Interaction effects

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Hi Ananda,
I just send you an email with an Excel template for calculating the tdifference test by Chin. Please pay attention that there is a small bug in the formula by Chin for unequal error terms. More information about that you can find in following article on pp. 199:
Marko Sarstedt, Jörg Henseler, Christian M. Ringle (2011), Multigroup Analysis in Partial Least Squares (PLS) Path Modeling: Alternative Methods and Empirical Results, in Marko Sarstedt, Manfred Schwaiger, Charles R. Taylor (ed.) Measurement and Research Methods in International Marketing (Advances in International Marketing, Volume 22), Emerald Group Publishing Limited, pp.195218
Greetings,
Christian
I just send you an email with an Excel template for calculating the tdifference test by Chin. Please pay attention that there is a small bug in the formula by Chin for unequal error terms. More information about that you can find in following article on pp. 199:
Marko Sarstedt, Jörg Henseler, Christian M. Ringle (2011), Multigroup Analysis in Partial Least Squares (PLS) Path Modeling: Alternative Methods and Empirical Results, in Marko Sarstedt, Manfred Schwaiger, Charles R. Taylor (ed.) Measurement and Research Methods in International Marketing (Advances in International Marketing, Volume 22), Emerald Group Publishing Limited, pp.195218
Greetings,
Christian

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Some hints when you use the Excel table:
As you can read in the recommended article above there are two different ttest depending on equal or unequal variances between the groups. Therefore you have to test first if the variances between your groups are equal or unequal. The necessary results of this Ftest you can find in the box right. Is this value above 0.95 or below 0.05 the variance have to be seen as unequal and you have to use the right column in the box which is in the middle. The typical cutting value for the test starts with a pvalue below 0.10.
Greetings,
Christian
As you can read in the recommended article above there are two different ttest depending on equal or unequal variances between the groups. Therefore you have to test first if the variances between your groups are equal or unequal. The necessary results of this Ftest you can find in the box right. Is this value above 0.95 or below 0.05 the variance have to be seen as unequal and you have to use the right column in the box which is in the middle. The typical cutting value for the test starts with a pvalue below 0.10.
Greetings,
Christian

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Dear PLS community,
There is a new download link for the above mentioned working paper (only in German) „Eine anwenderorientierte Einführung in die Partial Least Square (PLS)Methode”:
http://papers.ssrn.com/sol3/papers.cfm? ... id=2097324
Cheers,
Christian
There is a new download link for the above mentioned working paper (only in German) „Eine anwenderorientierte Einführung in die Partial Least Square (PLS)Methode”:
http://papers.ssrn.com/sol3/papers.cfm? ... id=2097324
Cheers,
Christian
Last edited by christian.nitzl on Thu Jul 05, 2012 1:36 pm, edited 1 time in total.

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Dear Christian, and everyone else,
first, thanks a lot for your excel sheet! It has been of great help already.
I have entered all my data this morning and got surprising results, already for the test of homogeneity of variances. Usually these values should range from 01, right? In my case, I got values of 2.4, etc. May this be caused by very uneven sizes of the two groups? (male: 1091, female: 355)  I know that generally group sizes should be rather similar.
Moreover, I have a question about the procedure of the multigroup analysis with more than 2 groups. I have other variables with up to 5 categories and I am very unsure about how to attack this topic.
Thanks in Advance,
best wishes,
Cornelia
first, thanks a lot for your excel sheet! It has been of great help already.
I have entered all my data this morning and got surprising results, already for the test of homogeneity of variances. Usually these values should range from 01, right? In my case, I got values of 2.4, etc. May this be caused by very uneven sizes of the two groups? (male: 1091, female: 355)  I know that generally group sizes should be rather similar.
Moreover, I have a question about the procedure of the multigroup analysis with more than 2 groups. I have other variables with up to 5 categories and I am very unsure about how to attack this topic.
Thanks in Advance,
best wishes,
Cornelia

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Dear Cornelia,
You are welcome!
Indeed your results seems strange for me too. Maybe there is a typing error or you overlook the sign “E” at the end what means your figure is very small. Please check this once again. The results for the test of homogeneity of variances have to be between 0 and 1 because it displays probabilities.
One way to do a test with more than two groups is to define a reference group and compare all other groups with this reference group. This is also a method used in regression analysis. A good example for that you can find in following literature: Eberl, M. (2010): An Application of PLS in MultiGroup Analysis: The Need for Differentiated CorporateLevel Marketing in the Mobile Communications Industry, in: Esposito Vinzi, V./Chin, W./Henseler J./Wang, H. (Hrsg.): Handbook of Partial Least Squares: Concepts, Methods and Applications, Berlin, S. 487514.
I hope that helps!
Christian
You are welcome!
Indeed your results seems strange for me too. Maybe there is a typing error or you overlook the sign “E” at the end what means your figure is very small. Please check this once again. The results for the test of homogeneity of variances have to be between 0 and 1 because it displays probabilities.
One way to do a test with more than two groups is to define a reference group and compare all other groups with this reference group. This is also a method used in regression analysis. A good example for that you can find in following literature: Eberl, M. (2010): An Application of PLS in MultiGroup Analysis: The Need for Differentiated CorporateLevel Marketing in the Mobile Communications Industry, in: Esposito Vinzi, V./Chin, W./Henseler J./Wang, H. (Hrsg.): Handbook of Partial Least Squares: Concepts, Methods and Applications, Berlin, S. 487514.
I hope that helps!
Christian

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Dear Christian,
you're right! I indeed oversaw the "E"  that makes the results a lot more logical! :)
Thanks a lot for your help, also for the advice on the multigroup comparison. Do you have any idea what would be a good comparison group there? Wouldn't the most suitable solution be to either take the entire sample as a comparison group or alternatively (in order to reduce differences in size) to extract a random sample from the entire sample in order to have some representativeness in the comparison group?
Thanks a lot!!
Cornelia
you're right! I indeed oversaw the "E"  that makes the results a lot more logical! :)
Thanks a lot for your help, also for the advice on the multigroup comparison. Do you have any idea what would be a good comparison group there? Wouldn't the most suitable solution be to either take the entire sample as a comparison group or alternatively (in order to reduce differences in size) to extract a random sample from the entire sample in order to have some representativeness in the comparison group?
Thanks a lot!!
Cornelia

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Dear everyone,
one more question from my side:
I have also checked for some moderating effects with metric variables and therefore created interaction variables which were integrated into the model.
Even though both variables (IV + mod) were  individually  positively related to the DV, the interaction variable has a negative path coefficient?
How do I interpret this value? Is this really a negative effect on the DV,  or is it rather the case that the inclusion of the moderator reduces the initial effect and that therefore the coefficient is negative.
Hope I have made my question clear, it seems a little confusing now I've written it down..
Thank you everyone,
Cornelia
one more question from my side:
I have also checked for some moderating effects with metric variables and therefore created interaction variables which were integrated into the model.
Even though both variables (IV + mod) were  individually  positively related to the DV, the interaction variable has a negative path coefficient?
How do I interpret this value? Is this really a negative effect on the DV,  or is it rather the case that the inclusion of the moderator reduces the initial effect and that therefore the coefficient is negative.
Hope I have made my question clear, it seems a little confusing now I've written it down..
Thank you everyone,
Cornelia

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Dear Cornelia,
ad 1) In my opinion you should use one of the group you already have as a reference group. Think about if there is a group which can serve you as a starting point. An “interesting” group, not a catchall like “Other” and large enough to be used across multiple studies.
ad 2) You should not interpret the direct effect from your “mod” to your “DV”. It is possible to have a negative interaction effect. That should not disturb you. It only means that your moderator have an negative effect on your direct path connection (slope). Here you can find an interesting link how to test and interpret moderator effects with an example in German: http://papers.ssrn.com/sol3/papers.cfm? ... id=2097324
Best,
Christian
ad 1) In my opinion you should use one of the group you already have as a reference group. Think about if there is a group which can serve you as a starting point. An “interesting” group, not a catchall like “Other” and large enough to be used across multiple studies.
ad 2) You should not interpret the direct effect from your “mod” to your “DV”. It is possible to have a negative interaction effect. That should not disturb you. It only means that your moderator have an negative effect on your direct path connection (slope). Here you can find an interesting link how to test and interpret moderator effects with an example in German: http://papers.ssrn.com/sol3/papers.cfm? ... id=2097324
Best,
Christian
Last edited by christian.nitzl on Thu Jul 05, 2012 1:36 pm, edited 2 times in total.

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Hi Christian, could you please send me this excel template. My email is oddotoddo2@msn.com.christian.nitzl wrote:Hey Iin,
if you send me your email I would can send you a example excel template for a ttest.
Best regards,
Christian
Thank you,
Todd
Is Ho that groups are equal?
IS the Ho that groups are equal? In other words if the pvalue is greater than 0.10 it means the groups are unequal....or is it the other way around?christian.nitzl wrote:Some hints when you use the Excel table:
As you can read in the recommended article above there are two different ttest depending on equal or unequal variances between the groups. Therefore you have to test first if the variances between your groups are equal or unequal. The necessary results of this Ftest you can find in the box right. Is this value above 0.95 or below 0.05 the variance have to be seen as unequal and you have to use the right column in the box which is in the middle. The typical cutting value for the test starts with a pvalue below 0.10.
Greetings,
Christian
Another question. If the path for both groups is non significant but the R2 attributed to the independent variable is greater than 0,02 (0.16 for one) is there a way to explain this as a relevant finding?

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H0 is the assumption that the groups are equal. That means that you can reject H0 if pvalue is ‘smaller’ than 0.10.
One explanation for your second question is that your sample size is too small for detecting a significant path coefficient. But the effect size is relatively high. With a high sample size ‘every’ path could become significant. But the effect size (the influence of a construct to another construct measured with R2) is not influenced by the sample size in this way. Therefore the insignificant path and the relative high R2 could be an indication that you power is small because your sample size is too small for your model. But this is only an idea! Maybe there are some other explanations.
Best regards,
Christian
One explanation for your second question is that your sample size is too small for detecting a significant path coefficient. But the effect size is relatively high. With a high sample size ‘every’ path could become significant. But the effect size (the influence of a construct to another construct measured with R2) is not influenced by the sample size in this way. Therefore the insignificant path and the relative high R2 could be an indication that you power is small because your sample size is too small for your model. But this is only an idea! Maybe there are some other explanations.
Best regards,
Christian