1]], that would be ideal, but not necessary. *HYPOTHESIS #2:* Within a given IV condition, DV2 is measured six times. At IV1=1, there is significantly less variation in these six measurements of DV2 than at IV1=0. Please let me know if I can provide additional clarification. I apologize for the confusion.  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/HowwouldIrunthefollowingmixedmodelanalysesinSPSStp5733793p5733797.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 
Dear Gene, I have done so below. I realized that what I was calling DV2 is in reality two closely related but separate dependent variables, and have defined them as precisely as I could. Please let me know if there is anything that I have explained poorly and I will correct it.
There are three independent variables (IV1, IV2, IV3) with two conditions each. Thirty subjects each undergo eight "blocks" of an experimental task, where each block is a unique configuration of IV conditions. That is, one of the blocks is [IV1=0, IV2=0, IV3=0], another block is [IV1=0, IV2=0, IV3=1], and so forth, until every configuration of the conditions has appeared exactly once. The order in which the configurations are presented in the actual experiment is determined randomly and is different for each subject. All three independent variables are hence withinsubjects. A "block" of this experimental task involves making 36 keypresses in response to pictures. Each keypress is coded as either "0" (inaccurate) or "1" (accurate). These 36 values are then averaged, yielding a continuous DV1 called "Accuracy" that is measured once per block. Exactly six times during the course of each block, the task requiring keypresses is momentarily paused and subject is presented with a threeoption multiple choice question ("A", "B", "C"). If the subject answers "B", DV2 = "0". If the subject answers "C", DV2 = "1". The remaining responses (that is, the "A" responses) are ignored. DV2 is thus measured between zero and six times per block, depending on how many "A" responses there are. The average of the "0"s and "1"s across an individual block (ignoring the "A" responses) is the measurement of DV3 for that block. If all six responses were "A", this block would not have a measurement of DV3, since it would require dividing by zero.  *HYPOTHESIS 1a:* At IV1=0, there is no correlation between [DV3] and [the effect of IV2 on DV1]. At IV1=1, the greater [DV3] is, the weaker [the effect of IV2 on DV1], and the smaller [DV3] is, the stronger [the effect of IV2 on DV1]. *HYPOTHESIS 1b:* Same as Hypothesis 1a, but replacing all instances of IV2 with IV3. *HYPOTHESIS 2:* At IV1=1, the variation among the [DV2] values within a block is significantly less than at IV1=0. (I am not completely sure what the correct way to perform this analysis is, as there are four IV1=1 blocks and four IV1=0 blocks per subject). To summarize: Three withinsubjects independent variables with two conditions each, for a total of eight conditions. DV1 and DV3 are both measured once per condition, with a total of eight measurements per subject. DV2 is measured six times per condition, with a total of 48 measurements per subject. 
Ok. So, given the analysis preprocessing, 36 records per participant is condensed to one record per participant.
*HYPOTHESIS 1a: 1a.1 At IV1=0, there is no correlation between [DV3] and [the effect of IV2 on DV1]. This statement does not make sense to me. I am unable to turn this statement into an analysis. Perhaps I'm not sufficiently creative. However, DV3 is a variable while "the effect of IV2 on DV1" implies a single coefficient. Since IV2 is dichotomous, its effect on DV1 is difference in the DV1 mean at IV2=0 and at IV2=1. 1a.2 At IV1=1, the greater [DV3] is, the weaker [the effect of IV2 on DV1], and the smaller [DV3] is, the stronger [the effect of IV2 on DV1]. Same story here. *HYPOTHESIS 1b:* Same as Hypothesis 1a, but replacing all instances of IV2 with IV3. Same story here. Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of sphericity Sent: Thursday, February 09, 2017 11:14 AM To: [hidden email] Subject: Re: How would I run the following mixedmodel analyses in SPSS? Dear Gene, I have done so below. I realized that what I was calling DV2 is in reality two closely related but separate dependent variables, and have defined them as precisely as I could. Please let me know if there is anything that I have explained poorly and I will correct it. There are three independent variables (IV1, IV2, IV3) with two conditions each. Thirty subjects each undergo eight "blocks" of an experimental task, where each block is a unique configuration of IV conditions. That is, one of the blocks is [IV1=0, IV2=0, IV3=0], another block is [IV1=0, IV2=0, IV3=1], and so forth, until every configuration of the conditions has appeared exactly once. The order in which the configurations are presented in the actual experiment is determined randomly and is different for each subject. All three independent variables are hence withinsubjects. A "block" of this experimental task involves making 36 keypresses in response to pictures. Each keypress is coded as either "0" (inaccurate) or "1" (accurate). These 36 values are then averaged, yielding a continuous DV1 called "Accuracy" that is measured once per block. Exactly six times during the course of each block, the task requiring keypresses is momentarily paused and subject is presented with a threeoption multiple choice question ("A", "B", "C"). If the subject answers "B", DV2 = "0". If the subject answers "C", DV2 = "1". The remaining responses (that is, the "A" responses) are ignored. DV2 is thus measured between zero and six times per block, depending on how many "A" responses there are. The average of the "0"s and "1"s across an individual block (ignoring the "A" responses) is the measurement of DV3 for that block. If all six responses were "A", this block would not have a measurement of DV3, since it would require dividing by zero.  *HYPOTHESIS 1a:* At IV1=0, there is no correlation between [DV3] and [the effect of IV2 on DV1]. At IV1=1, the greater [DV3] is, the weaker [the effect of IV2 on DV1], and the smaller [DV3] is, the stronger [the effect of IV2 on DV1]. *HYPOTHESIS 1b:* Same as Hypothesis 1a, but replacing all instances of IV2 with IV3. *HYPOTHESIS 2:* At IV1=1, the variation among the [DV2] values within a block is significantly less than at IV1=0. (I am not completely sure what the correct way to perform this analysis is, as there are four IV1=1 blocks and four IV1=0 blocks per subject). To summarize: Three withinsubjects independent variables with two conditions each, for a total of eight conditions. DV1 and DV3 are both measured once per condition, with a total of eight measurements per subject. DV2 is measured six times per condition, with a total of 48 measurements per subject.  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/HowwouldIrunthefollowingmixedmodelanalysesinSPSStp5733793p5733801.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 
*HYPOTHESIS 1a:
1a.1 At IV1=0, there is no correlation between [DV3] and [the effect of IV2 on DV1]. This statement does not make sense to me. I am unable to turn this statement into an analysis. Perhaps I'm not sufficiently creative. However, DV3 is a variable while "the effect of IV2 on DV1" implies a single coefficient. Since IV2 is dichotomous, its effect on DV1 is difference in the DV1 mean at IV2=0 and at IV2=1. I see. I was thinking that there would be some way to run a multivariate analysis on DV3, IV2, and DV1 and see if there is a mediation effect, but simply computing a difference in means might be better and simpler. In this case, the analysis simplifies to separating the data into four blocks of IV1=0 and four blocks of IV1=1 and computing, for each fourblock segment: The difference in DV1 mean at IV2=0 vs IV2=1 Mean DV3 (across the four blocks) I suppose it would be possible to run a simple correlation between mean DV3 and difference in DV1 mean, but would you happen to know if there is a way to include IV1 as a variable in this analysis, and obtain a single measure of significance for the effect of [IV1] on the correlation between [mean DV3] and [difference in DV1 mean at IV2=0 vs. IV2=1]? To analyze Hypothesis 2, I have been thinking about again separating the data into IV1=0 and IV1=1 segments, finding [DV2] variance for each of the four blocks within a segment, averaging across these variances, and then running a pairedsamples ttest. However I am not sure if this would be statistically valid and would greatly appreciate any feedback.  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/HowwouldIrunthefollowingmixedmodelanalysesinSPSStp5733793p5733806.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 
Let's set the experimental design and the variable definition elements aside and focus on the hypotheses. I'd like to switch to equations/equationpicture because I don't know that I am accurately understanding your language.
Can you present Hypothesis 1 in equation picture form? This may help me. Example: a mediation model (B1 and B2 are the coefficients) X > (B1) M > (B2) Y Example: an interaction (moderation) model. X (B1) + Y (B2) + X*Y (B3) > Z Or X > (B1) Z ^ (B3) Y (B2 on Z) Gene Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of sphericity Sent: Thursday, February 09, 2017 2:51 PM To: [hidden email] Subject: Re: How would I run the following mixedmodel analyses in SPSS? *HYPOTHESIS 1a: 1a.1 At IV1=0, there is no correlation between [DV3] and [the effect of IV2 on DV1]. This statement does not make sense to me. I am unable to turn this statement into an analysis. Perhaps I'm not sufficiently creative. However, DV3 is a variable while "the effect of IV2 on DV1" implies a single coefficient. Since IV2 is dichotomous, its effect on DV1 is difference in the DV1 mean at IV2=0 and at IV2=1. I see. I was thinking that there would be some way to run a multivariate analysis on DV3, IV2, and DV1 and see if there is a mediation effect, but simply computing a difference in means might be better and simpler. In this case, the analysis simplifies to separating the data into four blocks of IV1=0 and four blocks of IV1=1 and computing, for each fourblock segment: The difference in DV1 mean at IV2=0 vs IV2=1 Mean DV3 (across the four blocks) I suppose it would be possible to run a simple correlation between mean DV3 and difference in DV1 mean, but would you happen to know if there is a way to include IV1 as a variable in this analysis, and obtain a single measure of significance for the effect of [IV1] on the correlation between [mean DV3] and [difference in DV1 mean at IV2=0 vs. IV2=1]? To analyze Hypothesis 2, I have been thinking about again separating the data into IV1=0 and IV1=1 segments, finding [DV2] variance for each of the four blocks within a segment, averaging across these variances, and then running a pairedsamples ttest. However I am not sure if this would be statistically valid and would greatly appreciate any feedback.  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/HowwouldIrunthefollowingmixedmodelanalysesinSPSStp5733793p5733806.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 
How would one represent a covariation in equation picture format?
I confess I'm not completely sure how to represent "[IV1] moderates the covariation between [DV1 mean at IV2=1 minus DV1 mean at IV2=0] and [DV3]" in picture format. 
In reply to this post by Maguin, Eugene
Correction to my previous post. I meant correlation, not covariation.

In reply to this post by sphericity
Well, I'm not sure either and that's my problem.
So how about this translation? I want to also restate design elements. Three within subject conditions, IV1, IV2, IV3, all dichotomous, coded as 0,1, presented to 30 participants. Let their combinations (IV1, IV2, IV3 concantenated) be called Condition with values 000 through 111. Each condition consists six blocks of six trials in which three variables, DV1, DV2, DV3 are recorded. DV1 is the keypress value, 0 or 1. DV2 is presented at end of each block of trials and has values A=9=missing, B=0, C=1. Thus, 30 values of sysmis and 6 values of 0,1,9 per condition. DV3 is computed for the condition as a whole as the mean of DV2. Permissable values are sysmis, and fractions of numerators between and including 1 and 6. In long format you have 30**8*36 records. Let's say you aggregate by person and condition, defining, as you said, DV1 as the proportion, DV2 as sum of DV2, and DV3 as the proportion of DV2. So now you have 8 records per person arranged as follows for participant 14. Id cond* DV1 DV2 DV3 14 000 .22 4 .75 14 001 .32 3 .33 14 010 .42 1 1.0 14 011 .02 . . 14 100 .26 6 .17 14 101 .20 3 .66 14 110 .23 2 .50 14 111 .28 5 .00 * cond=000 implies IV1=0, IV2=0, IV3=0 Now this: [IV1] moderates the covariation between [DV1 mean at IV2=1 minus DV1 mean at IV2=0] and [DV3]. Let's say you are computing the dataset for this analysis. Using the data shown, compute and show the required values for id=14. I want to make sure we are on the same page. Gene Maguin Original Message From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of sphericity Sent: Saturday, February 11, 2017 7:17 PM To: [hidden email] Subject: Re: How would I run the following mixedmodel analyses in SPSS? How would one represent a covariation in equation picture format? I confess I'm not completely sure how to represent "[IV1] moderates the covariation between [DV1 mean at IV2=1 minus DV1 mean at IV2=0] and [DV3]" in picture format.  View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/HowwouldIrunthefollowingmixedmodelanalysesinSPSStp5733793p5733817.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 
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