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Stepwise Regression Perhaps the most widely used strategy for selecting inde- pendent variables for a multiple regression model is the stepwise procedure buy rumalaya gel online now muscle relaxant and nsaid. At each step of the procedure each variable then in the model is evaluated to see if discount rumalaya gel 30 gr line muscle relaxant hamstring, according to specified criteria rumalaya gel 30 gr mastercard muscle relaxant without aspirin, it should remain in the model. Suppose, for example, that we wish to perform stepwise regression for a model containing k predictor variables. Of all the variables that do not satisfy the criterion for inclusion in the model, the one that least satisfies the criterion is removed from the model. If a variable is removed in this step, the regression equation for the smaller model is calculated and the criterion measure is computed for each variable now in the model. If any of these variables fail to satisfy the criterion for inclusion in the model, the one that least satisfies the criterion is removed. If a variable is removed at this step, the variable that was removed in the first step is reentered into the model, and the evaluation procedure is continued. The nature of the stepwise procedure is such that, although a variable may be deleted from the model in one step, it is evaluated for possible reentry into the model in subsequent steps. If the F statistic for any of these variables is less than the specified cutoff value (4 if some other value is not specified), the variable with the smallest F is removed from the model. The regression equation is refitted for the reduced model, the results are printed, and the 11. Of these variables, the one with the largest associated F statistic is added, provided its F statistic is larger than the specified cutoff value (4 if some other value is not specified). The regression equation is refitted for the new model, the results are printed, and the procedure goes on to the next step. The following example illustrates the use of the stepwise procedure for selecting variables for a multiple regression model. After step 2 no other variable could be added or deleted, and the procedure stopped. To change the criterion for allowing a variable to enter the model from 4 to some other value K, click on Options, then type the desired value of K in the Enter box. To change the criterion for deleting a variable from the model from 4 to some other value K, click on Options, then type the desired value of K in the Remove box. Though the stepwise selection procedure is a common technique employed by researchers, other methods are available. The final model obtained by each of these procedures is the same model that was found by using the stepwise procedure in Example 11. Forward Selection This strategy is closely related to the stepwise regression procedure. Variables are retained that meet the criteria for inclusion, as in stepwise selection. The first variable entered into the model is the one with the highest correlation with the dependent variable. The next variable to be considered for inclusion is the one with the highest partial correlation with the dependent variable. The final model contains all of the independent variables that meet the inclusion criteria. Backward Elimination This model-building procedure begins with all of the variables in the model. This strategy also builds a model using correlations and a predetermined inclusion criterion based on the F statistic. The first variable considered for removal from the model is the one with the smallest partial correlation coefficient. If this variable does not meet the criterion for inclusion, it is eliminated from the model. The next variable to be considered for elimination is the one with the next lowest partial correlation. This procedure continues until all variables have been considered for elimination. The final model contains all of the independent variables that meet the inclusion criteria. The researchers used the Proactive/Reactive Rating Scale, obtained by presenting three statements to clinicians who examined the subjects. The respondents answered, using a scale from 1 to 5, with 5 indicating that the statement almost always applied to the child. An example of a reactive aggression statement is, “When this child has been teased or threatened, he or she gets angry easily and strikes back. Perform stepwise regression to find the variables most useful in predicting reactive aggression in the following sample of 68 subjects. Particularly plentiful are circumstances in which the outcome variable is dichotomous. A dichotomous variable, we recall, is a variable that can assume only one of two mutually exclusive values. These values are usually coded Y ¼ 1 for a success and Y ¼ 0 for a nonsuccess, or failure. Dichotomous variables include those whose two possible values are such categories as died–did not die; cured–not cured; disease occurred– disease did not occur; and smoker–nonsmoker. The health sciences professional who either engages in research or needs to understand the results of research conducted by others will find it advantageous to have, at least, a basic understanding of logistic regression, the type of regression analysis that is usually employed when the dependent variable is dichotomous. The purpose of the present discussion is to provide the reader with this level of understanding. We shall limit our presentation to the case in which there is only one independent variable that may be either continuous or dichotomous. The Logistic Regression Model Recall that in Chapter 9 we referred to regression analysis involving only two variables as simple linear regression analysis. The simple linear regression model was expressed by the equation y ¼ b0 þ b1x þ e (11. When the observed value of Y is myjx, the mean of a subpopulation of Y values for a given value of X, the quantity e, the difference between the observed Y and the regression line (see Figure 9. Even though only two variables are involved, the simple linear regression model is not appropriate when Y is a dichotomous variable because the expected value (or mean) of Y is the probability that Y ¼ 1 and, therefore, is limited to the range 0 through 1, inclusive. For example, the model is frequently used by epidemiologists as a model for the probability (interpreted as the risk) that an individual will acquire a disease during some specified time period during which he or she is exposed to a condition (called a risk factor) known to be or suspected of being associated with the disease. Logistic Regression: Dichotomous Independent Variable The simplest situation in which logistic regression is applicable is one in which both the dependent and the independent variables are dichotomous. The values of the dependent (or outcome) variable usually indicate whether or not a subject acquired a disease or whether or not the subject died. The values of the independent variable indicate the status of the subject relative to the presence or absence of some risk factor. In the discussion that follows we assume that the dichotomies of the two variables are coded 0 and 1.  