Logistic Regression. Using Some Very

¶ … logistic regression. Using some very simple numbers, make up a simple numerical example and explain how odds and probabilities were calculated. How are odds different from an odds ratio?

Odds is the ratio of the probability that an event will occur to the probability that it will not occur.

Odds in logistic regression are obtained by dividing the number of times something does happen by the number of times that it does not. For example, we may have a case of the odds of a student joining NASA upon graduation. In one specific hypothetical study, 14 people joined NASA after graduation from a certain school and 78 students declined. You divide the number of NASA-joiners (14) by those who declined (78). Result = .179. Conversely, we can investigate the probability or odds of students not joining NASA upon gradation. In this case, the equation is the reverse: 78/14= 5.57.

We can predict that the odds of a student from school joining NASA upon graduation is less than 1 in 5. Or that the probability of a student joining NASA is approximately 1 out of every 5 students in that certain school.

The minimum value of odds is 0. In order to work out odds, we ask whether the probability of the odds occurring is less or more than 1. When the odds are less than 1, we predict that the likelihood of the event occurring is extremely slight. When the odds, on the other hand, are greater than 1, the even is more likely, than not (or than the reverse), to occur. When both odds equal 1, both have an equal chance of occurring.

The odds ratio, on the other hand, not only compares the odds of events occurring in one group to the odds of it occurring in another group, but also measures effect size and describes the strength of association between two binary variables.. The odds ratio is also relevent to sample-based estimates.

As an example, we might have a group of men vs. women, or a control group vs. The experimental group and the odds ratio is used to assess effect or test the strength of association between the two groups, or the odds of the event that the effect of TV watching (to invent a hypothetical situation) has more of an effect on males than it has on females.

John plans to do a logistic regression using the default (enter) method. His friend Barbara suggests that he should do a sequential logistic regression instead, and his other friend, Linda, tells John that a stepwise logistic regression is the way to go. Discuss the advantages and disadvantages of these three options. What criteria should John use in order to decide which method is best for him?

The default Enter method

The default enter method enters all the variables at the same time. The positive aspect is that all variables are assessed to see whether any hold significance. All are included and so greater authenticity is likely assured and less bias may be the result.

On the other hand, the researcher may wish to investigate only a few of the variables in the study, considering others irrelevant to his objective. In this case, the Enter method is not only unhelpful, but also detrimental to the researcher.

Furthermore, Enter can also be confusing in the case of a large study where the researcher would have to wade through a huge amount of data in order to assess the significance of each. In both of these cases, John may prefer the stepwise or sequential approach.

2. The sequential logistic regression

The sequential logistic regression places the data in a certain sequence of order. This is beneficial for John if he intends his data to have certain priority (I.e if he considers some to be more important tthan others). If the reverse is the case, it can confuse him.

3. The Stepwise method

Here is where John can use the forward selection, the backwards elimination, or a combination of both.

In the forward selection, John tries out the variables one by one (starting with none at all) and including those that are statistically significant. In the backward elimination, the reverse occurs; John starts with all variables, tests them for significance and eliminates those that lack significance. John can also amalgamate both methods for greater security.

This method is advantageous for a study that yields a large number of possible explanatory variables, but there is no underlying theory which John can use to base his selection. Given the huge amount of potential candidates, screening out the variables that are significant can be helpful to John. He may be able to see some pattern from doing this.

The problems include that John needs an appreciably large study to do this. Moreover, since several ANOVAs are used to determine the inclusion or exclusion of variables and since these ANOVAs are carried out on the same data you may have bias and multiple comparisons.

Advice to John

John would use the default Enter method if his study has not indicated anything about the importance of the order of the variables or of their relation to the constant.

If his research does indicate a certain order for warbles or importance of some above others, he would use the sequential method.

If he would like to screen his data, he would use the stepwise.

Discuss logistic regression. You may want to discuss such aspects as the logic of the method, the primary purposes of the method, the various steps involved, different methods of performing the method, and so on.

Logistic regression (LR) is used when the dependent variable is binary or ordinal. Lets say when you want to know if someone will live or die -- you want to know the odds or probability of something -- that's when you do a logistic regression. This is binary (I..e either choice or more can occur - 1 or 2).

LR is useful for predicting whether something will, or will not happen. For instance, whether certain patients in a hospital may die from a certain disease. These are binary outcomes. LR is particularly useful when the dataset is large and the outcome is unpredictable and difficult to assess.