Mediation Example David A Kenny Example Dataset Morse

Mediation Example David A. Kenny

Example Dataset • Morse et al. – J. of Community Psychology, 1994 – treatment housing contacts days of stable housing – persons randomly assigned to treatment groups. – 109 people 2

Variables in the Example • Treatment — Randomized – 1 = treated (intensive case management) – 0 = treatment as usual • Housing Contacts: total number of contacts per during the 9 months after the intervention began • Stable Housing – days per month with adequate housing (0 to 30) – Averaged over 7 months from month 10 to month 16, after the intervention began 3

Downloads • Data • SPSS Syntax • SPSS Output 4

Step 1 REGRESSION /MISSING LISTWISE /STATISTICS COEFF /DEPENDENT stable_housing /METHOD=ENTER treatment. Unstandardized Standardized Coefficients Model B Std. Error Beta 1 (Constant) 12. 784 1. 607 treatment 6. 558 2. 474. 248 a. Dependent Variable: stable_housing t 7. 955 2. 651 Sig. . 000. 009 5

Step 2 REGRESSION /MISSING LISTWISE /STATISTICS COEFF /DEPENDENT hc 9 /METHOD=ENTER treatment. Model 1 (Constant) treatment Unstandardized Standardized Coefficients B Std. Error Beta 8. 063 1. 417 5. 502 2. 182. 237 t 5. 689 Sig. . 000 2. 522 . 013 6

Steps 3 and 4 REGRESSION /MISSING LISTWISE /STATISTICS COEFF /DEPENDENT stable_housing hc 9 /METHOD=ENTER treatment. Standardized Unstandardized Coefficients Model B Std. Error Beta 1 (Constant) 9. 024 1. 680 treatment 3. 992 2. 332. 151 hc 9. 466. 100. 410 a. Dependent Variable: stable_housing t 5. 372 Sig. . 000 1. 712 4. 646 . 090. 000 7

Morse et al. Example · Step 1: X Y · c = 6. 558, p =. 009 · Step 2: X M · a = 5. 502, p =. 013 · Step 3: M (and X) Y · b = 0. 466, p <. 001 · Step 4: X (and M) Y · c′ = 3. 992, p =. 090 8

Decomposition of Effects Total Effect = Direct Effect + Indirect Effect c = c′ + ab Example: 6. 558 ≈ 3. 992 + 2. 564 [(5. 502)(0. 466)] 9

Estimating the Total Effect (c) The total effect or c can be inferred from direct and indirect effect as c′ + ab. Note that we can determine c or 6. 558 from c′ + ab or 3. 992 + 2. 564 [(5. 502)(0. 466)] Holds exactly (within the limits of rounding error) in this case. 10

Percent of Total Effect Mediated 100[ab/c] or equivalently 100[1 - c′/c] Example: 100(2. 564/6. 558) = 39. 1% of the total effect explained 11

Strategies to Test ab = 0 • Joint significance of a and b • Sobel test • Bootstrapping 12

Joint Significance Test of a: a = 5. 502, p =. 013 Test of b: b = 0. 466, p <. 001 13

Sobel Test of Mediation Compute the square root of a 2 sb 2 + b 2 sa 2 which is denoted as sab Note that sa and sb are the standard errors of a and b, respectively; ta = a/sa and tb = b/sb. Divide ab by sab and treat that value as a Z. So if ab/sab greater than 1. 96 in absolute value, reject the null hypothesis that the indirect effect is zero. 14

Results a = 5. 502 and b = 0. 466 sa = 2. 182 and sb = 0. 100 ab = 2. 564; sab = 1. 1512 Sobel test Z is 2. 218, p =. 027 We conclude that the indirect effect is statistically different from zero. 15

http: //quantpsy. org/sobel. htm 16

Bootstrapping Structural Equation Modeling programs Hayes & Preacher macro called Indirect www. afhayes. com/spss-sas-and-mplus-macros-and-code. html Download Run the macro indirect Run this syntax INDIRECT y = housing/x = treatment/m = hc 9 /boot = 5000/normal 1/bc =1. 17

Dependent, Independent, and Proposed Mediator Variables: DV = stable_h IV = treatmen MEDS = hc 9 Sample size 109 IV to Mediators (a paths) Coeff se t p hc 9 5. 5017 2. 1819 2. 5216 . 0132 Direct Effects of Mediators on DV (b paths) Coeff se t p hc 9 . 4664 . 1004 4. 6462 . 0000 Total Effect of IV on DV (c path) Coeff se t p treatmen 6. 5580 2. 4738 2. 6510 . 0092 Direct Effect of IV on DV (c' path) Coeff se t p treatmen 3. 9922 2. 3318 1. 7121 . 0898 Model Summary for DV Model R-sq Adj R-sq F df 1 df 2 p 18 . 2204 . 2057 14. 9834 2. 0000 106. 0000

NORMAL THEORY TESTS FOR INDIRECT EFFECTS Indirect Effects of IV on DV through Proposed Mediators (ab paths) Effect se Z p TOTAL 2. 5659 1. 1512 2. 2289 . 0258 hc 9 2. 5659 1. 1512 2. 2289 . 0258 19

BOOTSTRAP RESULTS FOR INDIRECT EFFECTS Indirect Effects of IV on DV through Proposed Mediators (ab paths) Data Boot Bias SE TOTAL 2. 5659 2. 6049 . 0390 1. 1357 hc 9 2. 5659 2. 6049 . 0390 1. 1357 Bias Corrected Confidence Intervals Lower Upper TOTAL . 5150 5. 0645 hc 9 . 5150 5. 0645 ***************************** Level of Confidence for Confidence Intervals: 95 Number of Bootstrap Resamples: 5000 20

Compare Two Mediators INDIRECT y = stable_h/x = treatment/ m = hc 9 ec 9 / boot=5000/normal 1/ contrast 1 / bc =1. 21

Indirect Effects of IV on DV through Proposed Mediators Data Boot Bias SE TOTAL 3. 6696 3. 6767 . 0071 1. 3457 hc 9 2. 3693 2. 3991 . 0297 1. 0330 ec 9 1. 3003 1. 2776 -. 0226 . 8814 C 1 1. 0690 1. 1214 . 0524 1. 3701 Bias Corrected Confidence Intervals Lower Upper TOTAL 1. 3170 6. 6798 hc 9 . 5801 4. 6410 ec 9 -. 0153 3. 5945 C 1 -1. 6329 3. 7939 INDIRECT EFFECT CONTRAST DEFINITIONS: Ind_Eff 1 MINUS Ind_Eff 2 22

Hayes’ Process: http: //afhayes. com/spss-sas -and-mplus-macros-andcode. html 23

Thank You! • Thanks to Bob Calsyn for providing the data. • Sensitivity Analyses 24