![DV: categorical (dichotomous )
Exploring Relationships
Is a variable related to the proportions of another?
The first step is to examine the data using crosstabs
Chi square test
Logistic regression relies on an estimation procedure
Models the probability of an outcome
Transforms the probability of an event occurring into its
odds
In logistic regression the regression coefficient (b) can
be interpreted as the change in the log odds associated
with a one-unit increase change in the associate
predictor variable.
ln[Y/(1−Y)]=a + bX](https://image.slidesharecdn.com/m8-220922221756-b27c6b55/85/M8-logreg-ppt-1-320.jpg)
M8.logreg.ppt
- 1. DV: categorical (dichotomous ) Exploring Relationships Is a variable related to the proportions of another? The first step is to examine the data using crosstabs Chi square test Logistic regression relies on an estimation procedure Models the probability of an outcome Transforms the probability of an event occurring into its odds In logistic regression the regression coefficient (b) can be interpreted as the change in the log odds associated with a one-unit increase change in the associate predictor variable. ln[Y/(1−Y)]=a + bX
- 3. Multiple Regression Logistic Regression LOGIT Used to make predictions about an unknown event from known evidence DV continuous IV can be any level of measurement Assumes linear relationship Uses least squares estimation (computed coefficients that minimized the residuals for all cases) Normally distributed variables Equal variance Used to determine which variables affect the probability of a particular outcome DV categorical IV may be any level of measurement Doesn’t assume linear relationship but rather a logit transformation Uses maximum likelihood estimation (when the dependent variable is not normally distributed, ML estimates are preferred to OLS estimates because they are unbiased ) Doesn’t assume normal distribution, or equal variance Less stringent
- 4. DV: categorical The Odds Ratio Prob (event) Prob (not event) = e b 0 + b 1 x The left hand side of the equation is the odds: where the e is the base of the natural log. What this equation tells us is that the e, raised to the power of, say x1, is the factor by which the odds change when x1 increases by one unit, controlling for the other variables in the equation. When the coefficient is positive, the odds increase; when the coefficient is negative, the odds decrease. b 0 + b 1 x 1 + b 2 x 2 + b 3 x 3 + ….. = e Crude OR –simple logistic regression Adjusted OR- multiple logistic regression
- 5. Examining likelihood of event Likelihood conventionally expressed on a scale of 0 to 1 Many health outcomes are dichotomous: Depressed=1 (yes) vs Depressed=0 (no) Can be used to compare likelihood in groups: Case vs controls Males vs females Chemo vs no chemo
- 6. What logistic regression predicts probability of Y occurring given known values for X(s). In LR the DV is transformed into the natural log of the odds. This is called logit (short for logistic probability unit). Probabilities ranged between 0.0 and 1.0 are transformed into odds ratios that range between 0 and infinity. If the probability for group membership in the modeled category is above some cut point (the default is 0.50), the subject is predicted to be a member of the modeled group. If the probability is below the cut point, the subject is predicted to be a member of the other group. For any given case, logistic regression computes the probability that a case with a particular set of values for the independent variable is a member of the modeled category.
- 8. Logistic Regression Logistic regression estimates the probability of a certain event occurring using the odds ratio by calculating the logarithm of the odds Uses Maximum likelihood estimation (MLE) to transform the probability of an event occurring into its odds, a nonlinear model Odds ratio is the probability of occurrence of a particular event over the probability of non occurrence Odds ratio is useful in providing an estimate of the magnitude of the relationship between binary variables Allows one to examine the effects of the variables on the relationship- how y varies when x varies
- 9. model fit The probability of the observed results, given the parameter estimates, are used to determine how well the estimated model fits the data Likelihood index: If the model fits perfectly, the – 2LL, will equal 0. Goodness-of-fit statistic (similar to the F test in multiple regression) takes into consideration the difference between the observed probability of an event and the predicted probability—chi square distribution. Hosmer Lemeshow test (based on Chi Square) compares prediction to “perfect model”. When not significant, the null hypothesis that the model fits is supported, ie a non significant result indicates
- 10. R2 values quantify the proportion of the variance explained by the model In logistic regression the Nagelkerke statistic is used to estimate the Psuedo R squared, which is the magnitude of the relationship between the dependent variable and the set of independent variables in the model. The b-weights and constant associated with each IV are used in Logistic regression to determine the probability of a subject doing one thing or the other Instead of a score as with continuous variables, a probability ranging from 0 –1 is given. If the probability is greater than .05, the prediction is for the occurrence and if less than .05 for non occurrence Signs of the b-wgts show direction of relationship