Thanks to both Profs. Malone and Pandey. I also received following tweet from Prof David Kenny. This is just to share with you:

Ajoy Kumar Dey @AjoyKumarDey

@doinkboy

In Structural Equation Modeling can I interpret total effects for a path for which regression weight is insignificant? - 28 Jul

Dave Kenny @doinkboy

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@AjoyKumarDey I am assuming the effect you are referring to is the effect without the mediator. I think OK to interpret in some sense.

10:06 PM - 28 Jul 14

Thank you all for providing some meaningful guidance.

Ajoy,

First, I would base your interpretations on unstandardized, not standardized. But to answer the main question, your total effect may well be significant when the direct effect and the paths composing the indirect effect are not. I think a significant indirect effect is possible, if unlikely, but I'm not completely certain of that.

If you tell us more about your model, we may be able to help more.

Pat

If there are several non-significant regression weights then it suggest a need to modify the model by removing the non-significant paths (one at a time) and retest the modified model. However, such elimination of path(s) should not only be based on statistical indices but also on the theory or hypotheses underlying the proposed models. Further, the non-significant path coefficients may also be  indicator or evidence for non-existence of the hypothesized relationship.

Drawing conclusion regarding influence of a given variable on the basis of non-significant regression (path) coefficients should be done carefully and must have some strong statistical or empirical basis to do so.

If you are expecting low power (or effect size) due to some other factors as sample size, violation of certain assumptions related to distribution then is such case 'soft modeling' (PLS based modeling) may also be recommended.

In any case some more details are required to provide more helpful suggestions.

Thanks to both Profs. Malone and Pandey. I also received following tweet from Prof David Kenny. This is just to share with you:

Ajoy Kumar Dey @AjoyKumarDey

@doinkboy

In Structural Equation Modeling can I interpret total effects for a path for which regression weight is insignificant? - 28 Jul

Dave Kenny @doinkboy

Follow Follow

@AjoyKumarDey I am assuming the effect you are referring to is the effect without the mediator. I think OK to interpret in some sense.

10:06 PM - 28 Jul 14

Thank you all for providing some meaningful guidance.

Hello!

If you are using (standardized) path weights, you can only use them to compare the effect of different independent variables on dependent variable. For example, you can say that A has more effect than B on C. This was the only conclusion. significance of effects, are directly related to significance of relations. for example, if you haven't any mediator, effect would be equal to path weight.

significant testing, depends on Type I and type II errors and consequently statistical power too ( statistical power= 1-type II error ). From the practical point, the p-value equals to (path weight)/(standard error)

I would suggest to also look at the standard errors/deviation of your point estimates. The significance is determined by dividing the point estimate by it's standard deviation, which result in a t-value  [(estimate-true)/SD]. If the t-value is higher that |2| your path will be significant. So the non significance stems from the fact that your SD are at least half the size of your point estimate. However the larger the SD the more  your point estimate will fluctuate from sample to sample. 

Hello,

To answer your question in conmprehensive detail  I'd recommend 

Hayes, A. F. (2013). Introduction to mediation, moderation, and conditional process analysis. New York: The Guilford Press.

With the Process Macro you might not even need a SEM.

Best! 

I want to Saeed's point that standardized coefficients are still limited in comparing "strength" of effects. The issue is that the standard deviations by which you're dividing are derived from your sample and subject to the limitations of the sampling strategy.

Unless your sample is fully representative of the population of interest, the sampling process may affect the standard deviations of A and B differently, in terms of over- or under-estimating the population standard deviations. This distorts the comparison.

Pat

This morn I received following reply from Prof. Kenny. For the benefit of all those who are interested in this issue it is being reproduced below:

I quote

"Dear Ajoy,

You ask about interpreting the Total Effect even if is not significant. I do suggest you read Kenny & Judd, Psych Sci of last year. There we review this topic and we cite several papers which arrive at similar conclusions. The bottom line is that it is much easier for the Indirect Effect to be significant than the Total Effect. If one relied on significance tests, one would often conclude not Total and Direct Effect, but there is an Indirect Effect. Such a conclusion makes no sense. So it does seem to me to make sense to interpret the total and direct effects, even if they are not significant.

I hope this is of some help.

Dave

David A. Kenny

Fax 860 486-2760

Webpage http://davidakenny.net/kenny.htm"

unquote.

Ajoy

Statistically in regression, insignificant effect indicate no effect of the variable on the dependent one for the considered data. 

However, if their is theoretical basis, then pl look for other model form or scrutinize your data too. I am sure you will be getting some wonderful findings.

I am happy to inform that following the suggestions of Patrick we successfully analyzed our data with Multi group SEM using AMOS and obtained excellent model fit results. Now we are confident to report total effects which will be free of any bias. Thank you all

Can I test my hypotheses by explaining total effect in SEM-PLS. Research model also includes mediator