The expression $(1-(ab+bc+ca))^2 + (a+b+c-abc)^2$ is a measure of the goodness of fit in real factor analysis. It represents the squared difference between the observed data and the estimated data from the model. A smaller value indicates a better fit of the model to the data.
The expression $(1-(ab+bc+ca))^2 + (a+b+c-abc)^2$ is calculated by taking the squared difference between the observed data and the estimated data from the model, and then summing these squared differences across all variables. This sum is known as the sum of squared residuals.
No, the expression $(1-(ab+bc+ca))^2 + (a+b+c-abc)^2$ cannot be negative in real factor analysis. This is because the squared difference between the observed data and the estimated data is always positive, and the sum of these squared differences cannot be negative.
The expression $(1-(ab+bc+ca))^2 + (a+b+c-abc)^2$ provides a measure of the overall fit of the model to the data. A smaller value indicates a better fit, and therefore, a more accurate interpretation of the relationships between variables in the model. It also helps in comparing the fit of different models to determine which one best explains the data.
No, the expression $(1-(ab+bc+ca))^2 + (a+b+c-abc)^2$ is not the only measure of goodness of fit in real factor analysis. Other measures such as the root mean square error and the comparative fit index can also be used to evaluate the fit of a model to the data.