## #StackBounty: #regression #generalized-linear-model #negative-binomial-distribution #multiple-imputation #mice Combining imputations of…

### Bounty: 50

I’m doing some imputation with the MICE package. The outcome variables I am using are zero-inflated, and in the absence of imputation, I would analyze them with a zero-inflated negative binomial regression (ZINB). I would like to do the same with the imputed data; however, I have to manually combine parameters since MICE or its add-ons (as far as I know), do not generate estimates for ZINB.

My question is whether Rubin’s Rule for combining regression parameters (which, to my knowledge, is simply the mean) would apply to regression parameters for ZINB. I believe that regular linear multiple regression parameters can be combined in such a way because they are approximately normally distributed. Do regression parameters for ZINB (and for that matter, Poisson and logistic regression) approximate a normal distribution in the same way? In other words, is the Rubin’s Rule for combining ZINB and other generalized linear regression parameters the same as combining regression parameters from a linear multiple regression?

Thank you!

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## #StackBounty: #generalized-linear-model #least-squares #unbiased-estimator #generalized-least-squares Unbiased estimation for constrain…

### Bounty: 50

I am trying to understand the following. I have a series of measured ground true data $$Y = (y_1,y_2,ldots,y_m)$$ and a series of estimated data $$hat Y = (hat y_1, hat y_2,ldots,hat y_m)$$. Then, it is not uncommon to measure the error using Least Squares, in specific:
$$Err = sum_{i=1}^m (y_i-hat y_i)^2$$
and one usually tries to minimize this. This data can be matrix-valued, i.e., $$Y,hat Y$$ can be a series/vector of matrices. Now, I want to understand how to show that this estimator is unbiased given that this estimator is subject to some polynomial constraints $$p(y_i),p(hat y_i)$$ on the sets $$Y,hat Y$$ (the constaints are equivalent for both sets).

Usually, in a linear regression model, one writes $$hat y_i = b_0 + b_1x_i$$ and needs to prove that the following for the expectation values of the parameters $$b_0,b_1$$:

$$E[b_0]=tilde b_0$$ and $$E[b_1]=tilde b_1$$

where $$tilde b_0$$ and $$tilde b_1$$ are the real parameters $$(y_i = tilde b_0 + tilde b_1 x_i + epsilon_i)$$.

I guess my question is, what other ways are there to show that given $$Y$$ and $$hat Y$$ the LSE is an unbiased estimator? Are there other ways to define this unbiased notion? References would be greatly appreciated.

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## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!

## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!

## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!

## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!

## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!

## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!

## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!

## #StackBounty: #r #generalized-linear-model #stata #quasi-likelihood How flexible is Stata's ivpois? Could I use it for a (quasi) bi…

### Bounty: 50

According to this post on statalist, Stata’s `ivpois` (an instrumental variable approach) is pretty flexible, with very little assumptions.

The problem mentioned in the post is:

"I have a database with counts as dependent variable. This variable suffers from over-dispersion problem."

Wooldridge mentions:

"I would strongly recommend trying IVPOIS, too. Regrettably, this command name is a misnomer. It should be called something like IVEXPON, as it works for any exponential model with multiplicative error. It does not care whether the EEV is continuous or discrete, so it produces consistent estimators under much weaker assumptions."

My thought was, if it works for any exponential model, does that mean it also works for my model, which is technically a `quasibinomial`, but according to this fine post, that boils down to a `binomial` with robust standard errors?

Hence my question: How flexible is Stata’s ivpois? Could I use it for a (quasi) binomial distribution?

Get this bounty!!!