Logistic Regression – Basic RelationshipsLogistic regressionWhat logistic regression predictsLevel of measurement requirementsAssumptionsSample size requirementsMethods for including variablesComputational methodOverall test of relationshipBeginning logistic regression modelEnding logistic regression modelRelationship of Individual Independent Variables and Dependent VariableNumerical problemsStrength of logistic regression relationshipEvaluating usefulness for logistic modelsComparing accuracy ratesComputing by chance accuracyProblem 1Dissecting problem 1 - 1Dissecting problem 1 - 2Dissecting problem 1 - 3Dissecting problem 1 - 4LEVEL OF MEASUREMENT - 1LEVEL OF MEASUREMENT - 2PATTERNS OF MISSING DATA - 1PATTERNS OF MISSING DATA - 2Request simultaneous logistic regressionSelecting the dependent variableSelecting the independent variablesSpecifying the method for including variablesCompleting the logistic regression requestSample size – ratio of cases to variablesOVERALL RELATIONSHIP BETWEEN INDEPENDENT AND DEPENDENT VARIABLESNUMERICAL PROBLEMSRELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 1RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 2RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLE - 3CLASSIFICATION USING THE LOGISTIC REGRESSION MODEL: by chance accuracy rateCLASSIFICATION USING THE LOGISTIC REGRESSION MODEL: criteria for classification accuracyAnswering the question in problem 1 - 1Answering the question in problem 1 - 2Problem 2Dissecting problem 2 - 1Dissecting problem 2 - 2Dissecting problem 2 - 3Dissecting problem 2 - 4Slide 47Slide 48Slide 49Slide 50Request hierarchical logistic regressionSlide 52Selecting the control independent variablesAdding the predictor independent variablesSlide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Answering the question in problem 2 - 1Answering the question in problem 2 - 2Problem 3Dissecting Problem 3 - 1Dissecting Problem 3 - 2Dissecting Problem 3 - 3Dissecting Problem 3 - 4Dissecting Problem 3 - 5Slide 72Slide 73Slide 74Slide 75Request stepwise logistic regressionSlide 77Adding the independent variablesSlide 79Adding options to the outputIncluding a summary of stepsSpecifications for stepwise methodSlide 83Slide 84Slide 85Slide 86RELATIONSHIP OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLEIMPORTANCE OF INDIVIDUAL INDEPENDENT VARIABLES TO DEPENDENT VARIABLESlide 89Slide 90Answering the question in problem 3 - 1Answering the question in problem 3 - 2Steps in binary logistic regression: level of measurementSteps in binary logistic regression: missing dataSteps in binary logistic regression: initial sample sizeSteps in logistic regression: overall relationship and numerical problemsSteps in logistic regression: relationships between IV's and DVSteps in logistic regression: classification accuracy and adding cautionsSW388R7Data Analysis & Computers IISlide 1Logistic Regression – Basic RelationshipsLogistic RegressionDescribing RelationshipsClassification AccuracySample ProblemsSW388R7Data Analysis & Computers IISlide 2Logistic regressionLogistic regression is used to analyze relationships between a dichotomous dependent variable and metric or dichotomous independent variables. (SPSS now supports Multinomial Logistic Regression that can be used with more than two groups, but our focus here is on binary logistic regression for two groups.)Logistic regression combines the independent variables to estimate the probability that a particular event will occur, i.e. a subject will be a member of one of the groups defined by the dichotomous dependent variable. In SPSS, the model is always constructed to predict the group with higher numeric code. If responses are coded 1 for Yes and 2 for No, SPSS will predict membership in the No category. If responses are coded 1 for No and 2 for Yes, SPSS will predict membership in the Yes category. We will refer to the predicted event for a particular analysis as the modeled event.This will create some awkward wording in our problems. Our only option for changing this is to recode the variable.SW388R7Data Analysis & Computers IISlide 3What logistic regression predictsThe variate or value produced by logistic regression is a probability value between 0.0 and 1.0.If the probability for group membership in the modeled category is above some cut point (the default is 0.50), the subject is predicted to be a member of the modeled group. If the probability is below the cut point, the subject is predicted to be a member of the other group.For any given case, logistic regression computes the probability that a case with a particular set of values for the independent variable is a member of the modeled category.SW388R7Data Analysis & Computers IISlide 4Level of measurement requirementsLogistic regression analysis requires that the dependent variable be dichotomous.Logistic regression analysis requires that the independent variables be metric or dichotomous. If an independent variable is nominal level and not dichotomous, the logistic regression procedure in SPSS has a option to dummy code the variable for you.If an independent variable is ordinal, we will attach the usual caution.SW388R7Data Analysis & Computers IISlide 5AssumptionsLogistic regression does not make any assumptions of normality, linearity, and homogeneity of variance for the independent variables.When the variables satisfy the assumptions of normality, linearity, and homogeneity of variance, discriminant analysis is generally cited as the more effective statistical procedure for evaluating relationships with a non-metric dependent variable.When the variables do not satisfy the assumptions of normality, linearity, and homogeneity of variance, logistic regression is the statistic of choice since it does not make these assumptions.SW388R7Data Analysis & Computers IISlide 6Sample size requirementsThe minimum number of cases per independent variable is 10, using a guideline provided by Hosmer and Lemeshow, authors of Applied Logistic Regression, one of the main resources for Logistic Regression.For preferred case-to-variable ratios, we will use 20 to 1 for simultaneous and hierarchical logistic regression and 50 to 1 for stepwise logistic regression.SW388R7Data Analysis & Computers IISlide 7Methods for including variablesThere are three methods available for including variables in the regression