If you're only interested in prediction and want to keep all the explanatory variables in your model, you can

1) Run a principal component analysis (PCA) on your explanatory variables. See eg function dudi.pca in package ade4 for R

2) Use the row scores from the PCA as explanatory variables in your model. The advantage is that the scores are uncorrelated. You can even "filter" your data by selecting only the most important components in the PCA (which will be fewer than the original variables).

You can use the log-likelihood value to compare the models by using the Tweedie package in R.

For estimation based on Estimating function approach you can use the SIC (Score Information Criterion) implemented in the R package mcglm, see http://git.leg.ufpr.br/wbonat/mcglm.

However, your response variable is not Tweedie distributed.

Tweedie models are suitable for continuous random variable with exact zeros.

Your response variable presents only four different numbers (0, 1, 2, and 3).

Perhaps, a model for nominal response variables like the multinomial model represents better your response variable.

Renaud and Wagner,

Thank you very much for your reply.

Renaud, will the model using the scores be suitable to use for prediction; for getting the grade using the raw outputs from machine?

Wagner, response can take any values between 0 and 3. In fact it is the average of grades(0,1,2 or 3) given by several experts. So it includes 0,0.2,0.4,...

Azita

My concerning is because you have a bounded random variable. The Tweedie distribution is a positive random variable with a probability of exact zeros, but it is unbounded. The domain is from exacts 0 to infinity.

Perhaps, a better approach is to use the beta or simplex distribution with some additional feature to deal with exact zeros. Another approach is to use quasi-likelihood methods. Perhaps, the discussion for the second example of this paper

http://arxiv.org/abs/1504.01551

can be useful to explain my point.

The ideas proposed by Renaud can also be used in all these models in a similar way including prediction.

Wagner

Hello. Sorry for not replying for such a long time.

Wagnar, I see your point and I'm going to try zero inflated beta. I've found "zoib" in R and Stata. Are there any other function that you would recommend?

I'm not insisting to use all the predictors so some type of stepwise selection would be very helpful. Do you know any such function that I can use here.

Many thanks for your helps.

Perhaps, the betareg package although it does not provide functions for zero-inflated beta regression models. For model selection you can use the log-likelihood ratio test in the orthodox way. However, I prefer a more robust approach based on quasi-likelihood for fitting you can use the mcglm package available at

http://git.leg.ufpr.br/wbonat/mcglm

For model selection the SIC (Score information criterion) can be used.

If you decide persuade in this direction I can assist you.

Best

That would be extremely helpful!

I've had a look through the document for mcglm. This is your own work, fantastic!!

I have 5 response for each participant and I need to find a model for each of them using 8 covariates (1 factor and the rest numeric). All responses are between 0 and 3 and zero inflated. Do you think I can use mcglm?

What shall I use for the parameters as a starter?

Thanks

Yes, you can use the mcglm approach. In fact, it was designed to deal with multivariate response variables. You have to translate your response variables into the [0,1) interval, before run the analysis. Attached you find a simple example to guide you toward your data analysis. In general the mcglm package provides automatic initial values.

Please, let me know if you have doubts.

Best

Thanks Wagner.

Response values are in [0,1] range(include 1). Will that work? In the manual you have used a large data. My data has only 92 participants. Will mcglm be suitable?

And where can I find the attachment? Did you mean the manual?

Many thanks

Yes. 92 observations is OK.

I attached the file in this email. BoundedExample.R

Please let me know if you have problem to find the file.

I am not sure, how this website works.

Best

I've applied the example to my data and I've got some output.

I have G, R, B, A and S for outcomes and say C,T,U,V,W,X,Y,Z as covariates. Since some covariates had missing value I had to make a new data of complete cases (89 rows) since the model gives error message with missing values.

I've used the same link and variance functions (logit and binomialP). Now I have some questions(many) and would be grateful for your answer.

1- Does the model take into account the inflation at zero and also having some 1 as outcome?

2- To assess the fit, is that right to just plot the first 89 fitted values against G, the second 89 fitted against R and so on? If this is the right approach, this model doesn't show a good fit but I suppose this is just the starting point and I need to improve the model.

3- I'm trying to find a predictive model. So having C, T-Z find G,R,B,A and S. We still don't know if this model is possible ( if covariates can define outcomes). The aim is to see if there is a model that an inexpert person can use to get  G,R,B,A and S using C, T-Z. If the model works, using logit links doesn't seem to be interpretable. I think I read somewhere that log link can be used for beta regression. Is that right? I tried it here but asks for initial values. How do I choose the suitable initials?

4- mc_sic doesn't accept the fitted model as a valid object!

Sorry for being long winded  and thanks for your helps.

Hi Azita,

1 - Yes.

2 - The models are based on second-moment only. So, a plot the residuals versus fitted values is a good way to check the model. You are assuming only a relationship between the mean and variance, the models are quite robust to misspecification.

3 - If you included all your covariates in the mean model, you can use the Wald type test to check the significance of your covariates. It is obtained by using the summary() method for mcglm objects. About the log link functions for bounded response variable, you can use, but it is not make sense to me, because the log link allows all positive values for the mean of the response variables, while the response variable itself is restricted to a bounded interval.

4 - The SIC information criterion is quite different from the orthodox AIC and BIC. The idea is check if the inclusion of a new covariate is significant or not, but before fit the model using this covariate. I have to include some examples about how to use the SIC.

I would like to suggest to you send to me your data set, in this way I can check what's the problem with my mc_sic function. In general it works well until now. You can send me by email [email protected].

The mcglm package is under development, the methodology was recent proposed and the paper will be publish soon in the Journal of Royal Statistical Society - Series C. But, the package still requires improvements. Real data analysis and different users help me to improve the package.

Best