Model Definition - Advanced Tab

Select the Advanced tab of the Model Definition dialog box to access options to specify the particular model you want to analyze.

Variables

Click the Variables button to display a standard variable selection dialog box, in which you can select the dependent and independent variables. If more than one dependent variable is selected, regression analyses will be performed consecutively for each variable in the dependent variable list.

Method

Use the options under Method to choose a type of regression analysis.

All Effects

Select All Effects to enter all variables into the regression equation in one single block or step.

Forward stepwise/Backward stepwise. Select Forward stepwise or Backward stepwise to individually add or delete the independent variables from the model at each step of the regression (depending on your choice of F to enter or F to remove values) until the "best" regression model is obtained. The difference between the two methods is the starting point, or the initial model considered. The forward stepwise method starts with no variables. Thus, the first step in this case is a forward step, that is, STATISTICA determines which variable should enter the model based on your choice of F to enter. Conversely, the backward stepwise method starts with all of the variables in the model. Thus, the first step in this case is a backward step, that is, STATISTICA determines which variable should be removed from the model based on your choice of F to remove.

Intercept

Use the options under Intercept to specify a regression equation with an intercept (select Include in model) or without an intercept (intercept forced to zero, regression through the origin, select Set to zero). Regression without the intercept is often used in analyses of economic data in cases when, by definition, the regression line describing the relationship between some variables would be predicted to have a zero intercept. For example, if you were to correlate tax revenues with gross national product (GNP) then it is obvious that, if there is zero GNP, there is zero tax revenue. However, in the majority of applications (in particular in the social and natural sciences) variables of interest are measured on more or less arbitrary scales where the zero points have no special meaning. Therefore, the default setting of the intercept combo box is Include in model.

Tolerance

Enter the minimum Tolerance value that is considered acceptable by STATISTICA. The tolerance of a variable is defined as 1 minus the squared multiple correlation of this variable with all other independent variables in the regression equation. Therefore, the smaller the tolerance of a variable, the more redundant is its contribution to the regression (i.e. it is redundant with the contribution of other independent variables). If the tolerance of any of the variables in the regression equation is equal to zero (or very close to zero) then the regression equation cannot be evaluated (the matrix is said to be ill-conditioned, and it cannot be inverted).

The minimum value that can be specified here is 1.00E-25 (i.e., a number with 24 zeros past the decimal point). However, it is not recommended to reset this switch to such an extremely low value. If the tolerance of a variable about to be entered into the regression equation is less than the default tolerance value (.01) it means that this variable is 99 percent redundant with (identical to) the variables already in the equation. Forcing very redundant variables into the regression equation is not only questionable in terms of relevance of results, but the resultant estimates (regression coefficients) will become increasingly unreliable.

Ridge regression; lambda

Select the Ridge regression check box to perform a ridge regression analysis when you click OK in the Model Definition dialog box. Ridge regression is used when the independent variables are highly intercorrelated, and stable estimates for the regression coefficients cannot be obtained via ordinary least squares methods (see Hoerl, 1962; Schmidt & Muller, 1978; Rozeboom, 1979). Specifically, a constant (lambda) will be added to the diagonal of the correlation matrix, which is then re-standardized so that all diagonal elements are equal to 1.0 (and the off-diagonal elements are divided by the constant). In other words, ridge regression artificially decreases the correlation coefficients so that more stable (yet biased) estimates (beta coefficients) can be computed. A ridge regression results spreadsheet will be displayed when you click the Summary: Regression results button in the Multiple Regression Results dialog box. Note that the standard errors for B and beta are calculated using the formulas for standard regression. After selecting this option, you will need to enter a value for lambda.

The vector of standardized ridge regression estimates is given as follows:

bstandardized ridge = ( RXX + lambda * I )-1 RYX

RXX = correlation matrix of predictors

RYX  = vector of correlations between the response and the predictors

Lambda = user specified shrinkage parameter

I = identity matrix

The standardized coefficients are then placed on the raw scale via:

bi,ridge = ( sy/sxi ) bi,standardized ridge

where,

sy = standard deviation of the response

sxi = standard deviation of the predictor

The intercept is then given by

Batch processing/printing

Select the Batch processing/printing check box to send the regression output to a report. The default setting of the option is interactive processing (i.e. Batch processing/printing is cleared). In this mode you can determine (interactively) which spreadsheets to send to a report. In the Batch processing/printing mode, STATISTICA will perform the specified regression analysis (or set of analyses if more than one dependent variable was specified), automatically send all of the results to a report, and return to the Model Definition dialog box without additional user input. This option is particularly useful when you want to print the results of a stepwise regression after each step for several dependent variables. This option is available only if the Advanced options (stepwise or ridge regression) check box is cleared and one of the Output Report window options is selected n the Output Manager dialog box (click the button and select Output to display the Output Manager dialog box).

Print/report residual analysis

Select the Print/report residual analysis check box to include the spreadsheet with various residual statistics for each case in the output that is sent to a report. This option is available only if the Batch processing/reporting check box is selected.