What is the log-likelihood of the saturated model?

general non-zero
The log-likelihood of the saturated model is in general non-zero. The deviance (in its original definition) of the saturated model is zero. The deviance output from softwares (such as R) is in general non-zero as it actually means something else (the difference between deviances).

How do you interpret the log-likelihood of a model?

The log-likelihood value of a regression model is a way to measure the goodness of fit for a model. The higher the value of the log-likelihood, the better a model fits a dataset. The log-likelihood value for a given model can range from negative infinity to positive infinity.

What is a saturated model in logistic regression?

In general, a saturated model is defined as one where the number of parameters is equal to the number of distinct covariate patterns.

How do you calculate deviance from log-likelihood?

More precisely, the deviance is defined as the difference of likelihoods between the fitted model and the saturated model: D=−2loglik(^β)+2loglik(saturated model).

How do you show a model is saturated?

A model is saturated if and only if it has as many parameters as it has data points (observations). Or put otherwise, in non-saturated models the degrees of freedom are bigger than zero.

What is parsimonious model?

Parsimonious models are simple models with great explanatory predictive power. They explain data with a minimum number of parameters, or predictor variables. The idea behind parsimonious models stems from Occam’s razor, or “the law of briefness” (sometimes called lex parsimoniae in Latin).

What is a good log likelihood score?

Log-likelihood values cannot be used alone as an index of fit because they are a function of sample size but can be used to compare the fit of different coefficients. Because you want to maximize the log-likelihood, the higher value is better. For example, a log-likelihood value of -3 is better than -7.

How do you find the likelihood function?

The likelihood function is given by: L(p|x) ∝p4(1 − p)6. The likelihood of p=0.5 is 9.77×10−4, whereas the likelihood of p=0.1 is 5.31×10−5.

What is a saturated model in log linear regression?

A “log-linear model” is a statistical model for the natural logarithm (ln) of the expected frequency. The terms corresponding to main effects represent departures from equal marginal frequencies. The model with terms corresponding to all possible main effects and interactions is called the saturated model.

Is deviance the same as log likelihood?

Model deviance is a metric that can be used to assess how well a given model fits to the entered data. Deviance is calculated based on another metric known as likelihood (or log likelihood).

How do you measure deviance?

Deviance or delinquency are commonly measured in two ways: through official records concerning convictions and through self-reported measures.

How many parameters does a saturated model have?

As you can see, the measure model with three indicators is itself a saturated model. To be saturated it should have 3*4/2 + 3 = 9 parameters being estimated, which is the case.