# Logistic Regression, Part II Flashcards

1
Q

How do we find the odds?

A

P/1-P

2
Q

How do we find the probability?

A

O/1+O

3
Q

What are the assumptions for linear regression?

A

L: Linearity between Y and X; for linear regression to show association (direction and magnitude) between X and Y, the RL needs to be linear

I: Independence
Outcome of one observation is not dependent on another

N: Normality
For any fixed value of the independent value, the dependent variable is normally distributed

E: Error
Errors have homoscedasticity
Residuals have constant variance at any valueof X
(Expected and observed value of y differnece)

4
Q

Why do we use logistic regression with binary variables?

A

Change in proportion with each one unit change in X is non-linear.

5
Q

What is the linear model and what does each expression mean?

A

Yi = B0 + BiXi + Ei

Yi = independent variable (outcome)

B0 = Population y-intercept (alpha)

Bi = slope coefficient (beta) average change in Y when X changes in one unit

Xi= independent variable

Ei = random error term

Linear component =

B0 + BiXi

6
Q

What is the logistic regression model and what does each expression mean?

A

Ln(P/1-P) = B0 +BiXi+ B2X2+…

Outcomes is Ln(p/1-p)
Log odds of binary varaible

Independent variable denoted by x

Alpha is the log odds of outcomes when x = 0

Beta: change in log odds with one unit change in x when w = 1 versus x = 0

7
Q

What is another form for logistic regression model?

A

P = (e^alpha+betax)/ 1 +(e^alpha + betax)

This is because probability = O/1 + O

8
Q

Why do we use logistic regression instead of 2 by 2 tables?

A

2 by 2 tables rely on both dependent and independent variable being binary. Not possible when one is continous.

9
Q

How do we control for confounder in logistic regression model?

A

Remove them.

Ex: ln(p/1-p) = (-2.83) + 1.07x1 + 0.79x2 + 0.05x3

X2 and X3 are gender and alcohol abuse

X1 is HIV status

Estimate association for HIV status and death, controlling for gender and alcohol abuse.

Take e ^ beta of HIV status ONLY.

e^1.07 = 2.9153.

The odds of death for those with HIV positive is 2.9 times those without positive status, controlling for gender and alcohol abuse.

10
Q

What is relationship between MH method and logistic regression?

A

MH methods is THE SAME as multivariate logistic regression controlling for other variables.

11
Q

What is the basic form of the logistic regression model?

A

ln(p/1-p) = alpha +betax