PATH ANALYSIS CONCEPT AND EXAMPLE USING SPSS 16
Good night friends.. Howdy? Hope you’re fine today.. Hahaha.. Okay, this time I will give you a nice post about Path Analysis. Not only explaining you about the concept, but I also will give you an easy understandable example that we will execute by using SPSS 16.
You must have been remembered that in the former I have ever explained you about multiple regression analysis.. Had you understood its concept, it would have been helpful for you to understand this path analysis.
Note: In path analysis, we are introduced to what called “direct effect”, “indirect effect” and “total effect”. For make it easy, I will illustrate it like this:
A case to know the direct and indirect effect of variables A, B, and C to variable E by using D as the mediator variable.
For example, we have independent variables A, B and C that we want to know each of their effects to E as a dependent variable. Okay, in this case as I have said, we used a mediator variable, say D. Why do we use this variable? Something we can be confronted for a case that some independent variables can instantly effect the dependent one (direct effect) but for any condition, the independent variables cannot instantly effect the dependent one
Please look at the illustration above:
Here, we shall set two sub structural equation, right?
First, see that variable A, B and C can instantly effect variable D (direct effect). In SPSS, we regress independent variables A, B and C to variable D. So, this is the sub structural equation:
D = ρ DA + ρ DB + ρ DC + Є1
Second, Variable A, C and D can instanly effect E though variable B can’t. Just look to the arrow at the illustration given. Then, we make the sub structural equation:
E = ρ EA + ρ EC + ρ ED + Є2
For not wasting time, I will give an example with fictive data.. Nevermind, the example can be found but you should remember that you havo to understand the concept and philosophy.. Okay, if you want to practice, you can download the data here
Oops, you should also know that in path analysis, we also use the test of assumption in regression OLS. This classical test won’t be explained here because I have ever put it in a last post. When you have downloaded the data you can see that you’ll have data view alike:
First step: regress variable A, B and C to variable D. Just click Analyze, Regression, Linier. Then, put variable A, B and C in Independent Part and variable D in Dependent one.
You will have output:
Simultaneously, variable A, B and contribute 73,1 percent in explaining the changes happen in variable D and the rest for about 16,9 percent is explained by the other variables out of the model.
In Anova F test, see that simultaneously, the independent variables statistically has a significant effect to variable D that’s shown by Sig. value 0,000 less than Alpha 0,05 (rejecting null hypothesis and accepting the alternative one, so the F test is significant.
At coefficient, the partial t test, variable B and C statistically have a significant effect to variable D that’s shown by each Sig. value that less than Alpha, viz 0,048 and 0,000. Variable A statistically don’t have a significant effect to variable D (Sig. value is 0,615; more than Alpha 5 percent. For that case, we eliminate variable A.
The sub structural equation (using Standardized Beta) becomes:
D= 0,320B + 0,640C + Є1
Heemm, see that the sign of coefficient is positive, It means that variable B and C are positively effect variable D.
Interpretation of variable B: The increase for one unit of variable B will increase variable D for 0,320 unit with assumption that another independent variable is constant.
Interpretation of variable C: The increase for one unit of variable C will increase variable D for 0,640 unit with assumption that another independent variable is constant.
Next, we go to the second suu structural equation. Regress variable A, C and D to variable E. Just the same way and you will get this output:
The result shows that variable A, C and D can only explain the variance of variable E for 34,4 percent and the rest is explained by the other variables out of the model. Next, we see that simultaneous test ( F test) is still significant, shown by Sig. value 0,011 < (less than) 0,05. From partial test, only variable D that statistically significant to effect variable E (Sig. value 0,005 < Alpha 0,05). Here is the structural model:
E= 0,868D + Є2
Statistically, variable A doesn’t have direct effect to E because in our test, variable A is not significant to effect E. For its indirect effect doesn’t need to be counted because we have eliminated this variable when we regress it with the variable dependent D.
The indirect effect from B to E through the moderator variable D is 0,320 x 0,868 = 0,27776 or 0,28. For the direct one is suitable with the beginning ilustration. In a research, we must reckon this moderator variable by strengthening the theories related. See also that B doesn’t have a direct arrow to E; it means variable D just have the indirect effect (only by using moderator variable).
Variable C; we can count its indirect effect 0,640 x 0,868 = 0,5552 or 0,56. Okay, for the direct effect, remember that at second sub strutural we place variable E as dependent. From A,C and D, only D that statistically significant to effect variable E.
And now, there is one question for you my friends about this path analysis. Imagine that variable D (moderator variable) is not significant.. Is there any indirect effect?? Hehehe.. Can you give your argument? Right, hope that anyone can give argument for this question..l.o.l.
So, I suggest that we should be careful to choose the moderator variable for this path analysis. Read and deepen the theories related friends. You can also download some free ebooks about this analysis and moderator intervening concepts.
The last but not the least, we can find the total effect. Just totalize the direct and indirect effect. In our case (may be, because we just need fictive data), the direct effect is not significant, so for the total we only use the indirect one.. Total effect from B to E is 0,28 while total effect from C to E is 0,56. Heeemmm,, for the interpretation, I have explained it so long hahaha..
Okay, that’s all that I can tell you about this path analysis.. more or less, I apologize.. Keep spirit and success for us.. :-)