hi
smart pls have any goodness index?
how we can evaluate our model ? in amos and lisrel we see many indexes like NFI,GFI and ....
but in pls???
any goodness index
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kristianak
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Hengkov
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Hello Hesw,
According to Latan and Ghozali (2012a): GoF 0.10 (Small), 0.25 (Medium) and 0.36 (Large).
Latan, H and Ghozali, I. (2012a). Partial Least Squares: Concept, Technique and Application using Program SmartPLS for Empirical Research, BP UNDIP.
Or
According to Latan and Ghozali (2012b): GoF 0.35 (Small), 0.50 (Medium) and 0.61 (Large).
Latan, H., and Ghozali, I. (2012b). Partial Least Squares: Concept and Application Path Modeling using program XLSTAT-PLS for Empirical Research, BP UNDIP.
GoF greather is good.
Next, because you have only one endogenous variable, average R-square = R-square one endogenous variable, OK.
Regards,
Hengky
According to Latan and Ghozali (2012a): GoF 0.10 (Small), 0.25 (Medium) and 0.36 (Large).
Latan, H and Ghozali, I. (2012a). Partial Least Squares: Concept, Technique and Application using Program SmartPLS for Empirical Research, BP UNDIP.
Or
According to Latan and Ghozali (2012b): GoF 0.35 (Small), 0.50 (Medium) and 0.61 (Large).
Latan, H., and Ghozali, I. (2012b). Partial Least Squares: Concept and Application Path Modeling using program XLSTAT-PLS for Empirical Research, BP UNDIP.
GoF greather is good.
Next, because you have only one endogenous variable, average R-square = R-square one endogenous variable, OK.
Regards,
Hengky
Thanks for the literature tip!! Btw, do you know where you can get them? I searched for them but couldn't get a hold of any article.
So, I read Tenenhaus et al. (2005) and Henseler/Sarstedt (2012) today and according to them (especially the former) it's as follows:
Average communality = You add up all squared indicator-construct correlations and divide them by the total number of indicators in your model.
Actually it's the sum of [AVE(i) divided by the number of indicators of construct (i)] over all constructs in your model and then divided by the total number of indicators.
Or simply 1/n*sum [AVE(i)]. But somehow, in my case, the "simplified" mean of the AVE taken from the SmartPLS spreadsheets and the "correct" way to calculate it differed a bit. Maybe due to fewer decimals...
Example: construct 'Affect' has indicator correlations of aff_x1=0,869, aff_x2=0,789 and aff_x3=0,923. And another one 'Intention' has int_x1=0,846, int_x2=0,799, int3_x3=0,856.
Then, the average communality would compute as:
1/6 * (0,869²+0,789²+0,923²+0,846²+0,799²+0,856²) = 0,719.
The AVE (in a standardized case) for 'Affect' would be 1/3*(0,869²+0,789²+0,923²0,743)=0,743.
Average R² = mean of all endogenous variables' R²
Given the above example, if an average R² would be 0,234 the GoF would compute as: Square Root (0,719*0,234) = 0,41.
Am I wrong?
Henseler/Sarstedt (2012) have good overview table with results you can reproduce.
Henseler/Sarstedt (2012): Goodness-of-fit indices for partial least squares path modeling, in: Springer.
So, I read Tenenhaus et al. (2005) and Henseler/Sarstedt (2012) today and according to them (especially the former) it's as follows:
Average communality = You add up all squared indicator-construct correlations and divide them by the total number of indicators in your model.
Actually it's the sum of [AVE(i) divided by the number of indicators of construct (i)] over all constructs in your model and then divided by the total number of indicators.
Or simply 1/n*sum [AVE(i)]. But somehow, in my case, the "simplified" mean of the AVE taken from the SmartPLS spreadsheets and the "correct" way to calculate it differed a bit. Maybe due to fewer decimals...
Example: construct 'Affect' has indicator correlations of aff_x1=0,869, aff_x2=0,789 and aff_x3=0,923. And another one 'Intention' has int_x1=0,846, int_x2=0,799, int3_x3=0,856.
Then, the average communality would compute as:
1/6 * (0,869²+0,789²+0,923²+0,846²+0,799²+0,856²) = 0,719.
The AVE (in a standardized case) for 'Affect' would be 1/3*(0,869²+0,789²+0,923²0,743)=0,743.
Average R² = mean of all endogenous variables' R²
Given the above example, if an average R² would be 0,234 the GoF would compute as: Square Root (0,719*0,234) = 0,41.
Am I wrong?
Henseler/Sarstedt (2012) have good overview table with results you can reproduce.
Henseler/Sarstedt (2012): Goodness-of-fit indices for partial least squares path modeling, in: Springer.
I know, but for some reason the average AVE differs from the mean of the sum of all squared indicator correlations - at least in my model.needpls wrote:hi
Hengkov thx so much
and Joules i think that it is correct and u can see AVE in repport no need to compute it with hand.
best regards
There, i get an average AVE of 0,780 whereas the mean of the sum of all squared indicator correlations show 0,783. Does anyone know what the reason for that is?
Hengkov wrote:Hello Hesw,
According to Latan and Ghozali (2012a): GoF 0.10 (Small), 0.25 (Medium) and 0.36 (Large).
Latan, H and Ghozali, I. (2012a). Partial Least Squares: Concept, Technique and Application using Program SmartPLS for Empirical Research, BP UNDIP.
Or
According to Latan and Ghozali (2012b): GoF 0.35 (Small), 0.50 (Medium) and 0.61 (Large).
Latan, H., and Ghozali, I. (2012b). Partial Least Squares: Concept and Application Path Modeling using program XLSTAT-PLS for Empirical Research, BP UNDIP.
GoF greather is good.
Next, because you have only one endogenous variable, average R-square = R-square one endogenous variable, OK.
Regards,
Hengky
hi
can u say me how can i find this articles?
Goodness of Fit - Rule of thumb
Hi, guys.
I am a little bit confused by the two classifications of GoF given by:
1) Latan and Ghozali (2012a):
GoF >= 0.10 (Small)
GoF >= 0.25 (Medium)
GoF >= 0.36 (Large)
and
2) Latan and Ghozali (2012b):
GoF >= 0.35 (Small)
GoF >= 0.50 (Medium)
GoF >= 0.61 (Large)
I have a model which GoF is 0,279. According to the first article the model has a Medium GoF and according to the second one - a Small one.
And here is my question - when reporting the results of my study (Master thesis), should I state that the model has a Medium or a Small Goodness of Fit?
And one more question in that direction:
My model consists of seven constructs experiencing the following R Squares:
Construct 1: 0,019
Construct 2: 0,365
Construct 3: 0,095
Construct 4: 0,083
Construct 5: 0,343
Construct 6: (no value)
Construct 7: 0,241
And Communality:
Construct 1: 0,425
Construct 2: 0,617
Construct 3: 0,247
Construct 4: 0,562
Construct 5: 0,169
Construct 6: 0,367
Construct 7: 0,463
So, I computed the avr_Communality and avr_R_Squared and take the square root out of avr_Communality*avr_R_Squared. That is how I found GoF.
And here is my question:
When I calculate the avr for R_Square, should I sum all of the values for the seven constructs, including 0 for the missing value of Construct 6, and then divide it by 7 or should I exclude Construct 6 from both of the calculations of avr_Communality and avr_R_Squared and work only with the rest 6 constructs?
Thank you in advance :)
I am a little bit confused by the two classifications of GoF given by:
1) Latan and Ghozali (2012a):
GoF >= 0.10 (Small)
GoF >= 0.25 (Medium)
GoF >= 0.36 (Large)
and
2) Latan and Ghozali (2012b):
GoF >= 0.35 (Small)
GoF >= 0.50 (Medium)
GoF >= 0.61 (Large)
I have a model which GoF is 0,279. According to the first article the model has a Medium GoF and according to the second one - a Small one.
And here is my question - when reporting the results of my study (Master thesis), should I state that the model has a Medium or a Small Goodness of Fit?
And one more question in that direction:
My model consists of seven constructs experiencing the following R Squares:
Construct 1: 0,019
Construct 2: 0,365
Construct 3: 0,095
Construct 4: 0,083
Construct 5: 0,343
Construct 6: (no value)
Construct 7: 0,241
And Communality:
Construct 1: 0,425
Construct 2: 0,617
Construct 3: 0,247
Construct 4: 0,562
Construct 5: 0,169
Construct 6: 0,367
Construct 7: 0,463
So, I computed the avr_Communality and avr_R_Squared and take the square root out of avr_Communality*avr_R_Squared. That is how I found GoF.
And here is my question:
When I calculate the avr for R_Square, should I sum all of the values for the seven constructs, including 0 for the missing value of Construct 6, and then divide it by 7 or should I exclude Construct 6 from both of the calculations of avr_Communality and avr_R_Squared and work only with the rest 6 constructs?
Thank you in advance :)
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Hengkov
- PLS Super-Expert
- Posts: 1599
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- Real name and title: Hengky Latan
- Location: AMQ, Indonesia
- Contact:
Hi Lyudmi,
This is My books, no article.
Your communality construct very low, please check outer loading must higher than 0.6 or 0.7.
Next, construct 6, R-square = 0 it's mean this construct is exogenous. You just compute R-square endogenous for asses GoF.
Because PLS not provide any goodness of fit indices, Tenenhaus et al. (2004) create formula for compute GoF in PLS:
SQRT average Com * average R-squares
But Tenenhaus et al. (2004) not provide cut-off value for interpretation this GoF similar CB-SEM such, RMSEA < 0.8, CFI > 0.95, TLI > 0.90 etc.
We create rule of thumb similar effect size and q-predictive relevance for GoF above:
The basic idea and illustration below:
Communality / AVE recommendation Fornell and Larcker (1981) = 0.50
R-squares recommendation Hair et al. 0.25 (weak), 0.50 (moderate) and 0.75 (strong), so Latan dan Ghozali (2012b) create:
GoF small : SQRT 0.5 * 0.25 = 0.35
GoF medium: SQRT 0.5 * .50 = 0.50
GoF large : SQRT 0.5 * 0.75 = 0.61
GoF is important issue for develop in PLS.
References:
Fornell, C., and Larcker, D.F. 1981. “Evaluating Structural Equation Models with Unobservable Variables and Measurement Error,” Journal of Marketing Research (18:1), pp. 39-50.
Hair, J. F., Ringle, C. M., and Sarstedt, M. 2011. “PLS-SEM: Indeed A Silver Bullet,” Journal of Merketing Theory and Practice (19:2), pp. 139-150.
Latan, H., and Ghozali, I. 2012a. Partial Least Squares: Concept, Technique and Application SmartPLS, BP UNDIP.
Latan, H., and Ghozali, I. 2012b. Partial Least Squares: Concept and Application Path Modeling using XLSTAT-PLS, BP UNDIP
Tenenhaus, M., Amato, S., and Esposito Vinzi, V. 2004. “A global goodness-of-fit index for PLS structural equation modeling,” Proceedings of the XLII SIS Scientific Meeting, Vol. Contributed Papers, CLEUP, Padova, pp. 739–742.
Best Regards,
Hengky
This is My books, no article.
Your communality construct very low, please check outer loading must higher than 0.6 or 0.7.
Next, construct 6, R-square = 0 it's mean this construct is exogenous. You just compute R-square endogenous for asses GoF.
Because PLS not provide any goodness of fit indices, Tenenhaus et al. (2004) create formula for compute GoF in PLS:
SQRT average Com * average R-squares
But Tenenhaus et al. (2004) not provide cut-off value for interpretation this GoF similar CB-SEM such, RMSEA < 0.8, CFI > 0.95, TLI > 0.90 etc.
We create rule of thumb similar effect size and q-predictive relevance for GoF above:
The basic idea and illustration below:
Communality / AVE recommendation Fornell and Larcker (1981) = 0.50
R-squares recommendation Hair et al. 0.25 (weak), 0.50 (moderate) and 0.75 (strong), so Latan dan Ghozali (2012b) create:
GoF small : SQRT 0.5 * 0.25 = 0.35
GoF medium: SQRT 0.5 * .50 = 0.50
GoF large : SQRT 0.5 * 0.75 = 0.61
GoF is important issue for develop in PLS.
References:
Fornell, C., and Larcker, D.F. 1981. “Evaluating Structural Equation Models with Unobservable Variables and Measurement Error,” Journal of Marketing Research (18:1), pp. 39-50.
Hair, J. F., Ringle, C. M., and Sarstedt, M. 2011. “PLS-SEM: Indeed A Silver Bullet,” Journal of Merketing Theory and Practice (19:2), pp. 139-150.
Latan, H., and Ghozali, I. 2012a. Partial Least Squares: Concept, Technique and Application SmartPLS, BP UNDIP.
Latan, H., and Ghozali, I. 2012b. Partial Least Squares: Concept and Application Path Modeling using XLSTAT-PLS, BP UNDIP
Tenenhaus, M., Amato, S., and Esposito Vinzi, V. 2004. “A global goodness-of-fit index for PLS structural equation modeling,” Proceedings of the XLII SIS Scientific Meeting, Vol. Contributed Papers, CLEUP, Padova, pp. 739–742.
Best Regards,
Hengky
Thank you very much for the fast reply Hengky!
However, I want to ask you a couple of other things. You say:
"Next, construct 6, R-square = 0 it's mean this construct is exogenous. You just compute R-square endogenous for asses GoF. "
This means that the average Comunality should also be computed only for endogenous constructs (excluding Construct 6 from the calculation of avr_Communality), right?
Then you say:
"Communality / AVE recommendation Fornell and Larcker (1981) = 0.50"
meaning that both of them should be greater than 0.50 to be considered significant, right?
Concerning the above things, my model (a reflective one) and my data:
Communality
Construct 1: 0,425 < 0.50
Construct 2: 0,617 O.K.
Construct 3: 0,247 < 0.50
Construct 4: 0,562 O.K.
Construct 5: 0,169 < 0.50
Construct 6: 0,367 < 0.50
Construct 7: 0,463 < 0.50
Average variance extracted (AVE)
Construct 1: 0,425 < 0.50
Construct 2: 0,617 O.K.
Construct 3: 0,247 < 0.50
Construct 4: 0,562 O.K.
Construct 5: 0,169 < 0.50
Construct 6: 0,367 < 0.50
Construct 7: 0,463 < 0.50
R Sqrd
Construct 1: 0,019 <0.25
Construct 2: 0,365 0.25< weak <0.50
Construct 3: 0,095 <0.25
Construct 4: 0,083 <0.25
Construct 5: 0,343 0.25< weak <0.50
Construct 6:
Construct 7: 0,241 <0.25
Construct | Nr. of items | Mean | Standard deviation
Construct 1: 9 | 2,56 | 1,06
Construct 2: 4 | 2,42 | 1,32
Construct 3: 15 | 1,99 | 0,77
Construct 4: 4 | 3,99 | 0,88
Construct 5: 20 | 4,37 | 1,68
Construct 6: 10 | 3,59 | 1,19
Construct 7: 8 | 2,12 | 1
Squared Correlations among Constructs
sqr_AVE | C1 | C2 | C3 | C4 | C5 | C6 | C7
0,181 | 1,000
0,380 | 0,352 | 1,000 |
0,061 | 0,005 | 0,024 | 1,000 |
0,316 | 0,019 | 0,010 | 0,017 | 1,000 |
0,029 | 0,002 | 0,005 | 0,213 | 0,012 | 1,000 |
0,135 | 0,003 | 0,004 | 0,095 | 0,083 | 0,235 | 1,000 |
0,214 | 0,219 | 0,026 | 0,008 | 0,000 | 0,001 | 0,006 | 1,000
Can I do something to improve my model and results? Can I say that the model is reliable (GoF=0.334)?
Greetings,
Lyudmil
However, I want to ask you a couple of other things. You say:
"Next, construct 6, R-square = 0 it's mean this construct is exogenous. You just compute R-square endogenous for asses GoF. "
This means that the average Comunality should also be computed only for endogenous constructs (excluding Construct 6 from the calculation of avr_Communality), right?
Then you say:
"Communality / AVE recommendation Fornell and Larcker (1981) = 0.50"
meaning that both of them should be greater than 0.50 to be considered significant, right?
Concerning the above things, my model (a reflective one) and my data:
Communality
Construct 1: 0,425 < 0.50
Construct 2: 0,617 O.K.
Construct 3: 0,247 < 0.50
Construct 4: 0,562 O.K.
Construct 5: 0,169 < 0.50
Construct 6: 0,367 < 0.50
Construct 7: 0,463 < 0.50
Average variance extracted (AVE)
Construct 1: 0,425 < 0.50
Construct 2: 0,617 O.K.
Construct 3: 0,247 < 0.50
Construct 4: 0,562 O.K.
Construct 5: 0,169 < 0.50
Construct 6: 0,367 < 0.50
Construct 7: 0,463 < 0.50
R Sqrd
Construct 1: 0,019 <0.25
Construct 2: 0,365 0.25< weak <0.50
Construct 3: 0,095 <0.25
Construct 4: 0,083 <0.25
Construct 5: 0,343 0.25< weak <0.50
Construct 6:
Construct 7: 0,241 <0.25
Construct | Nr. of items | Mean | Standard deviation
Construct 1: 9 | 2,56 | 1,06
Construct 2: 4 | 2,42 | 1,32
Construct 3: 15 | 1,99 | 0,77
Construct 4: 4 | 3,99 | 0,88
Construct 5: 20 | 4,37 | 1,68
Construct 6: 10 | 3,59 | 1,19
Construct 7: 8 | 2,12 | 1
Squared Correlations among Constructs
sqr_AVE | C1 | C2 | C3 | C4 | C5 | C6 | C7
0,181 | 1,000
0,380 | 0,352 | 1,000 |
0,061 | 0,005 | 0,024 | 1,000 |
0,316 | 0,019 | 0,010 | 0,017 | 1,000 |
0,029 | 0,002 | 0,005 | 0,213 | 0,012 | 1,000 |
0,135 | 0,003 | 0,004 | 0,095 | 0,083 | 0,235 | 1,000 |
0,214 | 0,219 | 0,026 | 0,008 | 0,000 | 0,001 | 0,006 | 1,000
Can I do something to improve my model and results? Can I say that the model is reliable (GoF=0.334)?
Greetings,
Lyudmil