Question

In: Statistics and Probability

For what type of dependent variable are poisson and negative binomial regressions appropriate? Give an example...

For what type of dependent variable are poisson and negative binomial regressions appropriate? Give an example of such a variable. In what metric are these regression coefficients? What can we do to them to make them more interpretable, and how would we interpret the resulting translated coefficients?

(Understanding and Using Statistics for Criminology and Criminal Justice)

Expert Solution

Answer:

Given Data

In case of logistic regression the dependent variable must be a dichotomous variable

i.e it will take only two values.

Let be the dependent variable , it can be defined as

For logistic regression will be a categorial variable and there will be only 2 categories

Metric for logistic regression coefficiennt.

True values of varible.

Predicted values of variable based on the explanatory variables.

Construct a confusion Matrix

		predicted
		0	1
True	0	a	b
	1	c	d

From the above table we can see there are total n observation.

Out of these (a+d) many are classified correctly and (b+c) many are classified wrongly.

Accuracy is defined as a measure of the logistic regression.

Accuracy =

The higher the accuracy the better the classification

Interpretation of coefficient:

Let be the estimated coefficient in the logistic regression.

Define odds ratio =

the odds ratio can be interpreted as the estimated increase in the probability of sucess associated with one unit change in the value of the explanatory variables.

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orchestra answered 1 year ago

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