1. Measurement, Research Design And Statistics, I Week 13 1

2. Outline for this week Mediation Another Preacher and Hayes script Mediated moderation Some brief thoughts on missing data 2

3. Slides between red bumpers are from last time 3

4. Let’s do the Sobel test Exercise Health Aerobics.239 (SE =.052;  =.646) R 2 =.299 -.242 (SE =.160;  = -.310) -.627 (SE =.436;  = -.295) 4

5. Let’s do the Sobel test None of these p-values are less than.05. Thus aerobics DOES NOT significantly mediate the effect of exercise on health. Expressed differently, the effect of exercise cannot be reduced to just aerobics. Apparently, other kinds of non-aerobic exercise are important too. There WAS a substantial reduction in the unique effect of exercise…but not a total reduction. Moreover, that reduction was not significant. 5

8. Problems with the Sobel test The Sobel test is a Z-test for the indirect effect (a*b, or c – c’). All z-tests assume that the underlying sampling distribution of the statistic (here, of the indirect effect) is normal Unfortunately, many simulations have shown that indirect effects are not normally distributed. What to do? The return of bootstrapping…..

9. There is a big scholarship on mediation At least a dozen methods for testing mediation (MacKinnon, Lockwood, Hoffman, West, Sheets, 2002) The Baron & Kenny “steps” is called the “causal steps strategy”. Without the Sobel test, this offers no direct statistical test of whether c – c’ is significant.

10. Sobel test and the product-of- coefficients approach Most approaches (including the three on Preacher’s website) use the product of coefficients approach (multiply paths a and b) That resulting product is an estimate of the indirect effect (amount that c goes down when mediator added) The Sobel test (and close analogues like Aroian) concern themselves with finding a standard error to test the a*b product with Usually a p-value for the resulting z-statistic is computed with reference to the standard normal distribution

11. Is the normal distribution appropriate? Simulations have shown that the sampling distribution of a*b is normaly only in large samples One method that generates a better standard error is the distribution of the product approach (see MacKinnon), but this is not widely available

12. Bootstrapping A non-parametric resampling procedure Tests mediation without imposing normality on the sampling distribution Computationally intensive, it involves repeatedly sampling from the data and estimating the indirect effect in each resampled data set. By repeating this process thousands of times, an empirical approximation of the sampling distribution of the a*b product is built and used to construct confidence intervals for the indirect effect

13. How well do these non-parametric, empirical SE estimates work? MacKinnon’s extensive simulations examined the Type I error rates and power of these various ways of testing indirect effects (a*b product) They found that the distribution of product approach (not shown) and bootstrapping outperformed the Sobel test or causal steps (i.e., Baron & Kenny) approaches, on the grounds that they have higher power while maintaining reasonable control over Type I error.

14. Advanced topic Multiple mediation –The truth is that we often have multiple IVs and/or multiple mediators. –How can that be handled?

16. Instead of just one a*b, these models have : a 1 *b 1 a 2 *b 2 a j-1 *b j-1 a j *b j For those of you with these more complex scenarios, you’ll need to download the paper (previous slide) as well as an alternative SPSS macro (INDIRECT), which handles these scenarios If you have multiple DVs, Preacher recommends using the structural equation modeling program M-Plus, which generates bootstrapped estimates of indirect effects.

17. Qualifier Preacher and Hayes argue that “indirect effect” is a better term than “mediated effect” A mediated effect is thought of as a special case of indirect effects when there is only one intervening variable –Also, thanks to Baron & Kenny, a conclusion that a mediation effect is present implies that the total effect X  Y was present (and significantly greater than zero) initially It is quite possible that an indirect effect is significant even when there is no evidence for a significant total effect.

18. Preacher and Hayes example

19. X Therapy (1=CBT, 0=Alternative) Y Life Satisfaction X Therapy (1=CBT, 0=Alternative) Y Life Satisfaction M Positivity of attributions c c' a b

20. OLS Summary c a b c’

21. Sobel test

22. Boostrap test

23. Other summaries. (Newer versions also include the Fairchild R 2 estimate)

25. FAQ to Preacher and Hayes (1) “I am interested in conducting a one-tailed test. Is there a way of generating a one-tailed test in your macros?” All p-values generated by my macros are based on the assumption of symmetry in the sampling distribution of the effect. So if the effect is in the predicted direction, you can cut the p-value in half for a one-tailed p-value. For confidence intervals for indirect effects based on bootstrapping, request a 90% confidence interval to conduct the equivalent of a one-tailed test. Note that SOBEL prints only 95 and 99% confidence intervals and there is no way of changing that.

26. FAQ to Preacher and Hayes (2) “Can your macros be used with dichotomous outcomes or mediators?” Recently, SOBEL was modified to allow for dichotomous outcomes. However, they are not appropriate when a proposed mediator is dichtomous. Both SOBEL and INDIRECT have the intelligence to detect whether the outcome is dichotomous, and they estimate the coefficients of the model accordingly using logistic regression. (3) “I have evidence that one of the paths in my simple mediation model is not linear. Can I use the SOBEL macro anyway?” If you have reason to believe that one of the paths is nonlinear (e.g., exponential, quadratic), whether you should use a model that assumes linearity will depend on how comfortable you are with misspecifying the nature of the association by making the simplifying assumption of linearity.

27. FAQ to Preacher and Hayes (4) “I find the results from your SOBEL macro produce results for the individual paths differ from what I get in SPSS’s regression procedure. Is there something wrong with your macro?” “No. The coefficients and tests of significance from the SOBEL macro or script will be exactly the same as what you get from SPSS’s regression procedure when you analyze exactly the same data. 99% of the time, discrepancies are the result of users not acknowledging missing data. The macros use listwise deletion based on all variables in the model. So, for example, if some cases are missing data on Y, it will throw all those cases out of the analysis estimating the effect of X on M, even if those cases are complete on X and M. And cases missing on M will be thrown of the computation of the total effect of X on Y even though M is not relevant to the estimation of the total effect. This is standard practice in the estimation of models such as these. Indeed, one could argue that it would be inappropriate to piece together a causal model using tests of significance when the analyses for different paths are based on different subsets of the data. You can determine whether missing data is producing the discrepancies by comparing the sample sizes in your regression analysis versus what the macro is using.”

28. FAQ to Preacher and Hayes (5) “It appears that I have evidence of an indirect effect of X on Y through a proposed mediator, but there is no evidence of an association between X and Y. Is this possible? What should I do?” It is not only possible, but it is probably much more common than people realize. Modern thinking about intervening variable models do not impose the requirement that there be evidence of a simple association between X and Y in order to estimate and test hypotheses about indirect effects. (6) “I have a categorical IV with more than two categories. Can your macros be used?” The best approach is to dummy code the categorical IV and then use INDIRECT (another macro). If your IV has k categories, construct k-1 dummy variables and then run INDIRECT k-1 times. With each run, make one dummy variable the IV and the other one(s) the covariate(s). You will not get a single test of the indirect effect, but you will get indirect effects for each category relative to the reference category in the dummy coding scheme.

29. FAQ to Preacher and Hayes (7) “I have more than one IV and I would like to include them in the model simultaneously. Is this possible?” Yes, it is possible using INDIRECT. If you have k IVs, run INDIRECT k times, each time with one of the IVs as the IV and the others as covariates. You will not get a single estimate or test of the total indirect effect across all IVs, but you will get estimates and tests for each IV. This feature of INDIRECT is documented in the last paragraph of Preacher and Hayes (2008). (8) “What if I want to treat one or more of my variables as latent with multiple indicators?” For latent variable models, we recommend Mplus, for it has the ability to construct bootstrap confidence intervals for specific and total indirect effects in models with latent variables.

30. Walkthrough. First, download data Here, I used the Preacher and Hayes example

31. Second, you need to download the custom dialog file.

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35. Third, within SPSS, open the dialogue, which is now permanent

36. Fill in what you want…

37. Preacher himself used 5000 bootstrap samples.

38. Output ************************************************************************* Preacher And Hayes (2004) SPSS Script For Simple Mediation Written by Andrew F. Hayes, The Ohio State University http://www.comm.ohio-state.edu/ahayes/ VARIABLES IN SIMPLE MEDIATION MODEL Y satis X therapy M attrib DESCRIPTIVES STATISTICS AND PEARSON CORRELATIONS Mean SD satis therapy attrib satis.0803.9080 1.0000.4270.5134 therapy.5333.5074.4270 1.0000.4595 attrib.0830.9039.5134.4595 1.0000 SAMPLE SIZE 30 This shows the descriptives

39. Output DIRECT And TOTAL EFFECTS Coeff s.e. t Sig(two) b(YX).7640.3058 2.4984.0186 b(MX).8186.2990 2.7375.0106 b(YM.X).4039.1808 2.2337.0340 b(YX.M).4334.3221 1.3455.1897 INDIRECT EFFECT And SIGNIFICANCE USING NORMAL DISTRIBUTION Value s.e. LL 95 CI UL 95 CI Z Sig(two) Effect.3306.1985 -.0585.7197 1.6653.0959 BOOTSTRAP RESULTS For INDIRECT EFFECT Data Mean s.e. LL 95 CI UL 95 CI LL 99 CI UL 99 CI Effect.3306.3224.1690.0505.6956 -.0463.8057 NUMBER OF BOOTSTRAP RESAMPLES 2000 FAIRCHILD ET AL. (2009) VARIANCE IN Y ACCOUNTED FOR BY INDIRECT EFFECT:.1360 ********************************* NOTES ********************************** ------ END MATRIX ----- This is the equivalent to the ordinary least squares regressions we ran last week Boostrapped indirect Interesting effect size estimate XY M.764 (.306).433 (.322).819 (.299).404 (.181)

40. Output DIRECT And TOTAL EFFECTS Coeff s.e. t Sig(two) b(YX).7640.3058 2.4984.0186 b(MX).8186.2990 2.7375.0106 b(YM.X).4039.1808 2.2337.0340 b(YX.M).4334.3221 1.3455.1897 INDIRECT EFFECT And SIGNIFICANCE USING NORMAL DISTRIBUTION Value s.e. LL 95 CI UL 95 CI Z Sig(two) Effect.3306.1985 -.0585.7197 1.6653.0959 BOOTSTRAP RESULTS For INDIRECT EFFECT Data Mean s.e. LL 95 CI UL 95 CI LL 99 CI UL 99 CI Effect.3306.3224.1690.0505.6956 -.0463.8057 NUMBER OF BOOTSTRAP RESAMPLES 2000 FAIRCHILD ET AL. (2009) VARIANCE IN Y ACCOUNTED FOR BY INDIRECT EFFECT:.1360 ********************************* NOTES ********************************** ------ END MATRIX ----- Sobel test Interesting effect size estimate XY M.764 (.306).433 (.322).819 (.299).404 (.181)

41. Output DIRECT And TOTAL EFFECTS Coeff s.e. t Sig(two) b(YX).7640.3058 2.4984.0186 b(MX).8186.2990 2.7375.0106 b(YM.X).4039.1808 2.2337.0340 b(YX.M).4334.3221 1.3455.1897 INDIRECT EFFECT And SIGNIFICANCE USING NORMAL DISTRIBUTION Value s.e. LL 95 CI UL 95 CI Z Sig(two) Effect.3306.1985 -.0585.7197 1.6653.0959 BOOTSTRAP RESULTS For INDIRECT EFFECT Data Mean s.e. LL 95 CI UL 95 CI LL 99 CI UL 99 CI Effect.3306.3224.1690.0505.6956 -.0463.8057 NUMBER OF BOOTSTRAP RESAMPLES 2000 FAIRCHILD ET AL. (2009) VARIANCE IN Y ACCOUNTED FOR BY INDIRECT EFFECT:.1360 ********************************* NOTES ********************************** ------ END MATRIX ----- Sobel test Interesting effect size estimate XY M.764 (.306).433 (.322).819 (.299).404 (.181) Boostrapped indirect

42. Output DIRECT And TOTAL EFFECTS Coeff s.e. t Sig(two) b(YX).7640.3058 2.4984.0186 b(MX).8186.2990 2.7375.0106 b(YM.X).4039.1808 2.2337.0340 b(YX.M).4334.3221 1.3455.1897 INDIRECT EFFECT And SIGNIFICANCE USING NORMAL DISTRIBUTION Value s.e. LL 95 CI UL 95 CI Z Sig(two) Effect.3306.1985 -.0585.7197 1.6653.0959 BOOTSTRAP RESULTS For INDIRECT EFFECT Data Mean s.e. LL 95 CI UL 95 CI LL 99 CI UL 99 CI Effect.3306.3224.1690.0505.6956 -.0463.8057 NUMBER OF BOOTSTRAP RESAMPLES 2000 FAIRCHILD ET AL. (2009) VARIANCE IN Y ACCOUNTED FOR BY INDIRECT EFFECT:.1360 ********************************* NOTES ********************************** ------ END MATRIX ----- Sobel test Boostrapped indirect Interesting effect size estimate XY M.764 (.306).433 (.322).819 (.299).404 (.181)

43. We’ll do another example “Mediational hypothesis of age related memory loss”

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45. Age Complex Cognition Speed 45

46. Let’s look at a dataset Digit-symbol substitution test SPEED Letter Series test INDUCTIVE REASONING 46

47. Digit Symbol Test 47

48. Letter Series test 48

49. Step 1: Show that the initial variable is correlated with the outcome. Use Y as the criterion variable in a regression equation and X as a predictor (estimate and test path c). This step establishes that there is an effect that may be mediated. Age Letter Series 49

50. Steps 1-3 are done with regression 50

51. Step 1 51

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53. Step 1: Show that the initial variable is correlated with the outcome. Use Y as the criterion variable in a regression equation and X as a predictor (estimate and test path c). This step establishes that there is an effect that may be mediated. Age Letter Series c = -0.271, se =.017 53

54. Step 2: Show that the initial variable is correlated with the mediator. Use M as the criterion variable in the regression equation and X as a predictor (estimate and test path a). This step essentially involves treating the mediator as if it were an outcome variable. Age Digit Symbols 54

55. Step 2 is a step where the mediator (Digit Symbol) is the DV and the initial / exogenous variable (Age) is the IV 55

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57. Step 2: Show that the initial variable is correlated with the mediator. Use M as the criterion variable in the regression equation and X as a predictor (estimate and test path a). This step essentially involves treating the mediator as if it were an outcome variable. Age Digit Symbols a = -0.589, se =.034 57

58. Step 3: Show that the mediator affects the outcome variable. Use Y as the criterion variable in a regression equation and X and M as predictors (estimate and test path b). It is not sufficient just to correlate the mediator with the outcome; the mediator and the outcome may be correlated because they are both caused by the initial variable X. Thus, the initial variable must be controlled in establishing the effect of the mediator on the outcome. Age Digit Symbols Letter Series 58

59. For step 3, it’s actually easiest to add the mediator as “Block 2” in a hierarchical regression…it gives you some nice summary slides 59

60. Step 3: Click “next” to add the second predictor (Digit Symbols) 60

61. Step 3 61

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64. Step 3: Show that the mediator affects the outcome variable. Use Y as the criterion variable in a regression equation and X and M as predictors (estimate and test path b). It is not sufficient just to correlate the mediator with the outcome; the mediator and the outcome may be correlated because they are both caused by the initial variable X. Thus, the initial variable must be controlled in establishing the effect of the mediator on the outcome. Age Digit Symbols Letter Series b = 0.278, se =.007 64

65. Step 4: To establish that M completely mediates the X-Y relationship, the effect of X on Y controlling for M should be zero (estimate and test path c'). The effects in both Steps 3 and 4 are estimated in the same regression equation. Age Letter Series Letter Series Digit Symbols 65

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67. Step 4: To establish that M completely mediates the X-Y relationship, the effect of X on Y controlling for M should be zero (estimate and test path c'). The effects in both Steps 3 and 4 are estimated in the same regression equation. Age Letter Series Letter Series Digit Symbols c = -0.271, se =.017 c’ = -0.109, se =.015 67

68. Putting it all together Age Letter Series Digit Symbols c’ = -0.109, se =.015 c = -0.271, se =.017 b = 0.278, se =.007 a = -0.589, se =.034 c – c’ = -.279 – (-.109) c – c’ = -.170 68

69. Now we do the Sobel test. Sobel tests whether c – c’ is significantly different from zero. It does so using paths a and b, because a*b = c – c’ Age Letter Series Digit Symbols c’ = -0.109, se =.015 c = -0.271, se =.017 b = 0.278, se =.007 a = -0.589, se =.034 c – c’ = -.279 – (-.109) c – c’ = -.170 a * b = -0.589 * 0.278 a * b = -0.164 69

70. Sobel test input 70

71. Sobel test output 71

72. Conclusion Passed step 1 (Age (X) related to Letter Series (Y)) Passed step 2 (Age (X) related to Digit Symbols (M)) Passed step 3 (Digit Symbols (M) related to Letter Series (Y) when controlling for Age (X)) Step 4 revealed that adding the mediator did significantly reduce (Sobel test) the relationship between Age (X) and Letter Series (Y). However, the residual path between Age and Letter Series remained significant, suggesting that only partial mediation occurred. 72

73. Now, let’s use Preacher’s Sobel dialog 73

74. Enter variables 74 Will take a while to generate 1000 samples, especially with a big sample like this! This one took almost 5 minutes

75. 75 VARIABLES IN SIMPLE MEDIATION MODEL Y LS_COR X AGE M DS_COR SAMPLE SIZE 2808 DIRECT And TOTAL EFFECTS Coeff s.e. t Sig(two) b(YX) -.2706.0171 -15.8027.0000 b(MX) -.5805.0341 -17.0209.0000 b(YM.X).2780.0079 35.2138.0000 b(YX.M) -.1092.0150 -7.2914.0000 INDIRECT EFFECT And SIGNIFICANCE USING NORMAL DISTRIBUTION Value s.e. LL 95 CI UL 95 CI Z Sig(two) Effect -.1614.0105 -.1820 -.1407 -15.3196.0000 BOOTSTRAP RESULTS For INDIRECT EFFECT Data Mean s.e. LL 95 CI UL 95 CI LL 99 CI UL 99 CI Effect -.1614 -.1618.0102 -.1814 -.1415 -.1893 -.1357 NUMBER OF BOOTSTRAP RESAMPLES 1000 FAIRCHILD ET AL. (2009) VARIANCE IN Y ACCOUNTED FOR BY INDIRECT EFFECT:.0697

76. Now we do the Sobel test. Sobel tests whether c – c’ is significantly different from zero. It does so using paths a and b, because a*b = c – c’ Age Letter Series Digit Symbols c’ = -0.109, se =.015 c = -0.271, se =.017 b = 0.278, se =.007 a = -0.589, se =.034 c – c’ = -.279 – (-.109) c – c’ = -.170 a * b = -0.589 * 0.278 a * b = -0.164 76

77. 77 VARIABLES IN SIMPLE MEDIATION MODEL Y LS_COR X AGE M DS_COR SAMPLE SIZE 2808 DIRECT And TOTAL EFFECTS Coeff s.e. t Sig(two) b(YX) -.2706.0171 -15.8027.0000 b(MX) -.5805.0341 -17.0209.0000 b(YM.X).2780.0079 35.2138.0000 b(YX.M) -.1092.0150 -7.2914.0000 INDIRECT EFFECT And SIGNIFICANCE USING NORMAL DISTRIBUTION Value s.e. LL 95 CI UL 95 CI Z Sig(two) Effect -.1614.0105 -.1820 -.1407 -15.3196.0000 BOOTSTRAP RESULTS For INDIRECT EFFECT Data Mean s.e. LL 95 CI UL 95 CI LL 99 CI UL 99 CI Effect -.1614 -.1618.0102 -.1814 -.1415 -.1893 -.1357 NUMBER OF BOOTSTRAP RESAMPLES 1000 FAIRCHILD ET AL. (2009) VARIANCE IN Y ACCOUNTED FOR BY INDIRECT EFFECT:.0697

78. Preacher and Hayes have built a some more “general purpose” dialogs Indirect –Allows for the multiple mediation scenario Modmed –Allows for the combination of mediation and moderation Process –A “do everything” script Let’s focus on “Indirect”. We’ll start with THEIR published example. 78

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83. The “indirect” script 83

84. 84 Educ Sex Age Netnews Apnews Online Strick Computes the total direct and indirect effect of educ, controlling for….

85. 85 Educ Sex Age Netnews Apnews Online Strick …all this.

86. Let’s put this to work with another example Are the negative effects of age on everyday functioning (EPT, everyday problems test) mediated by basic cognition (memory, reasoning)? Does decline in underlying cognition “explain” decline in everyday function. We would need to control for education and gender (oldest adults had unequal access to education, and older men tend to be positively selected) 86

87. IV and DV 87 Education Gender Age Memory Reasoning Everyday Function

88. Add in mediators 88 Education Gender Age Memory Reasoning Everyday Function

89. Control for covariates 89 Education Gender Age Memory Reasoning Everyday Function

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91. 91 Dependent, Independent, and Proposed Mediator Variables: DV = PROBCB1 IV = AGE MEDS = MEMCB1 REASCB1 Statistical Controls: CONTROL= GENDER YRSEDUC Sample size 2524 IV to Mediators (a paths) Coeff se t p MEMCB1 -.1470.0073 -20.0044.0000 REASCB1 -.1340.0077 -17.4143.0000 Direct Effects of Mediators on DV (b paths) Coeff se t p MEMCB1.1949.0122 16.0102.0000 REASCB1.2984.0116 25.6766.0000 Total Effect of IV on DV (c path) Coeff se t p AGE -.0856.0051 -16.8137.0000

92. 92 Direct Effect of IV on DV (c-prime path) Coeff se t p AGE -.0170.0043 -3.9655.0001 Partial Effect of Control Variables on DV Coeff se t p GENDER -.1263.0569 -2.2212.0264 YRSEDUC.1114.0097 11.4545.0000 Model Summary for DV Model R-sq Adj R-sq F df1 df2 p.5713.5705 671.2378 5.0000 2518.0000.0000 ***************************************************************** BOOTSTRAP RESULTS FOR INDIRECT EFFECTS Indirect Effects of IV on DV through Proposed Mediators (ab paths) Data boot Bias SE TOTAL -.0686 -.0687.0000.0036 MEMCB1 -.0286 -.0288 -.0001.0023 REASCB1 -.0400 -.0399.0001.0027 Bias Corrected and Accelerated Confidence Intervals Lower Upper TOTAL -.0765 -.0621 MEMCB1 -.0331 -.0243 REASCB1 -.0464 -.0353

93. 93 ***************************************************************** Level of Confidence for Confidence Intervals: 95 Number of Bootstrap Resamples: 1000 ------ END MATRIX ----- DataBootstrappedBiasSEZ(Data)Z(Boot)p(Data)p(Boot) TOTAL-0.0686-0.06870.00000.0036-19.0556-19.08330.0000 MEMBCB1-0.0286-0.0288-0.00010.0023-12.4348-12.52170.0000 REASCB1-0.0400-0.03990.00010.0027-14.8148-14.77780.0000 Copied into Excel to compute Zs and ps

94. Review We learned moderation last week. How do you model interactions of continuous variables with regression? What is the difference between a moderator and a mediator? How do you test for the presence of each? 94

95. Control for covariates 95 Education Gender Age Memory Reasoning Everyday Function (PROBCB1) (REASCB1) (MEMCB1) (YRSEDUC)

96. Slides between red bumpers are from last time 96

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100. 100 Temporarily only as a macro

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103. 103 Highlight and run – NOTHING WILL VISIBLY HAPPEN

104. Core syntax MEDIATE Y = yvar/X = xlist/M = mlist/C = covlist [/SAMPLES = {z}(1000**)] [/CICONF = {ci}(95**)] [/TOTAL = {t}(0**)] [/OMNIBUS = {o}(0**)] [/CIMETHOD = {m}(1**)] [/CATX = {cx} {0**}]. Subcommands in brackets are optional ** Default if subcommand is omitted 104

105. First model: Same as before Age (X) effect on Problem Solving (Y) mediated by Reasoning and Memory (M1 and M2). Gender and Years of Education as Covariates (C) 105

106. Open a SECOND syntax window and type your syntax 106

107. Let’s deconstruct MEDIATE Y = PROBCB1/ X = AGE / M = MEMCB1 REASCB1 / C = GENDER YRSEDUC / SAMPLES = 1000 / CICONF = 95 / TOTAL = 1 / OMNIBUS = 1 / CIMETHOD = 1. 107 Dependent var (Single) IV Mediators Covariates # Bootstrap samples 95% confidence Also show total effect of Y Show combined indirect effects too 1=Percentile bootstrap method (2=monte carlo; 3=stratified boostrapping)

108. 108 Run MATRIX procedure: VARIABLES IN THE FULL MODEL: Y = PROBCB1 M1 = MEMCB1 M2 = REASCB1 X = AGE COVARIATES: GENDER YRSEDUC =============================================================================

109. 109 OUTCOME VARIABLE: PROBCB1 MODEL SUMMARY (TOTAL EFFECTS MODEL) R R-sq Adj R-sq F df1 df2 p.5291.2799.2791 326.5657 3.0000 2520.0000.0000 MODEL COEFFICIENTS (TOTAL EFFECTS MODEL) Coeff. s.e. t p Constant 2.2730.4454 5.1031.0000 AGE -.0856.0051 -16.8137.0000 GENDER.0992.0718 1.3824.1670 YRSEDUC.2871.0113 25.3880.0000 OMNIBUS TEST OF TOTAL EFFECT R-sq F df1 df2 p.0808 282.7013 1.0000 2520.0000.0000 =============================================================================

110. 110 OUTCOME VARIABLE: MEMCB1 MODEL SUMMARY R R-sq Adj R-sq F df1 df2 p.4857.2359.2350 259.3275 3.0000 2520.0000.0000 MODEL COEFFICIENTS Coeff. s.e. t p Constant 5.1920.6424 8.0821.0000 AGE -.1470.0073 -20.0044.0000 GENDER 1.0756.1035 10.3885.0000 YRSEDUC.2745.0163 16.8277.0000 =============================================================================

111. 111 OUTCOME VARIABLE: REASCB1 MODEL SUMMARY R R-sq Adj R-sq F df1 df2 p.5198.2702.2694 311.0350 3.0000 2520.0000.0000 MODEL COEFFICIENTS Coeff. s.e. t p Constant 4.2995.6730 6.3883.0000 AGE -.1340.0077 -17.4143.0000 GENDER.0533.1085.4916.6230 YRSEDUC.4095.0171 23.9626.0000 =============================================================================

112. 112 OUTCOME VARIABLE: PROBCB1 MODEL SUMMARY R R-sq adj R-sq F df1 df2 p.7559.5713.5705 671.2378 5.0000 2518.0000.0000 MODEL COEFFICIENTS Coeff. s.e. t p Constant -.0219.3488 -.0627.9500 MEMCB1.1949.0122 16.0102.0000 REASCB1.2984.0116 25.6766.0000 AGE -.0170.0043 -3.9655.0001 GENDER -.1263.0569 -2.2212.0264 YRSEDUC.1114.0097 11.4545.0000 OMNIBUS TEST OF DIRECT EFFECT R-sq F df1 df2 p.0027 15.7254 1.0000 2518.0000.0001 ============================================================================= Omnibus?

113. 113 INDIRECT EFFECT(S) THROUGH: MEMCB1 Effect SE(boot) LLCI ULCI AGE -.0286.0021 -.0329 -.0245 OMNIBUS.0236.0025.0188.0286 ---------- INDIRECT EFFECT(S) THROUGH: REASCB1 Effect SE(boot) LLCI ULCI AGE -.0400.0026 -.0452 -.0348 OMNIBUS.0261.0029.0203.0319 ---------- Omnibus?

114. An omnibus test is used to answer the question as whether there is evidence that variable or variable(s) X exerts an effect on Y without specifying which variable in the set of X variables is responsible for the effect or, in the case of a multicategorical X, the nature of the difference between group means that is responsible for that effect. An omnibus test of the direct effect of X is conducted by ascertaining whether the addition of the independent variable(s) in xlist to a model of yvar containing only proposed mediators in mlist and covariates in covlist improves the fit of the model, as indexed by a change in the squared multiple correlation that results when the xlist variables are added. The increase in R2 is transformed to a statistic distributed as F(k, df2) under the null hypothesis of no direct effect, where k is the number of X variables in the model and df2 is the residual degrees of freedom from the larger model that includes the k variables in xlist. 114

115. Omnibus, in other words Does X have a significant unique effect after controlling for the mediators? Does it add anything? It’s a way of addressing total mediation Note, it is a multiple-R test Not that useful… 115

116. What if we recast gender and education as X variables, instead of as covariates? 116

117. Gender and education as X-vars MEDIATE Y = PROBCB1/X = AGE GENDER YRSEDUC /M = MEMCB1 REASCB1 /SAMPLES = 1000 /CICONF = 95 / TOTAL = 1 /OMNIBUS = 1 /CIMETHOD = 1. 117

118. 118 OUTCOME VARIABLE: PROBCB1 MODEL SUMMARY (TOTAL EFFECTS MODEL) R R-sq Adj R-sq F df1 df2 p.5291.2799.2791 326.5657 3.0000 2520.0000.0000 MODEL COEFFICIENTS (TOTAL EFFECTS MODEL) Coeff. s.e. t p Constant 2.2730.4454 5.1031.0000 AGE -.0856.0051 -16.8137.0000 GENDER.0992.0718 1.3824.1670 YRSEDUC.2871.0113 25.3880.0000 OMNIBUS TEST OF TOTAL EFFECT R-sq F df1 df2 p.2799 326.5657 3.0000 2520.0000.0000

119. 119 OUTCOME VARIABLE: MEMCB1 MODEL SUMMARY R R-sq Adj R-sq F df1 df2 p.4857.2359.2350 259.3275 3.0000 2520.0000.0000 MODEL COEFFICIENTS Coeff. s.e. t p Constant 5.1920.6424 8.0821.0000 AGE -.1470.0073 -20.0044.0000 GENDER 1.0756.1035 10.3885.0000 YRSEDUC.2745.0163 16.8277.0000

120. 120 OUTCOME VARIABLE: REASCB1 MODEL SUMMARY R R-sq Adj R-sq F df1 df2 p.5198.2702.2694 311.0350 3.0000 2520.0000.0000 MODEL COEFFICIENTS Coeff. s.e. t p Constant 4.2995.6730 6.3883.0000 AGE -.1340.0077 -17.4143.0000 GENDER.0533.1085.4916.6230 YRSEDUC.4095.0171 23.9626.0000

121. 121 OUTCOME VARIABLE: PROBCB1 MODEL SUMMARY R R-sq adj R-sq F df1 df2 p.7559.5713.5705 671.2378 5.0000 2518.0000.0000 MODEL COEFFICIENTS Coeff. s.e. t p Constant -.0219.3488 -.0627.9500 MEMCB1.1949.0122 16.0102.0000 REASCB1.2984.0116 25.6766.0000 AGE -.0170.0043 -3.9655.0001 GENDER -.1263.0569 -2.2212.0264 YRSEDUC.1114.0097 11.4545.0000 OMNIBUS TEST OF DIRECT EFFECT R-sq F df1 df2 p.0271 53.1253 3.0000 2518.0000.0000

122. 122 INDIRECT EFFECT(S) THROUGH: MEMCB1 Effect SE(boot) LLCI ULCI AGE -.0286.0022 -.0332 -.0244 GENDER.2097.0238.1645.2637 YRSEDUC.0535.0046.0455.0636 OMNIBUS.0458.0039.0387.0541 ---------- INDIRECT EFFECT(S) THROUGH: REASCB1 Effect SE(boot) LLCI ULCI AGE -.0400.0027 -.0454 -.0348 GENDER.0159.0323 -.0475.0792 YRSEDUC.1222.0069.1090.1360 OMNIBUS.0804.0055.0698.0919

123. This program can dummy-code IVs for you, but you are limited (then) to a single IV ACTIVE had six sites, and the sites differed a lot Did memory or reasoning differences mediate any of these site differences? 123

124. Syntax for a categorical (nominal) IV MEDIATE Y = PROBCB1/X = SITE/M = MEMCB1 REASCB1 /SAMPLES = 1000 /CICONF = 95 / TOTAL = 1 /OMNIBUS = 1 /CIMETHOD = 1 /CATX = 1. 124

125. Catx = 1 makes first level the reference level 125 VARIABLES IN THE FULL MODEL: Y = PROBCB1 M1 = MEMCB1 M2 = REASCB1 X = SITE CODING OF CATEGORICAL X FOR ANALYSIS: SITE D1 D2 D3 D4 D5 1 0 0 0 0 0 2 1 0 0 0 0 3 0 1 0 0 0 4 0 0 1 0 0 5 0 0 0 1 0 6 0 0 0 0 1

126. 126 OUTCOME VARIABLE: PROBCB1 MODEL SUMMARY (TOTAL EFFECTS MODEL) R R-sq Adj R-sq F df1 df2 p.1419.0201.0182 10.3548 5.0000 2520.0000.0000 MODEL COEFFICIENTS (TOTAL EFFECTS MODEL) Coeff. s.e. t p Constant.4315.0851 5.0704.0000 D1 -.4913.1201 -4.0921.0000 D2 -.4972.1237 -4.0202.0001 D3 -.0610.1219 -.5006.6167 D4 -.6179.1201 -5.1467.0000 D5 -.6024.1190 -5.0626.0000 OMNIBUS TEST OF TOTAL EFFECT R-sq F df1 df2 p.0201 10.3548 5.0000 2520.0000.0000

127. 127 OUTCOME VARIABLE: MEMCB1 MODEL SUMMARY R R-sq Adj R-sq F df1 df2 p.0890.0079.0060 4.0284 5.0000 2520.0000.0012 MODEL COEFFICIENTS Coeff. s.e. t p Constant.3967.1198 3.3103.0009 D1 -.6143.1691 -3.6333.0003 D2 -.5478.1742 -3.1454.0017 D3 -.2879.1717 -1.6770.0937 D4 -.6100.1691 -3.6079.0003 D5 -.3187.1676 -1.9016.0573 ============================================================================= OUTCOME VARIABLE: REASCB1 MODEL SUMMARY R R-sq Adj R-sq F df1 df2 p.0981.0096.0077 4.9005 5.0000 2520.0000.0002 MODEL COEFFICIENTS Coeff. s.e. t p Constant.2788.1285 2.1699.0301 D1 -.3686.1813 -2.0337.0421 D2.3085.1867 1.6525.0985 D3 -.1082.1840 -.5880.5566 D4 -.3878.1813 -2.1392.0325 D5 -.4441.1796 -2.4722.0135

128. 128 OUTCOME VARIABLE: PROBCB1 MODEL SUMMARY R R-sq adj R-sq F df1 df2 p.7460.5565.5553 451.3609 7.0000 2518.0000.0000 MODEL COEFFICIENTS Coeff. s.e. t p Constant.2530.0574 4.4078.0000 MEMCB1.1986.0118 16.8673.0000 REASCB1.3575.0110 32.5454.0000 D1 -.2375.0810 -2.9312.0034 D2 -.4987.0837 -5.9575.0000 D3.0349.0821.4246.6712 D4 -.3581.0810 -4.4204.0000 D5 -.3803.0802 -4.7429.0000 OMNIBUS TEST OF DIRECT EFFECT R-sq F df1 df2 p.0120 13.6056 5.0000 2518.0000.0000

129. 129 INDIRECT EFFECT(S) THROUGH: MEMCB1 Effect SE(boot) LLCI ULCI D1 -.1220.0357 -.1914 -.0494 D2 -.1088.0358 -.1801 -.0406 D3 -.0572.0329 -.1238.0058 D4 -.1212.0343 -.1886 -.0572 D5 -.0633.0315 -.1292 -.0027 OMNIBUS.0012.0008.0004.0034 ---------- INDIRECT EFFECT(S) THROUGH: REASCB1 Effect SE(boot) LLCI ULCI D1 -.1318.0667 -.2637.0010 D2.1103.0668 -.0223.2430 D3 -.0387.0665 -.1705.0928 D4 -.1386.0693 -.2775 -.0082 D5 -.1588.0599 -.2804 -.0388 OMNIBUS.0027.0015.0010.0069

130. 130 Other interesting options to explore: http://afhayes.com/spss-sas-and-mplus-macros-and-code.html

131. Logistic note The classroom is obviously set up for LCD You have many ways you can bring these presentations to class: -on a flash drive (a little tricky to access…let’s check for “extension cords”) -on a CD -e-mail it to yourself, then open it on the class computer via webmail—might be too time consuming -Access through terminal server and save to local drive—might be too time consuming 131

132. Logistic note All students will be asked to evaluate all other students in class, and turn in their evaluations to me This won’t influence your colleague’s grades, but it will provide useful feedback to your colleagues I have posted an evaluation sheet to all of you in Sakai; you’ll need to print all copies (I think there will be 20 people) to have enough for the three classses. I’ll gather, we’ll “collate” and give back to the speakers 132

133. Logistic note Before (by 8:30 am) the class in which you present, upload slides & script to Sakai Speakers: Please get here early enough. I would like to load all talks on the desktop for easy access. PLEASE SAVE UNDER YOUR LAST NAME if at all possible. There is a danger in relying on the TS Audience: Please come to every class—out of respect and honor and shared burden. And PLEASE COME ON TIME! 133

134. Presentation ratings Forms to come via email this weekend PRINT THEM OUT, and bring them to class Tuesday (and the remaining three presentation days). They will be collected after each speaker, collated, and returned to the speaker by the next class. 134