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Moderation Analysis with RegressionCategorical Data AnalysisPacket CD03Dale Berger, Claremont Graduate University (dale.berger@cgu.edu) Statistics website: This document is designed to aid note taking during the associated PowerPoint presentation and to serve as a reference for later use. It provides selected formulas, figures, SPSS syntax and output, and references, along with detailed explanations of SPSS output.This document, the associated PowerPoint presentation, SPSS data files, supplemental reading, and other materials are available at under Resources.2Moderation analysis with regression3Examples of moderation (identify X, Y, and Z)3Model of salary for men and women4SPSS example of moderation with a dichotomous moderator 5SPSS point-and-click commands 6SPSS regression output and interpretations 7Figure presenting the findings 8Table presenting regression analysis 9Dummy mediator variable and centered continuous X variable10Multicollinearity and tolerance10SPSS example of moderation with a continuous moderator11SPSS output and table for presentation12Interpretations13Figure presenting the findings14Summary15References16Appendices: SPSS syntax for moderation analyses17Hayes’ SPSS macro PROCESS18Hayes’ SPSS macro MODMEDModeration Analysis with RegressionGroup differences in treatment effects often are especially important to measure and understand. If a treatment has greater effects for women than for men, we say that sex ‘moderates’ the effects of the treatment. When there is moderation, it may be misleading to describe overall treatment effects without taking group membership into account. Moderation analysis can guide decisions about interpreting effects and redesigning treatments for different groups.296164012890500Moderation is interaction. For example, among eighth grade children, drug use by a child can be predicted by drug use of their friends. However, the relationship is weaker for children who have greater parental monitoring. This finding can be displayed by showing that the slope of the regression line predicting the child’s drug use from drug use by friends differs with the level of parental monitoring. “Parental monitoring moderates the relationship between drug use by children and drug use by their friends, such that the relationship is weaker for children with stronger parental monitoring.” In general, Variable Z is a moderator of the relationship between X and Y if the strength of the relationship between X and Y depends on the level of Z. A moderator relationship can be illustrated with an arrow from Variable Z (the moderator variable) pointing to the arrow that connects X and Y (see Figure 2). A model can include both mediation and moderation. We can include a path from X to Z, indicating that Z may also mediate the relationship between X and Y. The X-Z path would not affect our analysis of the moderation effect. Z can be a moderator even if it has no direct effect on Y and thus no mediation effect. The effect of X on Y for a specific value of Z is called a simple effect of X on Y for that value of Z.Figure 2: Model Showing Z Moderating the X-Y RelationshipXZYXZYExamples of moderation (identify X, Y, and Z):The impact of a program is greater for younger adolescents than for older adolescents.416242512001500X =Y = Z =Learning outcomes are positively related to amount of study time for children who use either Book A or Book B, but the relationship is stronger for those who use Book B.X =Y =Z =The relationship between education and occupational prestige is greater for women than for men.X =Y =Z =Models of Salary for Men and WomenWe wish to test the null hypothesis that the relationship between salary and time on the job is the same for men and women in a large organization. We have data on salary, years on the job, and gender for a random sample of n=200 employees.Y = salary in $1000s; X1 = years on the job; X2 = gender (men = 0; women = 1)To test for an interaction, we create a special interaction term, X3 = X1 * X2.Regression analysis yielded the following model:Y' = 55.0 + 1.5X1 -3.4X2 + .7X3With this model, we can predict salary for any individual if we know X1 and X2 for that person.For men, X2 = 0, and also X3 = 0 because X3 = X1 * X2.Thus, for men, the regression model simplifies to Y' = 55.0 + 1.5X1.For women, X2 = 1, so also X3 = X1. Thus, for women, the regression model simplifies to Y' = 55.0 + 1.5X1 + (-3.4) + .7X1, or Y' = 51.6 + 2.2X1 We can use the models for men and women to create a diagram showing the simple effects for men and women. Elements of the original regression equation can be interpreted as follows.The constant (55.0) is the predicted salary for someone who has values of zero on all predictors. In this example, men with zero years on the job have X1 = 0, X2 = 0, and X3 = 0, so the constant is the predicted salary for men with zero years on the job, i.e., 55.0 or $55,000.If we did not have an interaction term in the model, then both men and women would be given the same regression coefficient on X1. Because there is an interaction term, the coefficient of 1.5 on X1 applies only to men (who have values of zero on the interaction term), so the model predicts average salary to be $1500 greater for each year on the job for men. This does not mean that every individual man is expected to earn $1500 more each year, but rather 1.5 describes the slope for men in the cross-sectional data. In general, the coefficient on X1 is the simple effect of X1 when X2 = 0.The coefficient of -3.4 on X2 is the modeled difference in salary between men and women who have zero years on the job. This is the difference in the constant for the models for men and women. The coefficient of .7 on the interaction term X3 indicates the difference in the regression weight for men and women. Because X3 = 0 for men and X3 = X1 for women, the weight on X3 is the additional weight given to X1 for women. The null hypothesis for the test of the regression weight on X3 is that this weight is zero in the population, which would mean that the slopes of the regression model for men and women are the same. If this null hypothesis is rejected, the conclusion is that the slopes are different. In the example, the slope is .7 greater for women, indicating that the average increment in predicted salary per year is $700 greater for women. In the regression models for men and women, the weight on X1 is 1.5 for men and 2.2 for women, a difference of .7. An assumption is that residuals from the model are reasonably homogeneous and normally distributed across levels of X1 and X2. If relationships are nonlinear, the nonlinear components should be included in the model.SPSS Example: Moderation Effects with a Dichotomous ModeratorOccupational prestige as measured by a standard scale is positively related to years of education, but is the relationship the same for men and women? For this example, we can use data from a national sample of U.S. adults given in 1991 U.S. General Social Survey.SAV, as provided by SPSS. This sample includes n=1415 cases with complete data on the three variables of occupational prestige, years of education, and gender.In this example, the dependent variable (Y) is occupational prestige and the independent variable (X) is years of education, while gender is a potential moderator (Z). Moderation in this example is indicated by an interaction between X and Z in predicting Y, which would indicate that the relationship between X and Y depends on the level of Z. A special term must be constructed to represent the interaction of X and Z. With regression we can test whether this term contributes beyond the main effects of X and Z in predicting Y. Mathematically, the interaction term can be computed as the product of X and Z. To demonstrate how this works in our example, we compute the product of Education (X) and Sex (Z) to create a new variable that we name EdxSex (XZ), and we include EdxSex in a final model to predict Y. SPSS Commands (Point and Click):Call up SPSS and the GSS1991 data file (available online or from Sakai, Resources, Data files, select file 1991 U.S. General Social Service.sav). First, create the interaction term. Click Transform, Compute…, in the Target Variable: window enter EdxSex, select educ and click the black triangle to enter educ into the Numeric Expression: window, click *, select sex and click the triangle. This should give educ * sex in the Numeric Expression: window. This expression can be typed into the window instead of selecting and clicking. You can click OK to run this computation, or you can click Paste to save the syntax in a syntax file to be run later. If you use Paste, go to the syntax window and run this computation because we need the new variable EdxSex for the next analysis. (Highlight the compute statement and the Execute command, press the triangle to run.)The regression analysis to test interactions is hierarchical, whereby we must enter the main effects of education and sex before we enter the interaction. Click Analyze, Regression, Linear…, select prestg80 and click the black triangle to enter it as the Dependent variable. Select educ and click the triangle to enter educ as the first independent variable. Click Next to go to the second block; select sex and click the triangle to enter sex as the second independent variable. Click Next to go to the third block; select EdxSex and click the triangle to enter EdxSex as the third independent variable in a hierarchical analysis.For illustration, we will ask for a lot of statistics. Click Statistics…, select Estimates, Model fit, R squared change, Descriptives, Part and partial correlations, and Collinearity diagnostics, and click Continue.Click Plots, select *ZRESID as the Y variable and *ZPRED as the X variable, check Histogram, and click Continue. Click Paste to save the syntax. Go to the syntax window and run the regression analysis. Table 1 shows selected SPSS output.Table 1: Test of Moderation Effects with a Dichotomous Moderator (N=1415)The first model uses only Education (X) to predict Y (Occupational Prestige). We see that education is a strong predictor, with r = beta = .520, t(1413) = 22.864, p < .001. The second model predicts Occupational Prestige (Y) from the additive effects of Education (X) and Sex (Z), assuming no moderation. From Unstandardized Coefficients we find the following:Predicted Y = = B0 + B1X + B2Z ; = 14.294 + 2.286X - .709ZThe coefficient B1 = 2.286 can be interpreted as indicating that for either males or females, one additional unit of X (one more year of education) is associated with 2.286 more units of predicted Y (+2.286 on the Occupational Prestige scale). However, if there is an interaction, the model may be misleading. If the effects of education are different for males and females, this simple model is not accurate for either group.The third model in Table 1 includes the interaction term, resulting in the following equation:= B0 + B1X + B2Z + B3XZ ; = 22.403 + 1.668X – 6.083Z + .412XZThe test of statistical significance of the interaction term yields t(1411)=2.050, p=.041. We conclude that the relationship between Education and Occupational Prestige differs for males and females. This also means that the sex difference on occupational prestige varies with level of education. (Statistical significance doesn’t necessarily indicate a large or important effect.)How does this work? It is instructive to compute the regression equations separately for males and females. In this data set, Sex (Z) is coded Z=1 for males and Z=2 for females. Thus, for males the equation reduces to = 22.403 + 1.668X – (6.083)(1) + .412X(1), which can be written as = 22.403 – 6.083*1 + 1.668*X + .412*X*1, or m = 16.320 + 2.080X.For females the equation is = 22.403 + 1.668X – (6.083)(2) + .412X(2), which can be written as = 22.403 – 12.166 + 1.668X + .824X, or f = 10.237 + 2.492X.The weight on the XZ interaction term (B3 = .412) is the difference in the regression weight on X for females and males (2.492 vs. 2.080). Thus, a test of B3 is a test of the sex difference in the regression weight on education when predicting occupational prestige.We can conclude that, on average, education has a statistically significantly stronger relationship with occupational prestige for females than for males. In the model without the interaction term, the regression weight of 2.286 on Education overestimates the relationship for males and underestimates the relationship for females. Of course, statistical significance does not imply that this difference is large enough to be theoretically or practically interesting.Acenter000n interaction is often illustrated effectively with a figure. Figure 7 shows the size and direction of the main effects and interaction, and where the modeled sex effect is largest, etc. This graph was made with Excel using regression weights from SPSS. You can access this Excel worksheet through under WISE Stuff in a file called Plotting Regression Interactions.XLS. It is important to note that the figure is a model of the relationship, not the actual data (which probably would not show such a nice regular pattern).Simulation studies have shown that statistical power to detect the effects of a dichotomous moderator variable can be very low if samples are small, the proportions of cases in the two groups are unequal, or if there is restriction of range on the predictor, especially in field studies with large measurement error, low co-occurrence of extreme values of predictors, and small effect sizes (McClelland & Judd, 1993).Presenting Results from Regression Analysis in a TableResults can also be presented in a table. Reasonable people may choose to report different statistics, depending on the goals of the study. Table 2 shows one way to present a selection of important information.Table 2: Moderation Effects of Sex on Education in Predicting Occupational Prestige (N=1415)StepVariablerR2 ChangeBSEBBeta1Education (years).520***.270***1.668 .318.518***2Sex (M=1; F=2)-.063**.001-6.0832.689-.0273Education x Sex ---.002*.412.201 ---(Constant)22.4034.300*p<.05; **p<.01; ***p<.001; Cumulative R squared = .273; Adjusted R squared = .271.B and SEB are from the final model at Step 3, and Beta is from the model at Step 2 (all main effects, but no interaction term).Table 2 summarizes key information with four conceptually distinct types of data, each of which can be useful. First, we have the simple correlations (r) which tell us how each individual predictor variable is related to the criterion variable, ignoring all other variables. We can see that Education is a much better predictor of Occupational Prestige than Sex, although both correlations are statistically significant. The correlation of the interaction term with the criterion is not easily interpreted, because this correlation is greatly influenced by scaling of the main effects; it is best omitted from the table.The second type of information comes from R2 Change at each step. Here the order of entry is critical if the predictors overlap with each other. For example, if Sex had been entered alone on Step 1, R2 Change would have been .004**, statistically significant with p<.01. (R2 Change for the first term entered into a model is simply its r squared.) Because of partial overlap with education, Sex adds only .001 R2 Change (not significant) when it is entered after Education is in the model. However, the interaction term adds significantly beyond the main effects (R2 Change = .002, p<.05), indicating that we do have a statistically significant interaction between Sex and Education in predicting Occupational Prestige. R2 Change measures and tests the effect sizes of components, while controlling for variables that were entered into the model earlier.The third type of information comes from the unstandardized B weights in the final model. These weights allow us to construct the raw regression equation, and we can use them to compute separate equations for males and females, if we wish. The B weights and their tests of significance on the main effects are not easily interpreted in the final model, because they refer to the unique contribution of each main effect beyond all other terms, including the interaction (which was computed as a product of the main effects). The test of B for the last term entered into the model is meaningful, as it is equivalent to the test of R2 change for the final term. In this case, both tests tell us that the interaction is statistically significant.The fourth type of information comes from the tests of regression weights for the model that contains only main effects (no interactions). These are tests of the unique contribution of each main effect beyond all other main effects. If the main effects do not overlap at all, the beta weight for each variable is identical to its r value. Here we see that Sex does not contribute significantly beyond Education in predicting Occupational Prestige (beta = -.027), although its simple r was -.063, p<.01. When there is an interaction, these main effects may be misleading.Dummy Variables and Centered Continuous Predictor Variables Interpretability of regression coefficients can be improved by ‘centering’ continuous predictor variables. Centering is accomplished by subtracting the mean from the variable. Thus, a centered score is a deviation score. Cohen, Cohen, West, and Aiken (2003, p. 267) recommend that continuous predictor variables be centered before interaction terms are computed, unless the variable has a meaningful zero (also see Marquardt, 1980). Centering reduces multicollinearity or overlap of the interaction term with other predictors and may improve interpretability, especially when zero is not meaningful on a scale (e.g., an SAT score of 0 is meaningless).In our example, the mean on Education is 13.02. We create a centered education variable by subtracting 13.02 from Years of Education for each case. We do not center the dependent variable, Occupational Prestige, because we wish to predict values on the original scale. For illustration, we also recode Sex to be a ‘dummy’ variable or ‘indicator’ variable, with values of zero or one (M=0; F=1). The syntax for this analysis is shown in Appendix A.Table 3: Moderation Effects of Sex on Education in Predicting Occupational Prestige, Education Centered and Sex Dummy Coded (N=1415)StepVariablerR2 ChangeBSEBBeta1Education (years).520***.270***2.080***.142.471***2Sex (M=0; F=1)-.063**.001-.720.599-.0273Education x Sex.002*.412*.201 .066(Constant)43.401.450*p<.05; **p<.01; ***p<.001; Cumulative R squared = .273; Adjusted R squared = .271.Education is ‘centered’ to a mean of zero.Because education is centered in Table 3, there is much less overlap between the interaction and the two main effects, so the B coefficients are much more stable (compare the SEB in the two tables). In Table 3 we show the simpler and more common convention of reporting B and beta for the final model. The beta values for the final model with uncentered data (not shown in Table 2) would have been .378, -.231, and .244, respectively, which are not easily interpreted because of the great overlap between the interaction term and the main paring Tables 2 and 3, we see that the R and R2 change values are the same. No conclusions are changed. We can interpret the constant in Table 3 (B0 = 43.401) as the mean value on Occupational Prestige when all predictors are zero, i.e., for males (Sex=0) at the mean of education (centered Education=0). We can also interpret the regression weight on Sex (B2 = .720) as the difference in Occupational Prestige for males and females at the mean on education. In contrast, in Table 2, the weight on Sex (B2 = -6.083) is the modeled difference between Occupational Prestige for males and females at zero years of education. That information is probably less interesting than the sex difference at the average level of education. Multicollinearity and ToleranceMulticollinearity is the proportion of variance in a predictor that can be predicted from other predictor variables; tolerance is one minus multicollinearity, or the proportion of variance in a predictor that cannot be predicted from other predictor variables. The tolerance for EdxSex = .036. This means that if we were to use multiple regression to predict EdxSex using all of the other predictor variables in the model with uncentered variables (Education and Sex), we would find R2 = .964, and 1 - R2 = 1-.964 = .036. If all predictors were independent, the R2 for predicting any one from the others would be zero, and tolerance would be 1.00. When predictor variables overlap substantially (high multicollinearity, low tolerance), regression weights are unstable. The error term for a regression weight is inflated in proportion to the inverse of tolerance. This term is the VIF (Variance Inflation Factor). For EdxSex, VIF = 27.5, and tolerance = 1/27.5 = .036. Centering reduces multicollinearity with the interaction term. However, the test of the interaction term is not affected by centering, as we can see by comparing the R2 Change, B, and SEB for the interaction term in Tables 2 and 3.When two predictors are highly correlated, it is likely that neither one will make a unique contribution to the model, even if each is a good predictor. In this case, it may be desirable to eliminate one of the predictors or to make a composite of the two. SPSS Example: Moderation Effects with a Continuous ModeratorWith two continuous predictors, the interaction term is again computed as the product of two predictors, and it is tested as the contribution of the interaction term beyond the main effects in predicting the dependent variable. However, presenting findings is more challenging.In this example, we will test whether mother’s education moderates the relationship between years of education and occupational prestige. Is the correlation between education and occupational prestige greater for those people whose mothers have more years of formal education? The data from this example are also from the 1991 U.S. General Social Survey.-21907517145000Table 4: SPSS Output for Moderation with a Continuous Moderator (N=1162)This moderation analysis is designed to detect a linear by linear interaction. That is, it tests the extent to which the strength of the linear relationship between a predictor and the dependent variable is a linear function of the level of a second predictor variable. The SPSS analysis for centered continuous predictor variables is shown in Table 4, and Table 5 illustrates a summary table presentation of these results. SPSS syntax for this analysis is shown in Appendix B.Table 5: Moderation Effects of Mother’s Education on Respondent’s Education in Predicting Occupational Prestige (N=1162)StepVariablerR2 ChangeBSEBBeta1Education (years).507***.258***2.624.133.554***2Mother’s Educ.148***.005**-.273.107-.071*3Educ x Mom Educ---.006**.081.027.077** (Constant)43.343.351*p<.05; **p<.01; ***p<.001; Cumulative R squared = .268, F(3, 1158) = 141.2, p < .001; Adjusted R squared = .266. Both predictors are ‘centered’ to a mean of zero.Education is a strong predictor of Occupational Prestige (r=.507, p<.001). Mother’s Education adds significantly on the second step (R2 Change = .005, p<.01). Notice that the beta for Mother’s Education in Model 2 in Table 4 is negative (-.076, p<.01) although the zero-order correlation is positive (r=.148, p<.001). This may be a surprising finding. Occupational Prestige is greater for those whose mothers have more education; however, on average, for people of a given level of education, Occupational Prestige is greater for those whose mothers have less education. For someone whose mother has average education (centered Mother’s Education = 0), each additional year of education is associated with 2.557 more points on the predicted Occupational Prestige scale. For someone with average education (centered Education = 0), each additional year of Mother’s Education is associated with .294 fewer points on the Occupational Prestige scale. Model 2 does not consider the interaction between predictors.We have a modest ‘suppression’ relationship (see Cohen, et al., 2003, pp. 77-78). An indicator of suppression is when the beta weight for a variable is not between zero and the correlation of that variable with the dependent variable (Y). The beta weight for Education in Model 2 (.539) is greater than the zero-order correlation (.507), indicating that mother’s education ‘suppresses’ the relationship between Education and Occupational Prestige when it is not controlled. Suppression may or may not be large enough to be practically or theoretically interesting. The interaction is statistically significant, which must be considered when main effects are interpreted. A figure can be very helpful to describe complex findings such as these.To construct a figure, we can use information from the regression model of the relationship between Education and Occupational Prestige for each of several levels of Mother’s Education. Following Cohen et al. (2003), we might select levels of Mother’s Education at the mean and at one standard deviation above and below the mean. In our example, the mean and SD for Education are 13.41 and 2.796, and for Mother’s Education these values are 10.79 and 3.443. For Mother’s Education, we could use a high value of 10.79 + 3.44 = 14.23 years, the mean of 10.79 years, and a low value of 10.79–3.44 = 7.35 years. In this example, it might be better to pick more meaningful high and low values for Mother’s Education, such as 16, 12, and 6 years, respectively. The model for uncentered variables is easier to use when generating a figure. If centered variables are used to create a figure, great care must be taken with conversions between the raw and centered scales. Here is an example.The final regression model for centered data in Table 4 is = 43.343 + 2.624*(ceduc) - .273*(cmaeduc) + .081*(ceduc * cmaeduc).For cases where Mother’s Education is 16, the value on cmaeduc is 16 - 10.79 = 5.21, which is 5.21 above the mean of maeduc. Entering 5.21 for cmaeduc, the regression equation becomes = 43.343 + 2.624*(ceduc) - .273*(5.21) + .081*(5.21)*(ceduc), or = 41.921 + 3.046*(ceduc). This is the model for cases where maeduc = 16.For cases where Mother’s Education is 6, the value on the centered scale (cmaeduc) is 6 - 10.79 = -4.79. When we replace cmaeduc with -4.79, the regression equation becomes = 43.343 + 2.624*(ceduc) - .273*(-4.79) + .081*(-4.79)*(ceduc), or = 44.651 + 2.236*(ceduc). This is the model for cases where maeduc = 6.The mean education for respondents was 13.41 years. For respondents with 6 years of education, ceduc = 6 – 13.41 = -7.41. For respondents with 20 years of education, ceduc = 20 – 13.41 = 6.59. We can use Excel with these values to generate a plot of the modeled relationships as shown in Figure 8 (generated with Plotting Regression Interactions.XLS, available on under WISE Stuff). The figure shows the size and direction of the effects more clearly than tabled numbers, and is more suitable for a nontechnical audience. -6667593345Mother’s Education00Mother’s Education Keep in mind that a modeled description of the data is not a complete description of actual data, and it may give a misleading impression of regularity in the data. Especially be careful not to over interpret patterns in the model at the extremes of observed data. In our model, the large effect of Mother’s Education when the respondents’ Education = 6 should not be taken seriously without additional evidence. Very few respondents had as little as six years of education. Estimates near the ends of the distribution are less reliable than estimates from the middle. Be sure to plot the raw data to assure that models are appropriate.Other IssuesMany additional issues are discussed in detail in comprehensive textbooks such as Cohen, et al. (2003) or specialized books such as Aiken and West (1991). Berger (2004) provided short introductions to categorical variables, correlation and causation, multicollinearity, interactions, centering, nonlinear relationships, outliers, missing data, power analysis and sample size, adjusted, and stepwise vs. hierarchical selection of variables. Summary and Final AdviceThe most important advice is to get close to your data and make sure that your models and descriptions are appropriate to the data. It is essential to examine the plot of residuals as a function of predicted Y. An assumption of regression analysis is that residuals are random, independent, normally distributed, and homoscedastic (equal variance at all values of predicted Y). A residual plot can help you spot extreme outliers or departures from linearity. Bivariate scatter plots can also provide helpful diagnostics, but a plot of residuals is the best way to find multivariate outliers. A transformation of your data (e.g., log or square root) may reduce the effects of extreme scores, make relationships more linear, and make the distributions closer to normal (see Tabachnick & Fidell, 2007, Chapter Four on “Cleaning Up Your Act”).PROCESS is an SPSS macro that you can load into your personal SPSS program to be part of your regression options. This program provides a simple point-and-click interface for a wide range of mediation and moderation models, including very complex examples of multiple mediated moderators. This program is introduced in CD04. Estimates and tests of mediation and moderation are based on assumptions. In particular, we must assume that residuals from the regression modules are reasonably normally distributed. Additionally, sampling must be random and independent if we wish to generalize to the population from which the sample was selected.In general, it is important to include effect sizes and directions of effects along with statistical significance. G*Power is a wonderful free program for power analysis that you can download from in mind that alternate models may also account for the data. A model that hypothesizes causal flow in a different direction may fit the data equally well and also produce statistically significant effects. Be on the lookout for omitted ‘lurking’ variables that may affect multiple variables in your model. Perhaps when these prior variables are included, the direct (unique) contributions of observed variables will change. You can find discussion of mediation analysis in program evaluation, a glossary of terms, and addition summary advice in Berger (2004).Moderation References (plus references in CD02)Aiken, L. S. & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage Publications.Kenny, D. [Excellent discussion of moderation.]Muller, D., Judd, C. M., & Yzerbyt, V. Y. (2005). When moderation is mediated and mediation is moderated. Journal of Personality and Social Psychology, 89, 852-863. Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Assessing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42, 185-227.Appendix A: SPSS syntax for moderation analysis with a dichotomous moderatorFirst, we create a dummy variable for sex and center education on its mean, 13.02 years. Then we calculate the interaction term. We need to execute this before running regression.RECODE SEX (1=0) (2=1) INTO PUTE CEDUC = EDUC - 13.PUTE CEDXSEXD = SEXD * CEDUC .EXECUTE .REGRESSION /variables=sexd,ceduc,cedxsexd,prestg80 /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS CI R ANOVA TOL CHANGE ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT prestg80 /METHOD=ENTER ceduc /METHOD=ENTER sexd /ent=cedxsexd /RESIDUALS HIST(ZRESID) .Appendix B: SPSS syntax for moderation analysis with a continuous moderator*Limit analyses to cases with complete data.USE PUTE filter_$=(educ >= 0 & maeduc >=0 & prestg80 >= 0).VARIABLE LABEL filter_$ 'educ >= 0 & maeduc >=0 & prestg80 >= 0 (FILTER)'.VALUE LABELS filter_$ 0 'Not Selected' 1 'Selected'.FORMAT filter_$ (f1.0).FILTER BY filter_$.EXECUTE .*Find the means for the new subset of cases.FREQUENCIES VARIABLES=educ, maeduc /STATISTICS=STDDEV MINIMUM MAXIMUM MEAN MEDIAN SKEWNESS SESKEW /HISTOGRAM NORMAL /ORDER= ANALYSIS .*Recenter education for this reduced sample with N=PUTE CEDUC2 = EDUC - 13.PUTE CMAEDUC = MAEDUC - 10.pute cedxmaed = ceduc2*cmaeduc.*Tables 4 and 5.REGRESSION /variables=ceduc2,cmaeduc,cedxmaed,prestg80 /DESCRIPTIVES MEAN STDDEV CORR SIG N /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA TOL CHANGE ZPP /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT prestg80 /METHOD=ENTER ceduc2 /METHOD=ENTER cmaeduc /ent=cedxmaed /RESIDUALS HIST(ZRESID) .You can download an Excel template for making figures like Figure 7 and Figure 8 in this section from . Go to WISE Stuff, Excel Downloads, Demonstrations using Excel, program Plotting Regression Interactions. You can literally copy (Ctrl-C) the column of unstandardized regression coefficients (B weights) from the SPSS Coefficients table and paste them (Ctrl-V) into the appropriate location in the Excel worksheet. Then, by entering the values you wish to plot, a figure is created automatically. Whenever you use templates or macros provided by someone else, make sure they are working correctly. The SPSS PROCESS macro from Hayes can greatly simplify mediation and moderation analyses, though it is important to understand the logic behind the analysis. PROCESS is especially useful for complex analyses. The next section CD04 introduces PROCESS. Just for fun (and to fill the page), here is an example of a model for a very complex analysis. ................
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