The differences you observe in the coefficients and p-values between `stepwiseglm`, `glmfit`, and `fitglm` can be attributed to the different algorithms and methodologies employed by these functions. Here's an explanation of each function and their differences:
1. `stepwiseglm`: This function performs stepwise model selection using generalized linear models (GLMs). It automatically adds or removes predictors to find the best subset of predictors based on a specified criterion (e.g., AIC, BIC). The selection process is based on statistical tests and model comparison. However, it's important to note that stepwise selection can be sensitive to the specific dataset and may not always produce the most accurate or stable results.
2. `glmfit`: This function fits a GLM using maximum likelihood estimation (MLE). It estimates the model coefficients by maximizing the likelihood of the observed data given the model. `glmfit` does not perform automatic variable selection or model comparison. It simply estimates the coefficients based on the specified predictors and response.
3. `fitglm`: This function also fits a GLM using maximum likelihood estimation (MLE). It is similar to `glmfit`, but it provides additional flexibility and options for specifying the model, including different link functions and error distributions. `fitglm` allows for more customization in the GLM fitting process.
The differences in coefficients and p-values between `stepwiseglm` and `glmfit` can arise due to the different approaches used for model selection and estimation. `stepwiseglm` may prioritize a subset of predictors based on the selection criterion, while `glmfit` estimates coefficients for all specified predictors without any selection process.
In your case, since you have already identified the two predictor variables using `stepwiseglm`, it might be more appropriate to use `fitglm` to fit the GLM with the selected predictors. `fitglm` provides more flexibility and control over the model specification and fitting process.
It's important to note that no single method guarantees the "best" choice of predictors or model. It's recommended to consider the specific characteristics of your data, the goals of your analysis, and the underlying assumptions of the GLM to make an informed decision.
