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I am structuring a model in which I would like to hypothesize that, though two paths might both be significant, one of the paths should be significantly (in the statistical sense) greater than the other.

The approach I thought of taking to prove the above, is as follows. Bootstrapping gives us t-values that test the significance of path coefficients (that is, whether the paths are significantly different from 0). I would assume that using the t-values, and the t-statistic forumula, we can derive the observed variance of each path coefficient. With this, we can recalculate a t-value that compares the path coefficient against an alternate value (another path coefficient). Alternatively, we can calculate confidence intervals for the paths.

Is my thinking correct on this? Is there another way to statistically compare path coefficients or calculate confidence intervals?

thanks!

Soumya

in addition to what i suggested above, i now realize after talking to a colleague that if the above technique to compare two paths is valid, then i need to calculate the variance of both exogenous paths and use a pooled variance t-test... right?

Step 1: Prove that both the paths are significant using boot strap or jack knife techniques(t-statistics)

Step 2: Compare beta values of the two paths. Greater beta implies greater impact on dependent construct

Thanks once again for the prompt reply Vivek!

Couple more questions if you would indulge:

1. Is it appropriate to compare path coefficients of two paths which originate from the same exogenous variable, but go to different endogenous variables?

2. How small/great must the difference between path be before we can assert with some confidence that they are indeed statistically different?

I was hoping that a t- difference test would adequately answer #2...

thanks!

Soumya

Paths can originate from any place. You just compare the beta values.
There is no method to compare the significance of path coeff differences

Hi,

the ideas of Soumya are correct.
We could compare paths using t-tests

t = (load1 – load2)/((SE1 ^2 + SE2 ^2)^0,5)

More details in viewtopic.php?p=1425&highlight=#1425

Reference in viewtopic.php?t=16 (EFRON)

Best regards.

Bido

Thanks prof Bido

I have a few doubts
1. Why do we have to see a significanct difference in path coefficients
2. If SE in bootstrap is used, will this value not change every time you run the bootstrap?

Regards

Vivek

Hi Vivek,

1) One path (Ho: coef_in_population = 0)
if sig. < 0,05 ==> we'll reject the Ho, then in the population the coef. will be different of zero (with 95% of confidence).
Comparing two paths (Ho: coef_1_in_popul = coef_2_in_popul)
if sig. < 0,05 ==> we'll reject the Ho, then in the population the coef. will be different one of another (with 95% of confidence).

When we are comparing two models, usually it is expected that the measurement model be invariant (the differences between loadings should have sig. > 0,05 or t < 2). In this way we will have the same constructs in all models, then we could compare the paths (structural).

2) You are correct, but this change is very small, even with just 50 resamples. For instance, when t > 2 (or sig<0,05) in a bootstrap, the value will be different in another bootstrap, but not < 2.

Best regards.

Bido

Thanks, prof.
Does this mean that we can compare all the path coefficients two at a time for significant differences? This could be used to identify the strongest paths in the model.

Regards

Vivek

Yes,
in the case of more than two paths at the same time, use ANOVA.

Best regards.
Bido

I hadn't thought of Vivek's concern #2, so I am glad to see it addressed before anyone asked me about it. And the ANOVA suggestion is very helpful too.

Thank you both for this fruitful discussion!