Stepwise Model Builder - Linear Regression

Overview and Workflow

Use the options in the Stepwise Model Builder - Linear Regression Startup Panel to compute the marginal predictor statistics given a current model; specifically, the variables listed in the Marginal Results Table will be entered one at a time into the linear regression containing the predictors listed in the Model Results Table, so that analysts can evaluate the unique contribution of each predictor candidate not in the equation.

Variable/predictor selection

First, select the variables for the analyses; select a Dependent or Y variable, and select two or more continuous or categorical (discrete) predictor candidates (X variables).

Next, select (highlight) the predictor candidates in the Marginal Analysis Variables pane, and click either the Full sample button or the Subsample button to compute the Marginal Results Table results.

Then select (highlight) the predictors in the Marginal Results Table that are to be entered into the full Model Results Table, and click the Add variable button to:

1) Estimate the parameters of the linear regression model including the selected predictors and any predictors previously entered into the regression equation

2) Re-estimate the results for all predictor candidates in the Marginal Results Table

Estimates from Subsample, Full sample

You can estimate the marginal analysis results (including those accessible via the options in the Marginal Results group box) using either a subsample of observations or all observations; you can also select (highlight) one or more predictors in the Marginal Results Table and re-estimate the respective marginal results for the Full sample or Subsample. The Sample column in the Marginal Results Table indicates whether the currently displayed results were computed from a random Subsample or the Full sample. When the results in the Marginal Results Table are re-estimated after you choose to Add variable or Remove variable from the Model Results Table, the same sample and sample option is used as before (Subsample or Full sample; note that a new subsample is drawn only when the Subsample button is clicked).

The Model Results Table statistics are always computed for the entire data set.

Categorical (discrete) predictors

When the model includes categorical (discrete) predictors, Statistica will estimate separate parameter estimates for each discrete value, assuming that the respective predictor would be entered "as a whole" into the equation, that is, with all discrete values that it contains.

This means that you cannot separate the set of discrete values available in a discrete predictor candidate, and all values will always be added or removed from models and selections in unison, even if only a single code is selected (highlighted) when the respective predictor is moved in/out of a results table.

When discrete predictors are removed from the prediction equation or the Marginal results table, the same logic applies.

Saving a project (in progress)

You can save a work-in-progress by clicking the Save project button located in the Project group box, and retrieve it later to continue work by clicking the Open project button. Note that after opening a previously saved project, the next time any results statistics or re-calculations are requested via the options in Stepwise Model Builder, the program will recompute all results necessary to enable you to resume the interactive model building. When working with large projects involving many predictors, this may require some time.  

Bootstrapping provides a way for analysts to assess the robustness of the parameter estimates and results in the Model Results Table from repeatedly drawn samples.  

Deploying models to Enterprise

Click the Deploy model button (in the Model group box at the top-right of the Startup Panel) to save models to Enterprise.

Option Descriptions

Select variables. Click this button to display a standard variable selection dialog box. Select a continuous variable as the Dependent or Y variable, and two or more Continuous and/or Categorical Predictors (predictor candidates). After exiting the variable selection dialog box (click the OK button), the respective variable names will be displayed in the Marginal Analysis Variables pane.

Marginal Analysis Variables. After selecting variables for the analyses, this pane will show the selected variable names, their type (Continuous or Categorical), and the variable number in the input file. You can select one or more predictors in this list by highlighting them; to run marginal analyses on the selected variables, click either the Full sample or Subsample button in the Run Marginal Analysis group box.

Set Linear Parameters.

Model parameters

Click this button to display the Linear Regression Parameters dialog box where you can select the type of parameterization to use for the general linear model

Dependent (Y) Variable. As described in the Introductory Overview, Statistica will compute parameter estimates and other results for a linear regression. This box displays the dependent or Y variable.

Project. Use the Save project and Open project options to save work in progress and to retrieve previously saved projects to continue working with the same variables and model.

Open project

Click this button to display the Open dialog box, which is used to browse to and select a previously saved project. Note that after opening a previously saved project, the next time any results statistics or re-calculations are requested via the options in Stepwise Model Builder, the program will recompute all results necessary to enable you to resume the interactive model building. When working with large projects involving many predictors, this may require some time.

Save project

Click this button to display the Save As dialog box, where you can enter a name and specify a location for the project.

Model.

Deploy model

Click this button to save the current linear regression model (equation) to Statistica Enterprise; models saved in Enterprise can be referenced by Enterprise analysis templates. This button is not available until a model is available in the Model Results Table.

Show model

Click this button to output the current linear regression model to a workbook. This button is not available until a model is available in the Model results table.

Run Marginal Analysis. Click either the Full sample or Subsample button to add the selected (highlighted) predictor candidates from the Marginal Analysis Variables pane to the Marginal Results Table, and to compute the respective marginal analysis results.

Full sample

To estimate the marginal analysis results for the full sample, click this button.

Subsample

To estimate the marginal analysis results from a subsample of observations, click the Subsample button; a sample of the size as specified in the Sample N field will be drawn prior to the computation of marginal results statistics.

Remove Variable

Select a variable in the Marginal Results Table, and click this button to remove the variable and return it to the Marginal Analysis Variables pane.

Marginal Results.

Correlations

Click this button to review the correlations of parameter estimates for each predictor candidate in the Marginal results table and the parameters in the current Marginal results table.

Marginal analysis

Click this button to review complete parameter estimation table for the model after entering each predictor candidate into the model one by one.

Graphs

Click this button to compute various diagnostic and residual statistics graphs, including:

• Scatterplots of observed values vs raw residuals for continuous predictors
• Mean plot with errors for categorical predictors

Results will be displayed in standard results spreadsheets and graphs, shown by default in workbooks.

Model Analysis.  

Graphs

Click this button to compute various diagnostic and residual statistics graphs, including a normal probability plot of residuals and scatterplots of predicted values vs raw residuals.

Bootstrap

Click this button to compute bootstrap error estimates (distributions) for the parameters and fit statistics. In the case that not all levels of one or more categorical predictor variables are sampled during bootstrapping, a message will be displayed and results for model coefficients will not be displayed.

Note: the following two options pertain only to Bootstrapping and are not applicable for Graphs or Validation. Specify:

Replications. The number of bootstrap replications

% in holdout sample. The proportion of hold-out cases in each bootstrap replication; if this value is 0 (zero), predictive accuracy is computed from the (100%) training sample (used for estimating the parameters)

The program will then create k replications of the data via random sampling with replacement, and designate a proportion p cases in each replication as the hold-out or testing sample. Next, the respective model will be fit to all cases not in the hold-out sample (in the training sample) in the respective replication. The parameter estimates and R squared statistic in each replication are also recorded. Thus, you can then evaluate the distribution of the parameter estimates and fit over the replications.

Model Results. Use these options to compute various model statistics and summaries for the current model with predictors listed in the Model results table, and computed from the full sample.

Covariances

Click this button to produce a covariance matrix of the parameter estimates.

Correlations

Click this button to produce a correlation matrix of the parameter estimates.

Summary

Click this button to produce several results tables describing the current model, including tables with summary tests for each effect (predictor) in the model and parameter estimates and standard errors, confidence intervals.

Marginal Results Table. Displays the marginal analysis results for the currently selected predictor candidates. Right-click on any column header in the Marginal Results Table to display a shortcut menu containing check boxes adjacent to available statistics; when a check box is selected, the respective column is added to the table; when a check box is cleared, the respective column is hidden in the table.

Total N

This field displays the number of all observations.

Sample N

The entry in this user-specified field determines the approximate sample size that is used to compute Subsample results. Note that the Sample N must be set to at least 500.

No

This column displays the variable numbers of the respective predictors in the input data.

Variables

This column displays the names of the predictors in the input data.

R² / Pr(f) / Pr(t). These columns display the results statistics.

Level

The values (codes) displayed in this column show the respective discrete values (categories) for categorical predictor candidates, so different parameter estimates are computed for each category. However, the categories of categorical variables can only be deselected/selected from/to the analyses in unison, that is, they cannot be separated, and the other results statistics (R squared) will be identical for all levels.

df. Degrees of freedom for Wald statistic.

Sample

This column indicates whether the respective marginal results were computed and will be recomputed by default from either a Subsample of cases or the Full sample (all observations). Note that the user-specified Sample N determines the approximate sample size that is used to compute Subsample results.

Notes:

Sorting the variable list. Click on the R² column in the Marginal Results Table to sort the table by the respective column values in ascending or descending order.

Selecting predictor candidates in the Marginal Results Table. To select predictor candidates in the Marginal Results Table, click on the respective predictor candidate. Use CTRL+click or SHIFT+click to select specific predictor candidates or lists of contiguous predictor candidates, respectively.

Re-calculating marginal results. Click the Full sample or Subsample button to recalculate the marginal analysis results for the highlighted (selected) predictor variables.

Adding variables to the Model Results Table. Click the Add variable button to move selected (highlighted) predictors into the model and to update the Marginal Results Table.

Add/Remove Model Variables.

Add variable

Click this button to add selected (highlighted) predictor candidates from the Marginal Results Table to the Model Results Table (into the final model). Note that multiple degree-of-freedom effects associated with categorical (discrete) predictor candidates are moved into the model in unison, even if only a single category or value for the respective predictor candidate is highlighted in the Marginal Results Table.

The results in the Mode Results Table are always computed for the full sample. After the model parameters are updated, the Marginal Results Table results are then recalculated for all predictor candidates currently not in the model.

Remove variable

Click this button to remove selected (highlighted) predictors from the Model Results Table and move them back into the Marginal Results Table.

Comment for Add/Remove

Optionally type comments concerning variables added or removed. These comments will be displayed in a column in the Model Building Summary output spreadsheet.

Model Results Table. The Model Results Table shows the parameter estimates and summary statistics for the current model, that is, the model with the predictors listed in the pane and computed from the full sample. Right-click on any column header in the Model Results Table to display a shortcut menu containing check boxes adjacent to available statistics; when a check box is selected, the respective column is added to the table; when a check box is cleared, the respective column is hidden in the table.

Note:

Removing variables. To remove predictors from the current model, highlight the respective predictors and then click the Remove variable button. The predictors will be removed from the model, the model will be re-estimated with the remaining predictors, and the Marginal Results Table will be recalculated for all predictor candidates including those that were removed from the model.