The SPSS Sample ProblemStage One: Define the Research ProblemMethod for including independent variablesStage 2: Develop the Analysis Plan: Sample Size IssuesStage 2: Develop the Analysis Plan: Measurement Issues:Stage 3: Evaluate Underlying AssumptionsStage 4: Estimation of Logistic Regression and Assessing Overall Fit: Model EstimationRequesting a Logistic RegressionSpecifying the Dependent VariableSpecifying the Independent VariablesSpecify the method for entering variablesSpecifying Options to Include in the OutputSpecifying the New Variables to SaveComplete the Logistic Regression RequestStage 4: Estimation of Logistic Regression and Assessing Overall Fit: Assessing Model FitInitial statistics before independent variables are includedSignificance test of the model log likelihoodMeasures Analogous to R²Correspondence of Actual and Predicted Values of the Dependent VariableThe Classification Matrices as a Measure of Model AccuracyStacked HistogramCheck for Numerical ProblemsPresence of outliersCook’s DistanceRequest the ScatterplotSpecifying the Variables for the ScatterplotThe Scatterplot of Cook's DistancesStage 5: Interpret the ResultsIdentifying the statistically significant predictor variablesDirection of relationship and contribution to dependent variableStage 6: Validate The ModelSet the Starting Point for Random Number GenerationCompute the Variable to Select a Large Proportion of the Data SetSpecify the Cases to Include in the First Validation AnalysisSpecify the Value of the Selection Variable for the First Validation AnalysisComputing the Second Validation AnalysisSlide 37Slide 38Specify the Cases to Include in the Second Validation AnalysisSpecify the Value of the Selection Variable for the Second Validation AnalysisGeneralizability of the Logistic Regression ModelSlide 1 The SPSS Sample ProblemTo demonstrate these concepts, we will work the sample problem for logistic regression in SPSS Professional Statistics 7.5, pages 37 - 64. The description of the problem can be found on page 39.The data for this problem is: Prostate.Sav.SPSS Sample ProblemSlide 2 Stage One: Define the Research ProblemIn this stage, the following issues are addressed:•Relationship to be analyzed•Specifying the dependent and independent variables•Method for including independent variablesSPSS Sample ProblemRelationship to be analyzedThe goal of this analysis is to determine the relationship between the dependent variable NODALINV (whether or not the cancer has spread to the lymph nodes), and the independent variables of AGE (age of the subject), ACID (a laboratory test value that is elevated when the tumor has spread to certain areas), STAGE (whether or not the disease has reached an advanced stage), GRADE (aggressiveness of the tumor), and XRAY (positive or negative xray result).Slide 3 SPSS Sample ProblemSpecifying the dependent and independent variablesThe dependent variable is NODALINV;; 'Cancer spread to lymph nodes', a dichotomous variable.The independent variables are:•AGE;; 'Age of the subject'•ACID;; 'Laboratory test score'•XRAY;; 'Positive X-ray result'•STAGE;; 'Disease reached advanced stage'•GRADE;; 'Aggressive tumor'Method for including independent variablesSince we are interested in the relationship between the dependent variable and all of the independent variables, we will use direct entry of the independent variables.Slide 4 Stage 2: Develop the Analysis Plan: Sample Size IssuesIn this stage, the following issues are addressed:•Missing data analysis•Minimum sample size requirement: 15-20 cases per independent variableSPSS Sample ProblemMissing data analysisThere is no missing data in this problem.Minimum sample size requirement:15-20 cases per independent variableThe data set has 53 cases and 5 independent variables for a ratio of 10 to 1, short of the requirement that we have 15-20 cases per independent variable.; We should look for opportunities to validate our findings against other samples before generalizing our results.Slide 5 Stage 2: Develop the Analysis Plan: Measurement Issues:In this stage, the following issues are addressed:•Incorporating nonmetric data with dummy variables•Representing Curvilinear Effects with Polynomials•Representing Interaction or Moderator EffectsSPSS Sample ProblemIncorporating Nonmetric Data with Dummy Variables All of the nonmetric variables have recoded into dichotomous dummy-coded variables.Representing Curvilinear Effects with Polynomials We do not have any evidence of curvilinear effects at this point in the analysis.Representing Interaction or Moderator Effects We do not have any evidence at this point in the analysis that we should add interaction or moderator variables.Slide 6 Stage 3: Evaluate Underlying AssumptionsIn this stage, the following issues are addressed:•Nonmetric dependent variable with two groups•Metric or dummy-coded independent variablesSPSS Sample ProblemNonmetric dependent variable having two groupsThe dependent variable NODALINV;; 'Cancer spread to lymph nodes' is a dichotomous variable.Metric or dummy-coded independent variablesAGE;; 'Age of the subject' and ACID;; 'Laboratory test score' are metric variables.XRAY;; 'Positive X-ray result', STAGE;; 'Disease reached advanced stage', and GRADE ;;'Aggressive tumor' are nonmetric dichotomous variables.Slide 7 Stage 4: Estimation of Logistic Regression and Assessing Overall Fit: Model Estimation In this stage, the following issues are addressed:•Compute logistic regression modelSPSS Sample ProblemCompute the logistic regressionThe steps to obtain a logistic regression analysis are detailed on the following screens.Slide 8 Requesting a Logistic RegressionSPSS Sample ProblemSlide 9 Specifying the Dependent VariableSPSS Sample ProblemSlide 10 Specifying the Independent VariablesSPSS Sample ProblemSlide 11 Specify the method for entering variablesSPSS Sample ProblemSlide 12 Specifying Options to Include in the OutputSPSS Sample ProblemSlide 13 Specifying the New Variables to SaveSPSS Sample ProblemSlide 14 Complete the Logistic Regression RequestSPSS Sample ProblemSlide 15 Stage 4: Estimation of Logistic Regression and Assessing Overall Fit:; Assessing Model FitIn this stage, the following issues are addressed:•Significance test of the model log likelihood (Change in -2LL)•Measures Analogous to R²: Cox and Snell R² and Nagelkerke R²•Hosmer-Lemeshow Goodness-of-fit•Classification matrices as a measure of model accuracy•Check