Dear Kara Ma

I will go through the questions one by one

• Does a larger path coefficient mean a more influential/or stronger effect?

Yes, it does. The larger the standardized path coefficient the more influence it has towards the variable it measures.

• Do I need to compare the differences between path coefficients to determine which factor is more influential?

Well, if you are interested in comparing the model among different groups, then you may try to use Multi-Group Analysis to test if the moderating variable has a significant difference or not. Assume that part of your structural model, you have latent variables A, B and gender as a moderating variable.

If you split the collected data into gender classes e.g.(women, men), and run the same model but with two different data, it is so likely that the standardized path coefficients are going to be different, however, the main question is the difference is significant or not. Therefore, via the use of Multi-Group Analysis.

For example:

Path (A --> B) (Women Data) (standardized path coefficient = 0.24)

Path (A --> B) (Men Data) (standardized path coefficient = 0.30)

You cannot simply say that variable A has more influence on men since their standardized path coefficient is higher than women. Instead, after running Multi-Group Analysis, if a significant difference is found, then you can interpret that based on the sign and the selected referenced level which is usually the one coded with 0.

if you are not interested in comparing the model among different groups, then I think that ranking the standardized path coefficients will give you information about which variable has more influence than the others.

If the causal relationship is significant, but the effect size is very small...how should I interpret the results?

At first, the main objective of the effect size f 2 allows assessing an exogenous construct’s contribution to an endogenous latent variable’s R2 value. [1]

you can use the following ranges to interpret the effective size (f2) values of 0.02, 0.15, and 0.35 indicate an exogenous construct’s small, medium, or large effect, respectively, on an endogenous construct. [1]

Source:

[1] Joseph F. Hair, G. Tomas M. Hult, Christian M. Ringle, Marko Sarstedt - A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) [2nd ed.]-Sage (2017) page 208

Dear Kara Ma ,

Are your estimates standardized or unstandardized?

Standardized estimates usually prevent the problem/challenge where a causal relationship is significant but the effect size is very small, and vice versa.

If you are comparing two paths that each link one IV to the same DV, then the standardized coefficients are equivalent to correlations, which can be compared.

Thank you Belal Edries , I get what you mean. In my model, there are 5 IV affect 1 DV, however, there are two path coefficients (factor1 VS. factor 2) very close to each other(0.254VS.0.248), can I conclude from here that factor 1 is more influential? however, for the f square effect size, factor 1 is smaller than factor 2(0.067VS.0.064), so how do I interpret this. As what I understand, they both mean effect strength right? So should I look at Path coefficients or f square?

Based on Cohen(1988), all my f square are small, does this means all the relationships are not important? I am so confused here

Thanks again for your help

Kara

Thank you David L Morgan and Elvis Munyaradzi Ganyaupfu . I am using Smart-PLS, the results show the path coefficients of original sample as well as the sample mean, I am using the former. I think it should be standardised.

Thanks

Kara

Statistical Significance of a Path Coefficient = p-values and/or t-values and/or Confidence Intervals

Substantive Significance or Effect Size of a Path Coefficient = f-square (Small=.02) (Medium=0.15) (Large=0.35) (Cohen, 1988, 1992)

Dear Kara Ma it is very normal for a novice researcher to be confused on each and every step of the graduate research process. Your confusion, however, would be clear with time and your efforts. First of all, SmartPLS produces only Standardized coefficients. A path coefficient certainly represents the contribution of a particular predictor in affecting the criterion or dependent variable. When we test more than one variables simultaneously, as is the case with your model, we can compare them to show which one is most important and so on. BUT, before we confer any findings from this output, we need to see whether path coefficients are STATISTICALLY SIGNIFICANT or not (by looking at p-values, t-values, and/or Confidence Intervals). f-square values are extra information about each predictor and its SUBSTANTIVE SIGNIFICANCE for the dependent variable. The caveat here is that even if the f-square value is not significant or small, you are good to go with statistical significance of the predictor in explaining your dependent variable.

Hi Kara Ma ,

Thanks for additional information, and certainly SmartPLS produces standardized coefficients, and based on the information . I hope the information provided by Muhammad Zia Aslam is sufficient to answer your questions regarding the effect sizes of a path coefficients you obtained. Regarding CI lower and upper limits,

if rules in your study strictly require the lower and upper limits of the CIs not to reach or exceed ±1, you can try alternate Confidence levels in your reporting tab and see how results change. CIs can be presented as 90% CI, 95% CI or 99% CI, though 95% CI is commonly used in many applications. However, the choice of whether to use a 90% or 95% CI is to some extent arbitrary, and depends on the level of “confidence” that the analyst/researcher wishes to convey in his or her estimate.

Thank you Muhammad Zia Aslam and Elvis Munyaradzi Ganyaupfu , that's very helpful! I am still confused that when the path coefficients and f square show different rank orders, which one do I look at? In my case, the "product-in-hand" has path coefficients of 0.254, f square of 0.064; "customer support" has path coefficients of 0.248, f square of 0.067. So which one is more influential? Or should I conclude they are both "key factors"?

In terms of f square, if it is very small, does it mean the effect is very weak? what's the meaning in a real business? although significant, but not meaningful right?

Best Regards

Kara

Dear Kara Ma , in your case both your predictors are equally important (with each adding almost 25% variance in the total variance accounted for the criterion or dependent variable). Furthermore, without mixing the statistical and substantive significance, just report that, though effect sizes are small, both variables are substantively significant as well. I suggest to read some methodology literature to be clear on this matter. Tq

Dear Kara Ma ,

I hope the perfect explanation given by Muhammad Zia Aslam addresses and clears out the confusion you had. Therefore, as long as the computed t-statistics and p-values (statistical significance) show that the estimated path coefficients of 0.254 for "product-in-hand" and 0.248 for "customer support" are statistically significant, both predictors are important. Each of these predictors accounts for approximately 25% of the variance in the dependent variable. If you want to stress out the relative importance of each of these predictors, then "product-in-hand" has a slightly/marginally higher (25.4%) variance (importance) relative to "customer support" (24.8%) variance on the dependent variable. Hence both "product-in-hand" and "customer support" are statistically significant (and important). In terms of substantive significance, the effect sizes attributed to "product-in-hand" f square of 0.064 and "customer support" f square of 0.067 are both approximately equal to 0.1 each. Based on the criterion shared above by Muhammad Zia Aslam , f-square = 0.1 which is still below 0.15, hence I can classify and regard effect sizes of both "product-in-hand" and "customer support" as small, in full agreement with Muhammad Zia Aslam .

I am not sure how some of the answers to this question reach the conclusion that a path coefficient of .25 accounts for 25 percent of the variance. Path coefficients are equivalent to simple correlations, not r-sq, so a path coef of .25 equals an r-sq of .0625.

Kara,

Is your dependent variable "latent" or "observed"?

Hi Elvis Munyaradzi Ganyaupfu , they are latent variables.

Standardized Path Coefficients are important because of the provided ease for interpretation of the output based on MEAN=0 and SD=1 for all involved variables.

So, we can interpret the relative contribution of multiple predictors in terms of 1 point or 1 Standard Deviation change in a particular independent variable might increase equal to the corresponding path coefficient value i.e., 0.254 point or 25.4% point in the of dependent variable.

I agree that Path Coefficient should be interpreted independent of the Determination of the Coefficient (R-square).

Kara Ma you can watch the following YouTube video for basic understanding about the interpretation of Regression output in OLS.

Mike Crowson's YouTube Channel:

https://youtu.be/W0BwlZv6Ul0

Thank you ! Muhammad Zia Aslam . I will watch the video.

Dear Kara Ma ,

I completely agree with the last comments/insights made by David L Morgan and Muhammad Zia Aslam . So Kara Ma , based on the fact that your dependent variable is latent, please advise if what you conducted is a Structural Equation Model (SEM) or Confirmatory Factor Analysis (CFA), and NOT Path Analysis (which assumes perfect measurement of observed variables - ie variables are measured without error) since path analysis is used to estimate a system of equations in which all of the variables are observed? I hope you will get sometime to read the attached file (especially pp.33), hope it might be of some help as well.