Hello,
In Chin and Newsted "SEM analysis with small samples" it says that if one were to use a "regression heuristic of 10 cases per predictor" the sample size requirement would be 10 times either the dependet LV with the largest number of idnependent LVs influencing it or the block with the largest number of formative indicators.
the only think I dont understand is what a "regression heuristiv of 10 cases per predictor" is?!??!? Can someone explain this phrase to me please?
Thanks a lot!!
Sample size rule of thumb
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Diogenes
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Hi Ken,
the correct way to compute the sample size is using Power analysis, but for the multiple regression analysis the results are about 10 cases/independent variable (heuristic).
See
viewtopic.php?t=474&highlight=power
viewtopic.php?t=103&highlight=g%2Apower
viewtopic.php?t=177&highlight=power
Best regards.
Bido
the correct way to compute the sample size is using Power analysis, but for the multiple regression analysis the results are about 10 cases/independent variable (heuristic).
See
viewtopic.php?t=474&highlight=power
viewtopic.php?t=103&highlight=g%2Apower
viewtopic.php?t=177&highlight=power
Best regards.
Bido
Sample size
hello
My question relates to the sample size calculation using G*power--
I have almost read all the posts regarding this topic-- but am still unable to use the G*power. I am testing two different models (not related to each other)
First PLS model- I have 4 first order factors(each wth 4 MVs) and one second order factor (superblock approach). How to find sample size for this model using G*power.
I mean, which options in the G*POWER should I select, i.e., among TEST FAMAILY and STATISTICAL TEST OPTIONS in G*POWER options.
Second PLS model-I have one independent (second order factor-superblock approach) and 3 dependent variables(first order factors with 5, 9, & 3 Ms respectively) in my model. how to find sample size using G*power options.
I would be thankful if someone helps me in this regard, if I use the power of 0.80 and medium effec effect size
I want to know the options to be selected in G*power.
Regards
Jahanvash Karim
My question relates to the sample size calculation using G*power--
I have almost read all the posts regarding this topic-- but am still unable to use the G*power. I am testing two different models (not related to each other)
First PLS model- I have 4 first order factors(each wth 4 MVs) and one second order factor (superblock approach). How to find sample size for this model using G*power.
I mean, which options in the G*POWER should I select, i.e., among TEST FAMAILY and STATISTICAL TEST OPTIONS in G*POWER options.
Second PLS model-I have one independent (second order factor-superblock approach) and 3 dependent variables(first order factors with 5, 9, & 3 Ms respectively) in my model. how to find sample size using G*power options.
I would be thankful if someone helps me in this regard, if I use the power of 0.80 and medium effec effect size
I want to know the options to be selected in G*power.
Regards
Jahanvash Karim
JAHANVASH KARIM
-
Diogenes
- PLS Super-Expert
- Posts: 899
- Joined: Sat Oct 15, 2005 5:13 pm
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Hi Jahanvash,
In this case we just have loadings (correlations), them you could use in G*Power:
- tests / correlation and regression / one correlation
- tail = two
- alpha = 0,05
- Power = 0,8
- rho = 0 (default)
Effect size (that will be detected as significant):
- small = 0,10 --> n = 782
- medium = 0,3 --> n = 84
- large = 0,5 --> n= 29
Best regards.
Bido
In this case we just have loadings (correlations), them you could use in G*Power:
- tests / correlation and regression / one correlation
- tail = two
- alpha = 0,05
- Power = 0,8
- rho = 0 (default)
Effect size (that will be detected as significant):
- small = 0,10 --> n = 782
- medium = 0,3 --> n = 84
- large = 0,5 --> n= 29
Best regards.
Bido
Effect size
Dear sir
Thank you very much for your prompt reply. I used the GPower and found the same results..
Here I have two other important questions regarding the same two models
Model 1... with one second order factor (reflective & superblock approach) and 4 first order factors (each with 4 MVs). this model is for confirming the factor structure of one instrument
Model 2... is the exention of Model 1 above--in which 3 paths lead from Second order factor towards 3 first order factors....x1 (with 2 MVs), X2 (with 7 MVs) and x3 (with 2 MVs)-------this model intends to find the predictive/criterion related validity of the instrument.
as you are aware that many journals now a days require REPORTING OF EFFECT SIZE....
HOW effect size is determined in GPOWER?
1) should I use the option-------- tests --correlation and regression------multiple R-square deviation from zero----DETERMINE------and put the computed R squares from model 2 in the Determine section (one by one for 3 r squares obtained for model 2? this will give me three effect sizes for each dependent variable
2) or should i use the option----Tests----Corelation and regression-----difference from constant (one sample case)---determine ------
3) should i calculate the effect size for both models or just for only second model? (i think logically it sounds just for second model where we have r square values for 3 dependent variables)
waiting for your kind response in this regard
Jahanvash karim
Thank you very much for your prompt reply. I used the GPower and found the same results..
Here I have two other important questions regarding the same two models
Model 1... with one second order factor (reflective & superblock approach) and 4 first order factors (each with 4 MVs). this model is for confirming the factor structure of one instrument
Model 2... is the exention of Model 1 above--in which 3 paths lead from Second order factor towards 3 first order factors....x1 (with 2 MVs), X2 (with 7 MVs) and x3 (with 2 MVs)-------this model intends to find the predictive/criterion related validity of the instrument.
as you are aware that many journals now a days require REPORTING OF EFFECT SIZE....
HOW effect size is determined in GPOWER?
1) should I use the option-------- tests --correlation and regression------multiple R-square deviation from zero----DETERMINE------and put the computed R squares from model 2 in the Determine section (one by one for 3 r squares obtained for model 2? this will give me three effect sizes for each dependent variable
2) or should i use the option----Tests----Corelation and regression-----difference from constant (one sample case)---determine ------
3) should i calculate the effect size for both models or just for only second model? (i think logically it sounds just for second model where we have r square values for 3 dependent variables)
waiting for your kind response in this regard
Jahanvash karim
JAHANVASH KARIM
-
Diogenes
- PLS Super-Expert
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- Joined: Sat Oct 15, 2005 5:13 pm
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Hi Jahanvash,
Your 2nd model doesn’t have two or more arrays arriving in one latent variable, them we just have simple regressions (inner model – structural) and correlations (outer model – measurement), for these reasons the Power analysis done before remains the same.
G*Power has a pdf document that explains the uses of the software (priori analysis to compute sample size; post hoc analysis to assess the power of a research already done; sensibility analysis to assess the effect size that will be detected as significant).
For more information about effect size and power analysis, see:
COHEN, Jacob. Statistical power analysis for the behavioral sciences. Academic Press. (2nd Ed. in 1988).
Best regards.
Bido
Your 2nd model doesn’t have two or more arrays arriving in one latent variable, them we just have simple regressions (inner model – structural) and correlations (outer model – measurement), for these reasons the Power analysis done before remains the same.
G*Power has a pdf document that explains the uses of the software (priori analysis to compute sample size; post hoc analysis to assess the power of a research already done; sensibility analysis to assess the effect size that will be detected as significant).
For more information about effect size and power analysis, see:
COHEN, Jacob. Statistical power analysis for the behavioral sciences. Academic Press. (2nd Ed. in 1988).
Best regards.
Bido
Power analysis of Hierarchical model
Dear Sir,
I am analyzing a (3rd order) Hierarchical model with PLS. Deails of the model is following:
1) A 3rd order construct which reflects 4 second-order constructs.
A ==> B
A ==> C
A ==> D
A ==> E(4) [construct E should be called second or first-order, I am not sure]
2) 3 second-order constructs which reflect 6 first-order constructs (2 for each)
B ==> F(4); B ==> G(3)
C ==> H(3); C ==> I(4)
D ==> J(4); D ==> K(4)
Number in bracket indicates number of indicators for that construct.
3rd order construct reflect Construct E (along with the above 3 second-order constructs) which is measured by 4 indicators
3) A relationship is stablished by connecting construct K to A
k ==> A
Can you please tell me how to do power test?
With G*Power how to perform power test? Which option has to be selected in G*Power?
In this model, I think Highest number of independent constructs impacting a dependent construct is 1. Is it right?
Plesea help me.
I would be very greatful. I am struck here.
Thank you.
I am analyzing a (3rd order) Hierarchical model with PLS. Deails of the model is following:
1) A 3rd order construct which reflects 4 second-order constructs.
A ==> B
A ==> C
A ==> D
A ==> E(4) [construct E should be called second or first-order, I am not sure]
2) 3 second-order constructs which reflect 6 first-order constructs (2 for each)
B ==> F(4); B ==> G(3)
C ==> H(3); C ==> I(4)
D ==> J(4); D ==> K(4)
Number in bracket indicates number of indicators for that construct.
3rd order construct reflect Construct E (along with the above 3 second-order constructs) which is measured by 4 indicators
3) A relationship is stablished by connecting construct K to A
k ==> A
Can you please tell me how to do power test?
With G*Power how to perform power test? Which option has to be selected in G*Power?
In this model, I think Highest number of independent constructs impacting a dependent construct is 1. Is it right?
Plesea help me.
I would be very greatful. I am struck here.
Thank you.
Computing sample size of the above hierarchical model
I thank Professor Diogenes Bido for his valuable help.
If we do power analysis for the above model -
1) A priory test (estimating sample size) using G*Power 3
Step 1: Go or click
Tests => Correlation and regression => Linear multiple regression: Fixed model, R2 deviation from zero
Step 2: From Type of power analysis select
A priory: Compute required sample size - given alpha, power, and effect size
For the above hierarchical model, we calculate sample size as follows:
Input: Effect size = 0.15 (medium), alpha err prob = 0.05, power 0.95, Number of predictor = 1
Output: sample size = 89 (apart from other output)
If we do power analysis for the above model -
1) A priory test (estimating sample size) using G*Power 3
Step 1: Go or click
Tests => Correlation and regression => Linear multiple regression: Fixed model, R2 deviation from zero
Step 2: From Type of power analysis select
A priory: Compute required sample size - given alpha, power, and effect size
For the above hierarchical model, we calculate sample size as follows:
Input: Effect size = 0.15 (medium), alpha err prob = 0.05, power 0.95, Number of predictor = 1
Output: sample size = 89 (apart from other output)
Calculating power
2) Post hoc test (calculating power)
Step 1: Follow step 1 written above
Step 2: From Type of power analysis select
Post hoc: Compute achieved power - given alpha, sample size, and effect size
For the above hierarchical model, we calculate power as follows:
Input: alpha err prob = 0.05, sample size 77, Number of predictor = 1,
Effect size = here I think we have to calculate effect size by clicking on "Determine =>" button placed
before "Effect size f^2" input box
If we click determine button we get another window to compute Effect size
If we select "From predictor correlations"
We need to specify correlation matrices
In our case number of predictor is 1 (maximum number of independent variable impacting dependent variable) so 1x1 metrics then which 1 correlation should be used from our hierarchical model?
Is this approach correct?
Step 1: Follow step 1 written above
Step 2: From Type of power analysis select
Post hoc: Compute achieved power - given alpha, sample size, and effect size
For the above hierarchical model, we calculate power as follows:
Input: alpha err prob = 0.05, sample size 77, Number of predictor = 1,
Effect size = here I think we have to calculate effect size by clicking on "Determine =>" button placed
before "Effect size f^2" input box
If we click determine button we get another window to compute Effect size
If we select "From predictor correlations"
We need to specify correlation matrices
In our case number of predictor is 1 (maximum number of independent variable impacting dependent variable) so 1x1 metrics then which 1 correlation should be used from our hierarchical model?
Is this approach correct?
-
Diogenes
- PLS Super-Expert
- Posts: 899
- Joined: Sat Oct 15, 2005 5:13 pm
- Real name and title:
- Location: São Paulo - BRAZIL
- Contact:
Hi,
See p.326 – 327 (Chin & Newsted, 1999) about “a priori analysis” to sample size definition.
About post-hoc, it is ok, but I have used the sensitivity analysis (in G*Power 3), then I am able to know what is the minimum value of R2 that will be detected as significant with this sample size.
Remembering that R2 = f2/(1 + f2)
Best regards,
Bido
See p.326 – 327 (Chin & Newsted, 1999) about “a priori analysis” to sample size definition.
About post-hoc, it is ok, but I have used the sensitivity analysis (in G*Power 3), then I am able to know what is the minimum value of R2 that will be detected as significant with this sample size.
Remembering that R2 = f2/(1 + f2)
Best regards,
Bido