Definition of SSE and SSO when calculating Q-Square
Posted: Mon Aug 17, 2020 10:20 am
Dear SmartPLS community members,
while writing the documentation of my model evaluation with SmartPLS I have some problems with the calculation and definition of SSO and SSE in SmartPLS 3.3.0.
While looking at the formula for SSO in different papers I find that SSO should be the sum of squares of observations for each variable. When looking at the SmartPLS output I find that SSO is always calculated as: Sample Size * Number of Indicators. (For example in the SmartPLS Book (German Version Page 188) SSO for ATTR is 1032,00 which equals 3 * 344.
So is it still true that SSO is the sum of squares of observations? Finally this leads to another problem, when calculating Q-Square. In my understanding Q-Square represents a comparison of the prediction errors of the model and the prediction errors of a simple estimation by the mean values? Where in the formula is the representation of the mean value estimation, when we calculate Q-Square = (1 - SSE/SSO)?
Can someone please explain to me if I miss any intermediate steps or how SSO is exactly calculated so that it is exactly 1 for every data point of the latent variable (Sample Size * Number of Indicators)?
I would be very grateful for every explanation.
Best regards
Fabian
while writing the documentation of my model evaluation with SmartPLS I have some problems with the calculation and definition of SSO and SSE in SmartPLS 3.3.0.
While looking at the formula for SSO in different papers I find that SSO should be the sum of squares of observations for each variable. When looking at the SmartPLS output I find that SSO is always calculated as: Sample Size * Number of Indicators. (For example in the SmartPLS Book (German Version Page 188) SSO for ATTR is 1032,00 which equals 3 * 344.
So is it still true that SSO is the sum of squares of observations? Finally this leads to another problem, when calculating Q-Square. In my understanding Q-Square represents a comparison of the prediction errors of the model and the prediction errors of a simple estimation by the mean values? Where in the formula is the representation of the mean value estimation, when we calculate Q-Square = (1 - SSE/SSO)?
Can someone please explain to me if I miss any intermediate steps or how SSO is exactly calculated so that it is exactly 1 for every data point of the latent variable (Sample Size * Number of Indicators)?
I would be very grateful for every explanation.
Best regards
Fabian