V14.12 - Moderated Multiple Regression in SPSS

in this video I'm gonna show you how to conduct a moderated multiple regression analysis in SPSS and it's a two-way moderated multiple regression because there are only two independent variables and therefore only one possible interaction effect one variable combined with the other to yield a product term which represents a two-way interaction in the context of a anova which is language similar to used in ANOVA where you have two independent variables and a two-way interaction between those two variables so I assume that you already know about hierarchical multiple regression because I'm gonna be doing that here I also assume that you know that I created a product term out of this variable in a previous video so in order to conduct the analysis going to analyze regression linear and add the dependent variable into the dependent Box and then the independent variables the main effects intelligence and academic motivation in block one and then click Next because this is a hierarchical multiple regression and put the product term of intelligence and academic motivation into block two now click on statistics you want the r-squared change and you want the part and partial correlations you want descriptives and collinearity Diagnostics I'm only clicking this for thoroughness to point out mostly that it's irrelevant for the purposes of evaluating multicollinearity associated with the product term of course it's going to have a high variance inflation factor but you also want to look at the possibility of collinearity between your two predictor variables maybe they're very highly related to each other click on continue and click ok so here's the output the descriptive statistics means and standard deviations not especially informative for the purposes of interpreting a moderated multiple regression unless you wanted to interpret the sanitized beta weights which is troublesome here are the correlations these are the bivariate correlations let me just create this all on one row we can see that intelligence correlated with GPA at 0.42 so higher levels of intelligence were associated with higher levels of academic achievement and academic motivation was correlated 0.35 with GPA so at least numerically intelligence was a greater predictor than academic achievement then academic motivation don't know if that's significantly different in terms of the correlations intelligence and academic motivation interestingly are very weakly related there is some correlation point zero six zero and that correlation is actually not statistically significant even on the basis of a single tailed test the absence of a correlation there does not preclude doing a moderated multiple regression you could still potentially observe an interaction between the two variables and that's why I carried on with the analysis and then finally the individual variables are obviously correlated fairly substantially with the product term because they actually help define this variable so positive correlations all around as you would expect in this study these are the variables entered and removed across the two models it's two blocks that I created so in the first block we have academic motivation and intelligence and then in the second block I added intelligence by motivation the dependent variable is GPA here is the model summary and the key statistic you'd want to look at in a moderated multiple regression is the r-squared change just like a hierarchical multiple regression you're interested mostly in the r-squared change so here the r-squared change was equal to 0.01 zero and that is statistically significant four point nine six six with one and 360 degrees of freedom and P equal point zero two six so the p-value is less than point zero five at model two which is suggesting that by adding the product term a statistically significant interaction was observed it hasn't increased the percentage of variance accounted for in the dependent variable very substantially it's really just one percent with intelligence and academic motivation included in the model excluding the product term the R square was equal to 0.28 to suggesting twenty eight point two percent of the variance in GPA was accounted for and that is statistically significant with an F of seventy point nine eight nine and two and 360 one degrees of freedom P less than point zero zero one adding the product term the interaction increase the percentage of variance accounted for by point zero one or one percent and that's why you see it go from 0.28 to two point two nine two so twenty nine point two percent with the model that included the main effects plus the interaction term and this R square the final model R square is statistically significant as well forty nine point five zero F value with three and 360 degrees of freedom P less than point zero zero one so all our squared values were statistically significant in this analysis including the all-important R squared change now what is the nature of this interaction is it consistent with the theory we don't know we have to do supplementary analyses now I do point out in a textbook that you can get some useful information from the coefficients table but the truth is that interpreting an interaction on the basis of just looking at values like beta weights or even semi partial correlations is not easy and ultimately you're going to have to rely on a visual presentation in my opinion but just to be thorough I'm going to go through these results at model one intelligence and academic motivation were both found to be unique contributors to the regression equation here are the standardized beta weights 0.4 zero and point 3 2 6 so intelligence a little bit larger of a standardized beta weight I don't know if it's statistically significantly larger but it's larger numerically here are the unstandardized beta weights so I assume you know how to interpret on standardized beta weights I cover that in detail in the multiple regression method enter video and material and the textbook the key point here is that they are both positive so higher levels of intelligence is associated with higher levels of academic achievement and higher levels of academic motivation are associated with higher levels of academic achievement and they're both statistically significant unique contributors to the model if we look at the semi partial correlations they are almost identical to the beta weights and that's because the correlation between intelligence and academic motivation was only point zero so it's really not a big correlation almost pointless to do a multiple regression really the part correlation and the standardized beta weights and even the zero order correlation are all very very similar a little bit of a difference here 0.35 versus 0.33 rounded tolerance and variance inflation factor is obviously very good I mean tolerance is nowhere near point one zero because the relationship between intelligence and academic motivations solo no problems here variance inflation factor is far from ten it's only at one point zero zero tiny no problems now looking at the model to which is the important bit let me just fix this up a little bit we can see that the intelligence by motivation product term the interaction effect was identified as statistically significant which is consistent with the r-square change value so in this case here evaluating the beta eight point zero zero one unstandardized the T value is two point two two eight and P less than point zero five in fact it's equal to point zero two six which is exactly the same as the significant F change value it's essentially the same analysis evaluating this unique effect in model two is essentially the same as testing the statistical significance of the difference between the two R squared values the R squared change it's the same analysis and here's that part correlation point zero nine nine or semi partial correlation now trying to interpret these effects on the basis of the results in the coefficients table as I mentioned not very easy I in the textbook I do some the squared semi partial correlations from model one associated with the main effects and then I square the semi partial correlation associated with the interaction term in model two and it sums to a value that's pretty close to the overall r-squared value now that does give you some hint of the unique effects the summed unique effects as well as the common effects that are associated with this multiple regression but I do mention in a textbook that as soon as you get two independent variables in an analysis the possibility of suppressor effects confounds the interpretation of these squared semi partial correlations and some semi partial correlations as well as the difference between the r-squared value and the sum of the semi partial correlations but it does give you some hint of what's going on in your data ultimately the intelligence by motivation interaction effect is tiny it's really quite small it's only a point zero one semi partial correlation there's not a lot going on here but it's statistically significant so to carry on things further to truly understand the nature of the effect you have to look at some scatter plots doing something like a spotlight analysis or a split slopes analysis in a scatter plot I'm gonna cover that in a separate video

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Length: 9min 36sec (576 seconds)

Published: Sun Mar 03 2019