04.2 Logistic Regression Flashcards
Differentiate between the null and the fitted model.
Mention; null deviance, fitted deviance
Why do we multiply them by -2?
Null:* assumes one parameter (the intercept) for all of the data points, which means you
only estimate 1 parameter. -2ln(L(NULL))–> how much is explained only by the intercept
Fitted: assumes you can explain your data points with p parameters and an intercept term, so you have p + 1 parameters. -2ln(L(FITTED))–>small values mean that the fitted model explains the data well.
Note: Multiplying by -2 converts the log-likelihood into a x2-distribution, which can then be used to test statistical significance
Likelihood ratio test:
* D = -2ln (L(null)/L(fitted))
* The logarithm of this likelihood ratio (the ratio of the null model to the fitted model) will produce a negative value, hence the need for a negative sign.
* D follows a …
* Non-significant chi-square values indicate that …
* The test can also be used to assess individual predictors (model with and w/o predictor).
A Wald test:
*Similar purpose than the t-test for the linear regression.
* It is used to…
Remark: t-test and Wald test assume …
Therefore, the t-test is appropriate for linear regression (test statistic follows t-distribution), while the Wald test is appropriate for logistic regression (test statistic follows 2 distribution).
Chi-Square distribution (the greater, the better).
a significant amount of the variance is unexplained.
test the statistical significance of each coefficient in the model hypothesis that ß= 0.
different distributions under the null hypothesis.
McFadden R^2
When will the value be close to 1?
When will the value be close to zero?
What is okay?
1- LL(Fitted)/LL(Null)
If the fitted model does much better than just a constant, in a discrete-choice model this value will be close to 1.
If the full model doesn’t explain much at all, the value will be close to 0.
Typically, the values are lower than those of R2 in a linear regression and need to be interpreted with care.
>0.2 is acceptable, >0.4 is already ok.
The presence of multicollinearity will not lead to biased coefficients, but…
* If a variable …
* If two variables are correlated at a rate greater than .6, .7, .8, etc. then …
The inclusion of irrelevant variables can…
* You can consult … and remove irrelevant variables.
it will have an effect on the standard errors.
which you think should be statistically significant is not, consult the correlation coefficients or VIF.
try dropping the least theoretically important of the two.
result in poor model fit.
your Wald statistics
