|
What is null model in regression? For my understanding, does it mean
In other words, using only the dependent variable without any independent variables / feature? So, it has nothing to do with null hypothesis? |
||||
|
No, I would say "null model" essentially has the same meaning as "null hypothesis": the model if the null hypothesis is true. What this means, in a particular case, of course depends upon the concrete null hypothesis. Your interpretations as "the average value" (you probably want to say "the marginal distribution on response variable") not taking into account any predictors, is one possibility, corresponding to the null hypothesis of an "omnibus test", testing all the parameters (except the intercept) simultaneously. But interest could well focus on a model of the form $$ y_i = \beta_0 + \beta_1^T x_{1i} + \beta_2^T x_{2i} + \epsilon_i $$ where $x_1$ contains the predictors you know are affecting the outcome, so are not wanting to test, while $x_2$ contains the predictors you are testing. So the null hypothesis will be $\beta_2 =0$ and the null model would be $y_i = \beta_0 + \beta_1^T x_{1i} + \epsilon_i$. So it depends. |
||||
|
|
|
A null model is actually related to a null hypothesis. Take the following univariate model: $Y=\alpha+\beta_{1}X + \epsilon$ My null hypothesis would normally be that $\beta_{1}$ is statistically no different from zero. $H_{0}: \beta_{1}=0$ (null hypothesis) $H_{A}: \beta_{1}\neq 0$ (alternative hypothesis) For a univariate linear model, such as the above, if we were to reject the alternative hypothesis then we could drop $\beta_{1}X$ from the linear model and we'd be left with $Y = \alpha + \epsilon$ Which is your Null model and the same as mean of $Y$. |
||||
|
In regression as described partially in the other two answer the null model is the null hypothesis that all the regression parameters are 0. So you can interpret this as saying that under the null hypothesis there is no trend and the best estimate/predictor of a new observation is the mean which is 0 in the case of no intercept. |
|||||||||
|
fit = lm(formula = y ~ 1, data)and you should see the mean ofy. Also, see MorganBall's answer. I would agree with his response the most. Also, a null model can be a model with $p$ predictors, with an alternative model being one with $p+k$, where k can be 1,2,... additional covariates. – Jon 15 hours ago