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Week 11 - Logistic Regression
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Terms in this set (23)
Generalized linear model
Models used for binary responses
Simple Linear Regression
Quantitative response, quantitative predictor
Maximum likelihood
Its goal is to find the most optimal way to fit the normal distribution to the data. OLS for GLM.
Ordinary Least Squares (OLS)
A method for estimating the parameters of a multiple linear regression model. The ordinary least squares estimates are obtained by minimizing the sum of squared residuals.
Likelihood function
A function that gives the probability of the observed data for various values of the unknown model parameters.
The parameter values that maximize the probability are the maximum likelihood estimates of the parameters.
Link
Serves for relating the parameter of interest (mu) with a linear predictor
Deviance
Is computed by means of the likelihood function, specifically. Is obtained by comparing the goodness model of the fitted and saturated model. An alternative to Sum of Squares.
Residuals in GLM
Pearson's Residuals
Deviance Residuals
Pearson's Residuals
Residuals directly scaled with the standard deviation of Y
Deviance Residuals
A discrepancy measure in the model's fit obtained by the sum of observations contributions
Wald's Test
Test for measuring Maximum Likelihood
Logistic Regression
A statistical analysis which determines an individual's risk of the outcome as a function of a risk factor. The outcome of interest has two categories.
1
Success
0
Failure
Disaggregated
Separated by observation, covariant and response per participant.
Aggragated
Summary of results by combinations.
Logit Link
A logistic function that returns values in the range between 0 and 1 from real numbers domain.
Goodness of fit
Analogue to the F-test for GLM.
receiver operating characteristic (ROC) curve
Plots hit rates against false alarms rates. Each line represents a particular level of sensitivity, and different points on given line represent different response criteria at the same level of sensitivity.
AUC Thresholds
0.9 - 1.0 - Excellent
0.8 - 0.9 - Very Good
0.7 - 0.8 - Good
0.6 - 0.8 - Bad
0.5 - 0.6 - Very Bad
Odds, Log Odds
Are like R2, indicate the relationship between two variables, which values correspond to an effect size.
Odds Ratio (OR)
Estimates how one odds relate to another odds { ad/bc }
Log odds
Convert the values of odds so that the value range starts at 0 and goes from negative to positive symmetrically depending on the relationship between odds.
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