Generalized Linear Models
y is categorical variables
Link function: the categorical variables and numeric variables together
Results obtained using the 0 or 1 probability values is selected to evaluate 0 or1
Functional relationship:
Direct proportion function:
logistics function S -shaped curve:
Odds ratio tendentious reaction of events
logistics function and probit regression function much like, but the logistics function is based on the binomial distribution, probit regression function based on a normal distribution.
Regression function Probit : cumulative probability of a normal distribution curve
logistics function does not require independent + homogeneity of variance + normality.
p is in accordance with how x change, find the partial derivative:
Wherein, [alpha] and β given by the previous data, is determined by the maximum likelihood estimation.
Overall samples with normal distribution is estimated, taking two different points mean hypothesis test, to find that the maximum likelihood function, is specifically listed in the likelihood function of μ derivative, the derivative is zero so that the maximum is found. And so on, you can take n points. Seeking variance is the same reason for SD derivation.
The end result is
According to the above ideas, rather than reverse image idea was:
It must be an overall normal distribution using MLE estimate parameters, then equivalent to the least squares method. If it is not normal, it is different.
ANOVA, Pearson’s r, t-test, regression
Generalized linear model using probability obtained, the probability that the original data back, computes the difference, the difference is in line with chi-squared distribution. LR
Evaluation index goodness of fit:
AIC when the interpretation of the same variable in the same number of variables will be comparable. The smaller the better.
K selection: If increasing the K value is such likehood vary widely, should preferably, but increased if the K value is such likehood little change, not desirable.
For small data, less than 40 , a flat data, the repetition is not sufficiently explain the law, so a correction is introduced. Modify the original data by expanding the amount of n decreases K .
