Week Twenty Three - Logistic Regression

In logistic regression, what does the baseline model in SPSS tell you?

Gives you the info you know just from knowing how many 0 outcomes and how many 1 outcomes there are e.g. # positive/#negative = 48/18 = 2.667 (= odds ratio or Exp(B)) e.g. a positive outcome is 2.667 more likely to occur than a negative, knowing just the proportion of outcomes either way. The B is in log odds, which are impossible to interpret, all you know is that if it's positive it means there's a higher chance of a positive outcome.

In logistic regression, when plotted, with increasing number of bands, the relationship between the predictor and the probability of an outcome will approach an __________ curve If there were no effect it would look like... Probability increases as the survival rating increases, BUT values are.... Linear function is necessarily *unbounded*...so

If there were no effect it would look like a straight line

What are the three steps for testing for differential item functioning in regression?

If these variables significantly improve model, then dif may be present.

In logistic regression you overcome the statistical problem of predicting dichotomous outcomes by thinking of outcomes in terms of....

In logistic regression you overcome the statistical problem of predicting dichotomous outcomes by thinking of outcomes in terms of probabilities

In logistic regression, odds grow... We transfer odds into log odds (logits) because log odds of __________outcome is a ______________ function of Survival Rating. So now we can turn the odds...

In logistic regression, odds grow... We transfer odds into log odds (logits) because log odds of positive outcome is a linear function of Survival Rating. So now we can turn the odds into a linear representation of data.

In logistic regression, remember to set your positive (or keyed outcome) to __ (but remember it's arbitrary really).

In logistic regression, remember to set your positive (or keyed outcome) to 1 (remember it's arbitrary really).

In logistic regression, the "variables in the equation box" gives us the b coefficient which tells us... And the odds ratio which gives us... If your B is positive then your Exp(b) (odds ratio)...

In logistic regression, the "variables in the equation box" gives us the b coefficient which tells us only that if it's positive it's a greater chance of a positive outcome compared to negative And the odds ratio which gives us how many times more likely you are to have a positive outcome than a negative one for every one point increase in the IV e.g. 1.08. (it can't be less than 0, but a number less than 1 indicates a decreasing chance of a positive outcome. If your B is positive then your Exp(b) (odds ratio) will be greater than one. And vice versa.

In logistic regression, we interpret ________, not ____________, as the latter are hard to interpret. We don't interpret b1 (the slope) directly, we take the __________of it, and interpret that (this transforms data back from __________ to _________).

In logistic regression, we interpret odds, not log odds, as the latter are hard to interpret.. We don't interpret b1 (the slope) directly, we take the exponent of it, and interpret that (this transforms data back from log odds to odds).

Thinking in terms of a clinician's ratings of survival chances (1-100) and a binary outcome (0 died 1 survived). What's the first step of turning this relationship into a way of predicting probability of survival?

Split the continuous variables into bands and take proportion of keyed outcomes for a given band. These bands could be smaller and more numerous if sample size was bigger (and therefore more nuanced and better quality data.

In logistic regression, what is, and represents what, in the regression equation?

Surv rate is just the survival rating in our example (1-100). Our continuous predictor.

The odds ratio is the _____________of b1. That is: The __________ change associated with the ___ point increase in ___________ (Exp(B) = eB = odds ratio). You get the exponent by dividing the _____ of two outcome odds ____ point apart on the IV.

The odds ratio is the exponent of b1. That is: The ratio change associated with the 1 point increase in predictor (Exp(B) = eB = odds ratio). You get the exponent by dividing the odds of two outcome odds one point apart on the IV.

In logistic regression, the more the sample size increases...

the more the proportion approaches a probability of a certain outcome

A conditional mean is the mean outcome _____________on the _________________. The ______________ of patients with positive outcome within each ______________________. Remember, the mean (also item difficulty). of a binary outcome is the ....

A conditional mean is the mean outcome conditional on the predictor variable. The proportion of patients with positive outcome within each rating band Remember, the mean of a binary outcome is the proportion of keyed outcomes

How is differential item function redefined for binary outcomes?

DEFINITION: Differential Item Functioning (DIF) is present when equally able members of different groups have unequal probabilities (chances) to pass the item

Dichotomous variables work fine as predictors in linear models because all they do is...

Dichotomies work fine as predictors in linear models because all they do is determine the difference in the model intercept (when the group variable is the only predictor in regression, then we simply obtain the difference in means of the two groups, which equals B1). If coefficient B1 is significant, then the means are significantly different for the two groups.

In logistic regression, block 1 asks

Does adding a predictor help us to predict outcomes significantly better? Can we improve on the baseline model? Interpret with chi-squared significance

In ordinary linear regression, parameters minimize the sum of squared errors In logistic regression, parameters ____________ the likelihood of observing the ___________ __________. Hypothesis testing in logistic regression use ____________ to see if there's a significant difference between: ________ ________ The difference of these two yields a _______________ statistic; Degrees of freedom = ______________ Are you looking for insignificance or significance?

In ordinary linear regression, parameters minimize the sum of squared errors In logistic regression, parameters maximizes the likelihood of observing the sample values. Hypothesis testing in logistic regression use chi squared to see if there's a significant difference between: The null model: the likelihood of obtaining the observations if the independent variables had no effect on the outcome The full model: the likelihood of obtaining the observations with all independent variables incorporated in the model. The difference of these two yields a Chi-Squared statistic; Degrees of freedom = # of predictors You're looking for significance!

In multiple logistic regression, how do you then interpret each B?

Increase in log odds for one unit increase in Xi with all the other X held constant

In logistic regression, instead of predicting the value of Y from X we... Different underlying equation, instead of score on outcome variable we have ... But similar insofar as we can do ...

Instead of predicting the value of Y from X we predict the log odds of the probability of Y occurring given the value of X. Different underlying equation but instead of outcome we have log transformed odds. But similar insofar as we can do stepwise, hierarchical regression etc, more or less same procedure, but different output on SPSS.

Linear regression is inappropriate for a binary outcome variable because it treats it as continuous . This means the outcome predicted will be a number that is: 1.) 2.) 3.)

Linear regression is inappropriate for a binary variable because it treats it as continuous. This means the outcome predicted will be a number that is: 1.) Unbounded (takes values less than 0 and greater than 1) 2.) Takes non-integer values 3.) Need to be dichotomised. How? e.g. is a 0.7 outcome a 1? e.g. dead or alive for example, male or female?

Logistic regression is used for examining ______________________ with no _____________________ (as outcome variables) e.g.

Logistic regression is used for examining *true dichotomies* with *no underlying response tendency* (as outcome variables) e.g. Died/didn't die Responded to treatment/didn't Passed exam or failed.

In logistic regression, what do you have in place of traditional r squared, and why don't you have traditional r squared?

You use Use Nagelkerke R Square, which is an estimate of how much variance your model explains. Can't use traditional as there's little variance to examine only 0 and 1. So this is pseduo r-squared.