## Frequently Asked Questions

Below please find answers to some common questions asked about my research, tools, or teaching. If you can't find the answer to your question below, feel free to contact me: akmontoya@ucla.edu

## Questions about MEMORE

Q: How can I get standardized regression coefficients as part of my MEMORE output?

A: MEMORE uses difference scores as part of it's analysis, and so standardized regression coefficients are not readily interpretable in this context. MEMORE does not have any built in features to output standardized regression coefficients. Researchers can standardize their moderators prior to entering them in the MEMORE command, then the coefficients for the moderators will represent the expected difference on the outcome for a one standard deviation difference on the moderator. Mediators and outcomes SHOULD NOT be standardized prior to being entered into the MEMORE analysis, as this will remove important information about mean differences.

Q: How do I conduct a power analysis or determine a planned sample size for my analysis with MEMORE?

A: The current version of MEMORE conducts mediation analysis and moderation analysis for within-subject designs. Power analysis for within-subject designs is described in Montoya (2022) and there is an R script which can conduct power analysis for simple mediation models with any inferential method available in MEMORE available on my github.

For moderation analysis, any tool which conducts power analysis for regression (e.g., G*power or pwr2ppl) can be used to conduct the power analysis. The moderation analysis is a simple regression predicting the difference in the outcome variables using the moderator. The coefficient for the moderator is the coefficient of interest for a test of moderation, so this should be set based on the expected effect size or smallest effect of interest.

For example with G*power:

You would set the Slope H1 based on the size of the effect that you expect. If it is difficult to think of this in the raw metric, g*power provides a calculator where you could specify the correlation, standard deviation of the residual, standard deviation of X (in this case your moderator) and standard deviation of Y (in this case the different between your Ys). This last one may be difficult to conceptualize, so a useful equation is SD(Y1-Y2) = SD(Y1) + SD(Y2) - 2rSD(Y1)SD(Y2). So if it is easier to think about, you can set the standard deviation of Y1 (SD(Y1)) the standard deviation of Y2 (SD(Y2)) and their correlation (r), and use this to calculate the standard deviation of the difference. Note that r here is different from rho in g*power, which is the correlation between the difference score on Y and X (the moderator).

Q: The dialog box version of MEMORE leads to errors when I use SPSS V28, what can I do?

A: A new release of MEMORE V2.1.2 is available which addresses this bug. Please download the new version here.

Q: How do I include covariates in my MEMORE analysis?

A: Because the effects are estimated within person there is no need to control for between person covariates (e.g., age) since you essentially have perfectly matched pairs. However, if you want to control for a within-subject variable, you can include it as another mediator in parallel (if you think it only confounds the M --> Y path) or in serial (prior to the mediator) if you think this variable may confound both the X --> M path and M --> Y path.

Q: Can MEMORE account for more than 2 conditions?

A: Yes! Judd, Kenny, and McClelland (2001) describe how to define contrasts of interest related to more than 2 conditions.

Mediation: I recommend reading Preacher and Hayes (2014) about handling multicategorical predictors in mediation. The same issue arises for within-subjects designs. You'll have to define contrasts of interest in order to to estimate the indirect effects of interest.

MEMORE does not have any built in functions to do these types of contrasts, but if the contrasts are pairwise comparisons then you can just enter the pairs in a set of MEMORE analyses. Alternatively, if the contrasts are more complex one would create a variable that is a combination of the variables you want to compare. For example if there are three conditions, and you want to compare the average of two conditions to the third (Y1+Y2)/2 - (Y3), then you can make a variable that is (Y1+Y2)/2 = Ycont and (M1+M2)/2 = Mcont, and enter that into the MEMORE command like so:

MEMORE Y = Ycont Y3 /M = Mcont M3 /model = 1.

Please note however, that I do not recommend using MEMORE for more than 2 measurement points longitudinally. Multilevel and longitudinal mediation models can more appropriately account for the time series nature of longitudinal data.

Moderation: I recommend reading Hayes & Montoya (2017) about handling multicategorical predictors in moderation. MEMORE can be used for evaluating any contrasts of conditions and whether that contract is moderated by a predictor variable. For example, if there are four conditions, and you want to compare Condition 1 and Condition 2 (together) to Condition 3 and Condition 4 (together) (Y1+Y2)/2 - (Y2+Y3)/2, then you can make a variable that is Y12 = (Y1 + Y2)/2 and Y34 = (Y3 + Y4)/2, then use MEMORE with Y12 and Y34 as the two outcomes:

MEMORE Y = Y12 Y34 /W = Mod /model = 2.

Q: How do I conduct a power analysis or determine a planned sample size for my analysis with MEMORE?

A: The current version of MEMORE conducts mediation analysis and moderation analysis for within-subject designs. Power analysis for within-subject designs is described in Montoya (2022) and there is an R script which can conduct power analysis for simple mediation models with any inferential method available in MEMORE available on my github.

For moderation analysis, any tool which conducts power analysis for regression (e.g., G*power or pwr2ppl) can be used to conduct the power analysis. The moderation analysis is a simple regression predicting the difference in the outcome variables using the moderator. The coefficient for the moderator is the coefficient of interest for a test of moderation, so this should be set based on the expected effect size or smallest effect of interest.

For example with G*power:

You would set the Slope H1 based on the size of the effect that you expect. If it is difficult to think of this in the raw metric, g*power provides a calculator where you could specify the correlation, standard deviation of the residual, standard deviation of X (in this case your moderator) and standard deviation of Y (in this case the different between your Ys). This last one may be difficult to conceptualize, so a useful equation is SD(Y1-Y2) = SD(Y1) + SD(Y2) - 2rSD(Y1)SD(Y2). So if it is easier to think about, you can set the standard deviation of Y1 (SD(Y1)) the standard deviation of Y2 (SD(Y2)) and their correlation (r), and use this to calculate the standard deviation of the difference. Note that r here is different from rho in g*power, which is the correlation between the difference score on Y and X (the moderator).

Q: The dialog box version of MEMORE leads to errors when I use SPSS V28, what can I do?

A: A new release of MEMORE V2.1.2 is available which addresses this bug. Please download the new version here.

Q: How do I include covariates in my MEMORE analysis?

A: Because the effects are estimated within person there is no need to control for between person covariates (e.g., age) since you essentially have perfectly matched pairs. However, if you want to control for a within-subject variable, you can include it as another mediator in parallel (if you think it only confounds the M --> Y path) or in serial (prior to the mediator) if you think this variable may confound both the X --> M path and M --> Y path.

Q: Can MEMORE account for more than 2 conditions?

A: Yes! Judd, Kenny, and McClelland (2001) describe how to define contrasts of interest related to more than 2 conditions.

Mediation: I recommend reading Preacher and Hayes (2014) about handling multicategorical predictors in mediation. The same issue arises for within-subjects designs. You'll have to define contrasts of interest in order to to estimate the indirect effects of interest.

MEMORE does not have any built in functions to do these types of contrasts, but if the contrasts are pairwise comparisons then you can just enter the pairs in a set of MEMORE analyses. Alternatively, if the contrasts are more complex one would create a variable that is a combination of the variables you want to compare. For example if there are three conditions, and you want to compare the average of two conditions to the third (Y1+Y2)/2 - (Y3), then you can make a variable that is (Y1+Y2)/2 = Ycont and (M1+M2)/2 = Mcont, and enter that into the MEMORE command like so:

MEMORE Y = Ycont Y3 /M = Mcont M3 /model = 1.

Please note however, that I do not recommend using MEMORE for more than 2 measurement points longitudinally. Multilevel and longitudinal mediation models can more appropriately account for the time series nature of longitudinal data.

Moderation: I recommend reading Hayes & Montoya (2017) about handling multicategorical predictors in moderation. MEMORE can be used for evaluating any contrasts of conditions and whether that contract is moderated by a predictor variable. For example, if there are four conditions, and you want to compare Condition 1 and Condition 2 (together) to Condition 3 and Condition 4 (together) (Y1+Y2)/2 - (Y2+Y3)/2, then you can make a variable that is Y12 = (Y1 + Y2)/2 and Y34 = (Y3 + Y4)/2, then use MEMORE with Y12 and Y34 as the two outcomes:

MEMORE Y = Y12 Y34 /W = Mod /model = 2.