Interpretation problems

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Jording
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Interpretation problems

Post by Jording » Fri Nov 08, 2013 8:24 am

Hello together,

I got a question related to the interpretation of my model. The model has two formative, latent variables. An exogen one with four indicators and an endogen one with six indicators. (VIF < 1,5 for each Indikator) The following values were calculated in SmartPLS:

1 Indikators -> LV exogen:
1.1 Weight 0,1920 T-Value 0,5088 Effect f² on endogen LV 0,0303
1.2 Weight 0,1142 T-Value 0,4929 Effect f² on endogen LV 0,0120
1.3 Weight -0,0931 T-Value 0,4429 Effect f² on endogen LV 0,0095
1.4 Weight 0,6888 T-Value 2,0249 Effect f² on endogen LV 0,2852

2 Indikators -> LV endogen:
2.1 Weight 0,8380 T-Value 2,6821
2.2 Weight -0,4158 T-Value 1,4068
2.3 Weight 0,3368 T-Value 1,6423
2.4 Weight -0,0073 T-Value 0,0425
2.5 Weight 0,3069 T-Value 1,5604
2.6 Weight 0,3476T-Value 1,6453

LV exogen -> LV endogen:
Pathcoefficient: 0,871 T-Value 26,551
R² = 0,7591

My interpretation problem is, how could it be that the effect sizes are relatively small and there is no really significant on the outer weights but the inner model has such great values?

Hope someone could help me to make the right interpretation.

Greetings
Timo Jording

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Diogenes
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Post by Diogenes » Fri Nov 08, 2013 7:12 pm

Hi Timo,

Your model is equivalent to “canonical correlation”, and this is one of the reason that I do not use canonical correlation analysis!

Even with so small multicollinearity, maybe some nonsignificant outer weights could be caused by it.

Suggestion:
- Run a principal component analysis to group the indicators in orthogonal PCs.
- Copy/paste these scores to your original dataset.
- Run a new model using these scores as indicators (no multicollinearity is guaranteed)

Best regards,
Bido

Jording
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Post by Jording » Sat Nov 09, 2013 12:37 pm

Hi Bido,

thanks very much for the fast Info. Yes, you are right, now thinks are clearer :). The correlation matrix demonstrates that all Indicators are highly significant correlated. (Wonder why the VIF was so small?)

Rotation is a good hind but wouldn’t it deform the results/findings?

I think maybe the indicators shouldn’t be separated. They all together have a significant, positive influence on the endogen LV.

LV exogen 1 -> LV endogen: Pathcoefficient: 0,871; T-Value 26,551; R² = 0,7591

To check how large the influence of each indicator is and if the relationships are significant, I compare the outcome of each indicator in its own relation to the endogen LV.

Indicator 1.1 -> LV endogen: Pathcoefficient 0,8032; T-Value 10,9547; R² 0,6452
Indicator 1.2 -> LV endogen: Pathcoefficient 0,6586; T-Value 6,1194; R² 0,4337
Indicator 1.3 -> LV endogen: Pathcoefficient 0,6032; T-Value 6,1296; R² 0,3639
Indicator 1.4 -> LV endogen: Pathcoefficient 0,8657; T-Value 24,2673; R² 0,74947

The Interpretation would be:
There is a significant, positive relation between LV 1 and the endogen LV.
The highest Influence in this relation comes from indicator 1.4 and the smallest one from 1.3 but all relations are significant, positive.

What do you think of this? Did I ignored something?

Thanks and best regards
Timo

Jording
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Post by Jording » Sat Nov 09, 2013 2:18 pm

Addition:

For the inner model (LV exogen 1 -> LV endogen) I constructed a new Indicator which is a combination of all four indikators. (correlation between alle Indikators is high)

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