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enter image description hereI have this SPSS output and I'm wondering how I report variance for the model. Additionally, how much of the variance was explained by exercise both directly and indirectly (through both mediators) in happiness? Thank you in advance!

Y  : Happiness
X  : Exercise

M1 : Relatedness M2 : Competence

OUTCOME VARIABLE: Relatedness

Model Summary R R-sq MSE F df1 df2 p .2829 .0800 .4367 28.2704 1.0000 325.0000 .0000

Model coeff se t p LLCI ULCI constant 3.5178 .2306 15.2555 .0000 3.0641 3.9714 Exercise .2396 .0451 5.3170 .0000 .1509 .3282

Standardized coefficients coeff Exercise .2829

OUTCOME VARIABLE: Competence

Model Summary R R-sq MSE F df1 df2 p .6189 .3830 .2399 100.5572 2.0000 324.0000 .0000

Model coeff se t p LLCI ULCI constant 1.6941 .2239 7.5669 .0000 1.2537 2.1346 Exercise .2564 .0348 7.3631 .0000 .1879 .3248 Relatedness .3923 .0411 9.5422 .0000 .3114 .4732

Standardized coefficients coeff Exercise .3350 Relatedness .4341

OUTCOME VARIABLE: Happiness

Model Summary R R-sq MSE F df1 df2 p .7792 .6072 .1148 166.4364 3.0000 323.0000 .0000

Model coeff se t p LLCI ULCI constant .1510 .1680 .8991 .3693 -.1795 .4815 Exercise .1011 .0260 3.8841 .0001 .0499 .1522 Relatedness .4356 .0322 13.5325 .0000 .3722 .4989 Competence .2029 .0384 5.2796 .0000 .1273 .2785

Standardized coefficients coeff Exercise .1526 Relatedness .5569 Competence .2344

************************** TOTAL EFFECT MODEL **************************** OUTCOME VARIABLE: Happiness

Model Summary R R-sq MSE F df1 df2 p .4174 .1742 .2398 68.5732 1.0000 325.0000 .0000

Model coeff se t p LLCI ULCI constant 2.3070 .1709 13.5007 .0000 1.9708 2.6431 Exercise .2765 .0334 8.2809 .0000 .2108 .3422

Standardized coefficients coeff Exercise .4174

************** TOTAL, DIRECT, AND INDIRECT EFFECTS OF X ON Y **************

Total effect of X on Y Effect se t p LLCI ULCI c_cs .2765 .0334 8.2809 .0000 .2108 .3422 .4174

Direct effect of X on Y Effect se t p LLCI ULCI c'_cs .1011 .0260 3.8841 .0001 .0499 .1522 .1526

Indirect effect(s) of X on Y: Effect BootSE BootLLCI BootULCI TOTAL .1754 .0270 .1217 .2286 Ind1 .1043 .0206 .0632 .1451 Ind2 .0520 .0137 .0274 .0807 Ind3 .0191 .0060 .0088 .0319

Completely standardized indirect effect(s) of X on Y: Effect BootSE BootLLCI BootULCI TOTAL .2648 .0396 .1834 .3408 Ind1 .1575 .0303 .0966 .2153 Ind2 .0785 .0207 .0410 .1219 Ind3 .0288 .0089 .0133 .0476

Indirect effect key: Ind1 Exercise -> Relatedness -> Happiness Ind2 Exercise -> Competence -> Happiness Ind3 Exercise -> Relatedness -> Competence -> Happiness

CatahoulaLola
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  • The formatting on your question is making it very difficult for someone to help you. Can you edit the question and use markdown tables to make the output look like it does when SPSS prints it out? https://www.codecademy.com/resources/docs/markdown/tables – R Carnell Dec 05 '23 at 01:03
  • @RCarnell apologies! I've added a picture, hopefully that will help. Thank you! – CatahoulaLola Dec 05 '23 at 19:18

1 Answers1

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I'm not exactly sure what you want to report when you say "variance". The model $R^2$ for the full mediation model, which includes both mediators and the focal variable, is .6072. Your three predictors (exercise, relatedness, and competence) jointly explain about 61% of the variability in your outcome (happiness). The $R^2$ for the model for competence is .383, so exercise and relatedness jointly explain about 38% of the variability in competence. The $R^2$ for the model for relatedness is .08, so exercise explains about 8% of the variability in relatedness.

The question of "how much variance is explained in the outcome by each variable in the model" is not answerable from the output given. You can run the regression separately (i.e., outside of PROCESS) and report whatever statistics you want from those models (e.g., semi-partial $R^2$). Though there is a relationship between partial correlations and standard regression coefficients, it is complicated. You can also report the "proportion mediated", which is the ratio of the indirect effect to the total effect.

Noah
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  • Thank you so much @Noah! Perhaps I am getting caught up in terminology (variance, variation, variability). I'm trying to make a statement regarding the amount of variance (or perhaps variability) in happiness, that is explained by exercise both directly and indirectly through both mediators. Would I be safe to make the claim that "Exercise both directly and indirectly explains 61% of variability (or variance?) in happiness" ? I read that overall model statistics aren't exactly the most interesting part of a meditation and perhaps I am overreaching by trying to include this statement. – CatahoulaLola Dec 07 '23 at 01:06
  • On a similar note, I recognize that the coefficients are quite small. Does this negate their meaning and importance?

    Thanks again!!

     – CatahoulaLola Dec 07 '23 at 01:07
  • You can't say that "Exercise both directly and indirectly explains 61% of the variability in happiness" because it only explains 17% of the variability in happiness. The other mediators are affected by a whole host of other unmeasured factors that explain the rest. I would say you are overreaching to include this statement and you should not say it; it is not the standard part of a mediation analysis. Reporting and interpreting model $R^2$s is fine, but not how much variance is explained "directly and indirectly". – Noah Dec 07 '23 at 07:49
  • I don't see any small coefficients. Small is relative. The raw coefficients are scale-dependent so there is no obvious way to claim a given number is small unless you have a reference point for what a moderate effect looks like. Standardized coefficients look moderate to me; remember a standardized coefficient of 1 is the largest effect you will ever see, basically an impossibility in psychology. So .3 isn't necessarily "small". – Noah Dec 07 '23 at 07:51
  • you have been incredibly helpful! I cannot thank you enough!! I hesitate to take more of your time but, I would love your insight into the indirect effects (IND1: .10; IND2: .05; IND3: .02) I've been told they're less than ideal, would you agree? Is there a way to "talk them up" so to speak? My poetic license for statistics is lacking. Again, thank you so much for your time and expertise. – CatahoulaLola Dec 07 '23 at 20:40
  • They don't look small to me, but again "size" is context-dependent. The confidence intervals for all of them exclude 0 so you have evidence of some associations. Not sure in what sense they are "less than ideal". They simply are what they are. You can quantify them using proportion mediated if you want, which will yield a standardized effect size measure. If you found my answer helpful, please consider upvoting and marking the question as solved. – Noah Dec 08 '23 at 00:51
  • Thank you so much @Noah! I truly appreciate your time and expertise. – CatahoulaLola Dec 08 '23 at 18:37