ASA Connect

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Nicole

The assumption that a rv is Poisson entails that its mean is equal to its variance, which is a pretty strong assumption that often fails with real-world data. I would suggest replacing the Poisson with a negative binomial assumption. The negative binomial is the marginal distribution for a Poisson random variable when the rate parameter has a Gamma(alpha,beta) distribution. It's often used as a robust alternative to the Poisson.

Blaise F Egan

On second thoughts, Stanley Lazic is right - the underdispersion is caused by the bounded nature of the data, so neither a Poisson nor a negative binomial is appropriate. I would go for a cumulative logistic regression. That would give you P(y <=1), P(y <=2),...P(y <=6). (No need for P(y <=7) as it is known to be 1.)

Blaise F Egan

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.

Hello All,

I was conducting an analysis in which the main point was to determine if an interaction was significant. My outcome was a a count of how many correct answers a participant received from a set of 7 questions (range from 0 to 7 although everyone had at least 1 correct answer). All predictors, excepting one were categorical. It was first suggested that I use a linear regression model but upon reviewing the data it didn't appear that the assumptions were met despite a sample size of about 500. I then went on to use Poisson regression as I have been taught that such a model is good for count data but the model fit statistics suggested that the model wasn't a good fit (Value/DF ~ 0.21), that it was in fact underdispersed. 

My question is,

1. What other steps should I have taken with the data in order to get a better model (if I am to keep all of the predictors in the model), especially if my main point is to determine if the interaction is significant?

2. Should the dependent variable just have been transformed and then utilized in a linear regression model or does that lose interpretation?

3. It seems that treating something as continuous when it is not is the default but is that always the case?

4. What are some good sources of underdispersion,also what does that mean in a general sense?

Thanks for any insight you all are able to provide.