Stepwise Regression with Diagnostic Checking

Stepwise regression with diagnostic checking

Stepwise regression is the process of building statistical models by adding or reducing predictor variables. This technique usually involves a series of tests, including T- tests and F- tests to produce the most effective models. The variables to be added or subtracted are selected using the test results of the estimated coefficients. Even though stepwise regression is one of the most efficienttools in data analysis, it requires one to have experience in statistical testing to produce the most desirable results. Unlike most regression models, stepwise regression models require a keen eye to know if they make sense or not.

Diagnostic checking in stepwise regression

As stated, stepwise regression is an essential tool in data manipulation. However, there are many drawbacks that could affect the quality of results obtained from stepwise regression models, which could lead to misinterpretation of these results. Some of the drawbacks that are considered especially unfavorable include:

  • Heteroscedasticity
  • Serial correlation of error terms
  • Nonlinearities
  • Structural changes in regression coefficients
  • Omitted variables
  • Functional misspecification

Thus, a high quality diagnostic check for these situations is necessary to make sure that the models produced are accurate. Diagnostic checks are pure procedures and exploratory tools for extracting information about data structure in connection with residual plots and other diagnostic tools.

How stepwise regression works

There are two ways of performing stepwise regression:

  • Starting with all the available predictor variables: In this method, you delete one variable after the other as the regression model develops or progresses. If you have a small number of variables and you wish to get rid of a few, this is the method to use. The variable with the least “F –to –remove” value is eliminated from the model at each step. Below is how you can effectively calculate the “F –to –remove” value:
  1. Calculate a t –statistic for the predicted coefficient of each and every variable in the regression model.
  2. Square the t –statistic value, and this will create the “F –to –remove” value.
  • Starting the test without predictor variables: Also known as theforward method, this technique requires you to add one variable at a time as the regression model develops. It is the perfect method to use when you have a huge set of predictor variables. Here, you will create an “F –to –add” statistics using the same steps above. However, the system will compute the statistic for the variables that are not in the model. In this technique, the variable that has the highest “F –to –add” value will be added to the model.

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Advantages and disadvantages of step wise regression

Stepwise regression has many advantages over other regression methods. Here are a few:

  • The capability to manage a huge amount of potential predictor variables, which helps fine-tune regression models to select the most appropriate predictor variables from the given options.
  • It is much faster than other automated model selection methods
  • Since stepwise regression allows you to watch how variables are added or removed from the models, you can obtain valuable information about the nature and quality of the available predictor variables.

But just like other regression techniques, stepwise regression has its drawbacks. They include the following:

  • Stepwise regression models have numerous potential predictor variables but very little data to predict meaningful coefficients. Data can be added to these models but this does not help much.
  • The R squared values are often too high
  • If the model has multiple predictor variables that are highly correlated, only one variable will be used
  • Chi square and F tests listed next to the output variables do not have any distributions
  • The P values given in stepwise regression models are not accurate
  • The confidence intervals and predicted values are too narrow
  • The adjusted r squared statistics may be high and then drop drastically as the model develops. If you experience this when working with a stepwise regression model, look for the variables that were removed or added before this happened and adjust the model accordingly.
  • Collinearity is usually a major problem. Too much collinearity may cause the program you are using for regression to put, or rather, dump all the predictor variables into the model.

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