Using Correlation and Regression: Mediation, Moderation, and More

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1 Using Correlation and Regression: Mediation, Moderation, and More Part 2: Mediation analysis with regression Claremont Graduate University Professional Development Workshop August 22, 2015 Dale Berger, Claremont Graduate University Statistics website: This document is designed to aid note taking during the presentation and to serve as a resource for later use. It provides selected formulas, figures, SPSS syntax and output, and references, with much more detail than PowerPoint slides that accompany the presentation. This document, data files, supplemental reading, and other materials are available on a Google Drive site for which members of the class will receive a link. If you have difficulty accessing these materials, please contact me at [email protected]. We won t cover all of this material in the on-line presentation. 2 Model for mediation with regression 3 Baron and Kenny; Tests of mediation 4 Conceptual examples and exercises 5 Models for applications of mediation analysis 6 SPSS application and demonstration: Does education mediate the relationship between sex and occupational prestige? 6 Point-and-click SPSS commands for descriptives and regression 9 Regression output for applying the logic of Baron and Kenny 11 Figure for mediation model; Testing mediation 12 Direct, indirect, and total effects 12 Presenting results 13 Multiple mediators, SEM 14 References 14 Links to SPSS macros for complex models 15 SPSS syntax for mediation analysis 16 Tips on using Word to create a figure showing mediation Part 2: Mediation Analysis with Regression 1

2 Mediation Analyses with Regression This paper describes mediation analysis using multiple regression. Prerequisite knowledge is familiarity with basic multiple regression applications. Mediation Analysis with Regression A conceptual model of how a treatment impacts upon an outcome provides a useful framework for testing the effectiveness of the treatment. A simple test of a treatment effect might be focused on the relationship between the level of treatment implementation (X) and an outcome (Y). This relationship can be conceptualized as a causal model where the treatment has a direct causal impact on the outcome, as shown in Figure 1. Figure 1: Black Box Model Treatment X c Outcome Y c = regression weight on X when predicting Y A limitation of this simple black box model is that it provides little information on how the treatment produces its effects, or why the treatment fails if no effects are found. A more sophisticated theoretical model identifies processes by which the treatment is presumed to have effects. This model can be conceptualized as a causal model where the treatment (X) has an impact on an intervening mediator variable (M), which in turn has an impact on the outcome (Y), as shown in Figure 2. Figure 2: Mediation Model Mediator M a b Treatment X c' Outcome Y a = regression weight on X when predicting M b and c' are the regression weights on M and X, respectively, when both are used together to predict Y Part 2: Mediation Analysis with Regression 2

3 If the entire effect of the treatment operates through the mediator, the regression weight c' is zero. If c' is smaller than the regression weight c in the first model, then M is said to partially mediate the effects of X on Y. Mediation analysis can help us understand how treatments work, and guide development and modification of treatments to make them more effective. Donaldson (2001) provides an excellent discussion of applications of mediation and moderation analysis in treatment development. The logic of establishing mediation from Baron and Kenny (1986) Following Baron and Kenny (1986), if M mediates an X-Y causal relationship then: (1) X significantly predicts Y (path c is significant) (2) X significantly predicts M (path a is significant) (3) M significantly predicts Y in the presence of X (path b is significant) (4) when M is in the model, the effect of X on Y is reduced (c' is less than c). With complete mediation, path c' is zero. Tests of statistical significance of mediation A measure of the mediation effect is the difference between c and c'. This difference is equal to the product of the paths to and from the mediator. Thus, c - c' = ab. The total effect of X on Y (c) can be decomposed into a direct component (c') and an indirect component (ab), c = c' + ab. An early test of statistical significance of the indirect component ab uses an approximation of the standard error of ab as proposed by Sobel (1982): S ab b s 2 2 a a s 2 2 b, where a and b and their standard errors can be taken from the regression analyses. The ratio ab/s ab is assumed to be distributed as a standardized normal z. An alternate error term is based on Goodman (1960). Critique: Mediation can be demonstrated in some cases (e.g., suppression) where path c is not significant. Newer tests of mediation based on bootstrapping are preferred by statisticians because they do not require the untenable assumption of normally distributed errors for a*b. Bootstrapping tests are included in SPSS macros available free from Hayes (2014). His program PROCESS can handle a wide range of mediation and moderation analyses, and has the option to include a point-and-click menu within SPSS REGRESSION. A test that has intuitive appeal is simply to test both a and b. If both paths are statistically significant, there is mediation. This approach to assessing mediation is relatively easy to explain to a nontechnical audience. Here are some excellent Internet resources for more technical information on mediation analysis and tests of statistical significance: Andrew Hayes free download: Book info: David Kenny David MacKinnon: Part 2: Mediation Analysis with Regression 3

4 Regression analyses of mediation models The four key path coefficients in the conceptual model can be estimated as B or beta weights in regression analyses as described below. M a b X ( c ) c' Y a = regression weight on X when predicting M b and c' are the regression weights on M and X, respectively, when both are used together to predict Y c = regression weight on X when predicting Y Examples of mediation models (identify Y, X, and M) 1. Does knowledge mediate the effects of an education intervention on drug attitudes? Y = attitude toward marijuana use X = type of intervention (video or brochure) M = knowledge of the physiological effects 2. Does cognitive therapy reduce depression by changing perceptions of locus of control? Y = X = M = 3. Does drug use by friends mediate the relationship between parental monitoring and drug use by children? Y = X = M = 4. Does education level mediate the relationship between sex and occupational prestige? Y = X = M = Part 2: Mediation Analysis with Regression 4

5 Part 2: Mediation Analysis with Regression 5

6 SPSS Example 1: Estimating and testing mediating effects Compared to females, on average males hold jobs with higher occupational prestige, 45.5 vs. 43.9, respectively, t(1413) = 2.35, p =.019. Can this relationship be explained by a sex difference in average level of education? Within the framework of a mediation model, we are interested in testing potential mediating effects of education on the relationship between sex and occupational prestige. From a national survey of N=1517 U.S. adults we have complete data from 1415 people on sex (X, coded 1=Male; 2=Female), years of formal education (M), and a measure of occupational prestige (Y), taken from 1991 U.S. General Social Survey.SAV, as provided by SPSS (also available at ). The first step should always be to look at your data carefully, checking for errors, problems with the distributions, coding, etc. This is easily done with SPSS FREQUENCIES. Load SPSS and the data file. Click Analyze, Frequencies, and select the three variables of interest (sex, educ, and prestg80). Click Statistics, select Mean, Std. deviation, Minimum, Maximum, Skewness, and Kurtosis. Click Continue. Click Charts, select Histogram with normal curve, and click Continue. Click Format, select Suppress tables (default 10 categories is OK), click Continue. To save this syntax, click Paste. The syntax is shown in Appendix A. In the syntax window, click the triangle to run the current procedure. N Mean Std. Deviation Skew ness Std. Error of Skew ness Kurtosis Std. Error of Kurtosis Minimum Max imum Valid Mis sing Statis tics sex Respondent's prestg80 R's Occ upational Prestige educ Highest Year of School Sex Completed Score (1980) The summary measures of skew and kurtosis don t raise alarms, but we must also examine the plots of the data. Is it important that 99 cases are missing data on occupational prestige? Maybe. Valid 1 Male 2 Female Total s ex Re s pondent's Se x Cumulative Frequency Percent Valid Percent Percent Both male and female groups are large, so sex will be OK as a predictor. Note that a dichotomous variable should not be used as a dependent variable in ordinary regression. Part 2: Mediation Analysis with Regression 6

7 These two distributions are quite well behaved. There is no severe skew and no substantial problem with extreme scores. The most extreme score is someone with zero years of formal education. Given that the mean is about 12 years and the standard deviation is about three years, this case is about four standard deviations below the mean. Because we have a large sample with over 1,000 cases, this one case won t have much impact. We do have a problem with missing data. By default, SPSS regression analysis uses listwise deletion of missing cases. One analysis will involve only sex and education, while another analysis will involve all three variables. If we don t deal with the missing data, we will have different sets of cases in each analysis. We must use the same set of data throughout. One way to deal with the problem is to use only cases with complete data on all of our variables. In SPSS, click Data, click Select Cases, select If condition is satisfied, click If, highlight sex, click the black triangle, click >=, click 0, click &, highlight educ, click the black triangle, click >=, click 0, click &, highlight prestg80, click the black triangle, click >=, click 0, and click Continue. You can click OK, or you can Paste this syntax into your syntax file to keep a record of what you did, but then you need to run the syntax before re-running the frequencies. Statis tics N Mean Std. Deviation Skew ness Std. Error of Skew ness Kurtosis Std. Error of Kurtosis Minimum Max imum Valid Mis sing sex Respondent's prestg80 R's Occ upational Prestige educ Highest Year of School Sex Completed Score (1980) Part 2: Mediation Analysis with Regression 7

8 An alternative method to limit regression analyses to cases that have complete data on all variables of interest is to insert a first line listing all variables of interest (See Appendix A): /variables=sex,educ,prestg80 Now we are ready to run the regression analyses for mediation. The first analysis will use sex to predict education, giving us estimates for coefficient a. In SPSS click Analysis, Regression, Linear, select sex as the Independent variable, select educ as the Dependent variable. Click Statistics, select Estimates, Model fit, Descriptives, and Part and partial correlations. Click Continue. Click Paste. The second analysis will include two models. The first will use only sex to predict occupational prestige (coefficient c), and the second model will use both sex and education to predict occupational prestige (coefficients c' and b). Click Analysis, Regression, Linear, remove educ as the Dependent variable and select prestg80 instead as the Dependent. We can keep sex as the Independent for the first model. Click Next, select educ as the Independent variable for the second block. This will generate a second model with both sex and educ as predictors. Click Statistics, select Estimates, Model fit, R squared change, Descriptives, and Part and partial correlations. Click Continue. To generate a plot of residuals, click Plots, select Histogram, click Continue. The plot of standardized residuals is quite close to normal. Now we are eager to see the path coefficient estimates that our analyses have generated. What are paths a, b, c, and c'? Part 2: Mediation Analysis with Regression 8

9 Model 1 (Constant) Respondent's Sex Table 1: Regression Predicting Education with Sex (N=1415) Unstandardized Coefficients Coefficients a Standardized Coefficients Std. B Error Beta t Sig Correlations Zeroorder Partial Part a. Dependent Variable: Highest Year of School Completed Table 2: Regression Predicting Occupational Prestige with Sex and Education (N=1415) Coe fficie nts a 1 2 (Cons tant) Respondent's Sex (Cons tant) Respondent's Sex Highest Year of School Completed Unstandardized Coefficients Standardiz ed Coefficients Std. B Error Beta t Sig a. Dependent Variable: R's Occupational Pres tige Score (1980) Correlations Zeroorder Partial Part We will go through the four steps described by Baron and Kenny (1986). Most analysts today agree that Steps 2 and 3 are the critical steps. Step 1: Show that there is an effect of X on Y that could be mediated (path c in the causal model shown in Figure 1). To do this, use the outcome variable (Y) in a simple regression model with the predictor variable (X) as the only predictor. Estimate and test the regression weight, which is the value for path c. Model 1 in Table 2 shows an unstandardized regression weight of for X (Sex: M=1; F=2) in predicting Y (Occupational Prestige). Thus, c = The standard error is.699, which gives t = /.699 = (df=1413, p=.019). We have satisfied the first condition necessary for mediation. This indicates that in our set of data, as we increase X by one unit (Male=1; Female=2), the predicted value on Y (Occupational Prestige) decreases by units. Females average units lower than males on the Occupational Prestige scale. Education level is ignored in Step 1. In special cases with suppression relationships, it is possible that mediation can be shown even when path c by itself is not statistically significant. For example, we may find that the simple correlation between X (e.g., a speeded math test) and Y (e.g., math ability) is not statistically significant, but a mediator M (e.g., test of speed) is related to that part of X that is independent of Y. When M is included in the model, the ability of X to predict Y is improved, and thus all three paths shown in Figure 2 are important even though path c in Figure 1 may be small and not statistically significant. Part 2: Mediation Analysis with Regression 9

10 Step 2: Show that the predictor variable (X) is related to the potential mediator (M). To do this, use a regression model with X as the only predictor of M. Estimate and test the regression weight, which corresponds to path a in Figure 2. Table 1 shows an unstandardized regression weight of for X (Sex) in predicting M (Education). Thus, a = The standard error is.158, which gives t = -.410/.158 = (df=1413, p=.010). We have satisfied the second condition necessary for mediation. This indicates that in our set of data, as we increase X by one unit (Male=1; Female=2), the predicted value on M (Years of Education) decreases by.410 years. In this sample, the average Years of Education is.410 years less for females compared to males. Step 3: Show that the mediator (M) predicts the outcome (Y) in the presence of the initial predictor (X). Use a regression model with Y as the criterion, and both X and M as predictors. Estimate and test the weight on M. This corresponds to path b in Figure 2. The second model Table 2 shows the unstandardized regression weight of for M (Education) in predicting Y (Occupational Prestige) when controlling for X (Sex). Thus, b= The standard error is.101, which gives t = 2.286/.101 = (df=1412, p<.001). We have satisfied the third condition necessary for mediation. In our set of data, as we increase M by one unit (one more year of education) while controlling for X (sex), the predicted value on Y (occupational prestige) increases by units. This is the average difference in occupational prestige for people who differ by one year on education within each sex group in our model. Step 4: For complete mediation, show that the effect of X on Y is zero when we control for M. Use a regression model with Y as the criterion, and both X and M as predictors. Estimate and test the weight on X (path c' in the causal model in Figure 2), to show that it is zero. The second model in Table 2 shows the unstandardized regression weight of for X (Sex) in predicting Y (Occupational Prestige) when controlling for M (Education). Thus, c' = The standard error is.600, which gives t = -.709/.600 = (df=1412, p=.237). This coefficient is not statistically significantly different from zero; however we have not shown that the coefficient is equal to zero. The 95% confidence interval for c' is ± (t)*(se c'), or ±(1.96)*(.600), or ±1.176, which gives a confidence interval from to In our set of data, as we increase X by one unit (change from male to female) while holding constant the effects of M (education), the predicted value on Y (occupational prestige) decreases by.709 units. For people at any one level of education (say 12 years), we predict that the occupational prestige is.709 units higher for males compared to females. However, this difference is not statistically significant. The mediation effect can be measured as the reduction in the regression weight for X on Y when M is included: c- c' = (-1.647) (-.709) = Alternatively and equivalently (within rounding error), the mediation effect can be calculated as the product of the indirect paths from X to Y through M: (-.410) * (2.286) = If Step 4 is not satisfied, we may have partial mediation rather than complete mediation. Part 2: Mediation Analysis with Regression 10

11 Figure 3: Mediation Model with Computed Path Coefficients M Education (years) a= X Sex (1=M; 2=F) (c= ) c'= b=2.286 Y Occupational Prestige a = regression weight on X when predicting M b and c' are the regression weights on M and X, respectively, when both are used together to predict Y c = regression weight on X when predicting Y On Steps 2 and 3, we found that paths a and b were both statistically significant, which we take as evidence consistent with a mediating effect of education on the relationship between sex and occupational prestige. The Sobel test of the indirect path ab (Sobel, 1982), which is generally more conservative (MacKinnon & Dwyer, 1993), gives z = , two-tailed p=.010. However, as noted earlier, the preferred method for testing the statistical significance of the mediation effect is with bootstrapping, which does not require assumptions of normality. The program PROCESS from Andrew Hayes at can be imported to work from a menu within SPSS, allowing appropriate tests for many mediation and moderation models (more later). Each of the tests support the conclusion that the observed sex difference in occupational prestige can be explained partly by the difference in education levels. However, sex differences in education may not explain the entire sex difference in occupational prestige. A consistent set of cases should be used for all analyses of a given model. If three separate analyses are run for Steps 1, 2, and 3, it is possible that different cases will be used in each analysis because of missing data. If this happens, you may find that the equation c- c' = ab does not apply. In general, it is good practice to pay close attention to the number of cases in each analysis, to be sure that you have the expected number of cases. It is important to keep in mind that we have not conclusively established mediation or even causality. Other models may also be consistent with our data. For example, we may have ignored an important additional variable that can account for some or all of the observed relationships, or causal flow may operate in directions different from our model (Campbell & Kenny, 1999). When data are from a cross-sectional design (all data collected at the same time), causal inference may be problematic. Perhaps it is best to describe the analysis as hierarchical regression analysis rather than mediation analysis. Mediation implies causation. Part 2: Mediation Analysis with Regression 11

12 Direct effects, indirect effects, and total effects The total effect of X on Y is simply the regression weight on X when X is used alone to predict Y. How well does X predict Y when no other variables are considered? In our example, the total effect of X on Y (i.e., sex on occupational prestige) is Mean occupational prestige is units lower for females compared to males. The direct effect of X on Y is the regression weight on X when predicting Y with all mediators in the model. What is the unique effect attributable to X in the presence of all other variables? In our example, the direct effect of X on Y is On average, for males and females with the same level of education, the mean occupational prestige is.709 units lower for females. The indirect effect of X on Y is the difference between the total effect and the direct effect, which is (-1.647) (-.709) = in our example. The indirect effect can also be computed as the product of the paths through the mediator(s). In our example, this computation gives x = (the discrepancy from is only rounding error). On average,.938 units of the overall sex difference in occupational prestige can be attributed to differences in education. The indirect effect is the mediation effect. The total effect is equal to the direct effect plus the indirect effect: = (-.709) + (-.938). In the notation of mediation analysis: c = c' + a*b Presenting mediation findings A mediation model is a causal model. Hypothesized causal flow between variables can be represented very nicely by weights on arrows between circles (variables). Education (years) ** 2.286*** Sex (1=M; 2=F) (-1.647*) Occupational Prestige Note: *p<.05; **p<.01; ***p<.001 Figure 4. Effects of Sex and Education on Occupational Prestige, with Total Effects Shown in Parentheses (N=1415) The unstandardized weights on each path are expressed in the units of the variable at the point of the arrow. If the units of the variables are interpretable, then unstandardized units add useful information. For example, in Figure 4, we can see that females in this sample are points lower than males on the occupational prestige scale, and.410 years lower on years of education. Part 2: Mediation Analysis with Regression 12

13 If units on the dependent variables are not easily interpreted, it is better to report standardized path coefficients. These are taken from the same regression analyses as the unstandardized weights. In this example, the standardized weights produce Figure 5. Education (years) **.518*** Sex (1=M; 2=F) (-.063*) Occupational Prestige Standardized weights are more easily compared to each other. We can see that the total effect of Sex on Occupational Prestige (i.e., the correlation r = -.063) is actually quite small. Thus, Sex accounts for only (-.063) 2 =.004, or.4% of the variance in Occupational Prestige. Similarly, Sex is a weak predictor of Education. On the other hand, Education is a strong predictor of Occupational Prestige when Sex is included in the model. For presentation, we can format the arrows to give greater width to those paths that have larger beta weights. Multiple mediators *p<.05; **p<.01; ***p<.001 Figure 5. Standardized Effects of Sex and Education on Occupational Prestige, with Total Effects Shown in Parentheses (N=1415) More than one mediator can be posited between an X and Y variable. The logic outlined here can be used to estimate and test the effects of each hypothesized mediator in turn. However, the unique contribution of each will be influenced by correlations among the mediators. You can download SPSS, MPlus, and SAS macros to conduct mediation and moderation analyses (and many other sophisticated analyses) from a wonderful website provided by Andrew Hayes: Structural Equation Modeling (SEM) Mediation models also can be estimated with structural equations programs, such as AMOS, EQS, or LISREL. These programs are especially useful when several related observed variables are used to measure a latent concept. The programs compute weights on each variable to optimally account for observed covariances between all pairs of observed variables within the constraints of a model. Tests of statistical significance are provided for hypothesized causal pathways. In an accessible paper, James, Mulaik, and Brett (2006) described and compared the SEM and the Baron and Kenny approaches to mediation analysis. Part 2: Mediation Analysis with Regression 13

14 References Baron, R. M. & Kenny, D. A. (1986). The moderator-mediator distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, Berger, D.E. (2004). Using regression analysis. Chapter 17 in Handbook of Practical Program Evaluation, 2 nd ed. Wholey, J., Hatry, H., & Newcomer, K. (Eds.). San Francisco: Jossey Bass, pp Campbell, D. T., & Kenny, D. A. (1999). A primer on regression artifacts. New York: Guilford. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3 rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates. Donaldson, S. I. (2001). Mediator and moderator analysis in program development. In S. Sussman (Ed.), Handbook of program development for health behavior research (pp ). Newbury Park, CA: Sage. Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55, Hayes, A.F. (2015). Hayes has a marvelous collection of SPSS and SAS macros that can be loaded directly into your version of SPSS to become a menu item. James, L. R., Mulaik, S. A., & Brett, J. M. (2006). A tale of two methods. Organizational Research Methods, 9(2), Kenny, D. A. (2011). Mediation. Website: See also Data to Text macro: MacKinnon, D. (2008). Introduction to statistical mediation analysis. Routledge Academic. MacKinnon, D. P. & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17(2), MacKinnon, D. P., Lockwood, C. M., Hoffman, J. M., West, S. G., & Sheets, V. (2002). A comparison of methods to test the significance of the mediated effect. Psychological Methods, 7(1), Marquardt, D. W. (1980). You should standardize the predictor variables in your regression models. Journal of the American Statistical Association, 75, McClelland, G. H., & Judd, C. M. (1993). Statistical difficulties of detecting interactions and moderator effects. Psychological Bulletin, 114, Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7, Part 2: Mediation Analysis with Regression 14

15 Sobel, M. E. (1982). Asymptotic intervals for indirect effects in structural equations models. In S. Leinhart (Ed.), Sociological methodology (pp ). San Francisco: Jossey-Bass. Remember, Google is your friend (but exercise caution in what you find online)! Appendix A: SPSS syntax for mediation analysis *Regression analysis to estimate path a. REGRESSION /variables=sex,educ,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 educ /METHOD=ENTER sex /SCATTERPLOT=(educ,*ZPRED ) /RESIDUALS HIST(ZRESID). (Path a is the regression weight on sex in predicting educ.) *Regression analysis to estimate paths c, c, and b. REGRESSION /variables=sex,educ,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 sex / method=enter educ /scatterplot=(prestg80, *zpred). (Path c is the regression weight on sex in predicting prestg80 in the first model in this hierarchical analysis; Paths c' and b are the regression weight on sex and educ, respectively, in predicting prestg80 in the second model in this hierarchical analysis.) Appendix B: SPSS macros to test complex models, with or without covariates. Hayes (2015): Accessed 10 July The macro PROCESS can handle multiple mediators as well as interactions (moderation). Kenny, D. A. (2011) Accessed 10 July This mediation macro called MedText produces draft text description of mediation analyses for simple models. Part 2: Mediation Analysis with Regression 15

16 Tips on using Word to create a figure for presentation of a mediation model The goal is to show a visual analog to the underlying mathematical relationships in the model. Figure 5 is an example, where the thickness of the lines reflects the strength of the relationships. Open a blank page in Word. Click the Insert tab; Shapes; select the oval icon. Your cursor becomes a large + sign. Hold down the left mouse button, slide down and right to create an oval of desired size. The default oval is filled with blue. Edit the circle by right-clicking on it to open a new menu. At the bottom, select the option Format Shape. This opens a new window where you can select Fill as No fill, Line Color as black, and Line Style as 1pt width. Copy the oval by right-clicking to open a menu; Select Copy (or use Ctrl-c). Re-enter the menu and select Paste (or use Ctrl-v). Repeat to make a third oval. Select each oval in turn to move it to the desired position. Fine adjustments to a location for a selected object can be made with the arrow keys. Hold down Ctrl with the arrow keys for finer adjustments To create the text inside the ovals, click Insert, Text box, Simple text box to open a box with instructions inside. Replace that text with the text you want. To center the text, highlight the text and press the centering icon (or press Ctrl-E). You can bold the font if you choose. To remove the lines and fill, right click on the box to open a new menu. Select Fill as No fill and Line Color as No color. You can copy the box twice and then edit the text in each copy for the other two variables. Click on an object to select it (display shows handles around the object as shown above); move the cursor over an edge of the object to display a cursor with arrows pointing in four directions; then right-click to open the editing window for the whole object. Move the text box into the desired position over the ovals. If you forgot to select No fill, the text box may obscure part of the oval. To lock the oval and text box together, hold down Ctrl and select both so that the handles are displayed for both, then with the four-arrow icon showing, right-click to open a menu, and select Group. To draw the arrows, click Insert, Shapes, and select an arrow. Draw an arrow in an open space by holding down the left mouse and dragging. Click on the arrow and make two copies. Move each to the desired location. Click to open the handles, right click to open the editing window, select Format object, edit to the desired color, width, and dash type. You can group all components together, or use a screen shot to keep everything together. A screenshot can be resized if desired. Part 2: Mediation Analysis with Regression 16