Applying L M Functions to GLMs: An Introduction
As we previously learned about Poisson regressions, it's now time to delve into how Linear Model (LM) functions can be applied to Generalized Linear Models (GLMs). These functions are essential for understanding and utilizing the outputs of GLMs. The original authors of these languages often utilized LM functions, and they form a backbone for both LMs and GLMs. This intersection of LMs and GLMs provides valuable shortcuts for accessing model parts, thereby simplifying the process of extracting model outputs.
LM Functions in GLMs
LM functions allow us to easily access specific components of models, making it possible to view model outputs with functions like print. In contrast, using print alone provides limited information about the model. However, when we use summary, model outputs are displayed automatically, much like LM outputs. Alternatively, we can explicitly print model outputs using the print function, which reveals several useful details, including what model was fit or called, estimated coefficients, degrees of freedom (which represents how many extra observations there are), null deviance, residual deviance (the GLM version of residuals), and AIC scores for the model. While summary provides more detail than print alone, its first part is omitted here to save space.
Model Fit and Summary
The next portion of a GLM summary includes the assembly of deviance residuals, which can be helpful in understanding model fit. This section displays coefficients along with their standard errors, z-scores, and p-values. These metrics allow us to determine if coefficients explain more variability than would be expected by chance alone. Furthermore, some data models may require special over-dispersion parameters due to overdispersedness or having fewer variants or zeros than the model suggests. The model itself provides similar deviance and degree of freedom information as output.
Fischer Scoring Iterations
The last summary part provides us with Fischer scoring iterations, which can be helpful if R has trouble fitting a model. Additionally, the tidy function in the broom package offers a standardized model output. If we only want to focus on regression coefficients, we can extract them using the confitt() function, providing coefficient estimates for models that might require plotting or future analysis similar to the coefficient() function. We can also estimate and display coefficient intervals using the confident() function, which may take some time to run in R for larger models. Furthermore, we can change the intervals estimated using the level option and only estimate confidence intervals for specific parameters using the param option.
Predicting Future Events
As data scientists often aim to predict future events with linear models, the predict() function can be used with GLMs to utilize a fitted model with new data and make predictions. If no new data file is specified, the predict() function returns predictions based on the data used for fitting the model. However, if new data is specified, the prediction function will return data from the prediction, which corresponds to the new data frame.
Exploring GLMs with Geo Data
This article aims to explore GLMs using an example dataset that examines daily civilian non-firefighter injuries in Louisville, Kentucky. This data requires modeling using a Poisson distribution because it is count data with many zeros.
"WEBVTTKind: captionsLanguage: enwelcome back during the previous exercises you learned about Poisson regressions now you will learn how L M functions can be applied to GL ends these functions help us understand and use GLM outputs besar has many functions for interacting with linear models and by extension GL ends in fact both lms and GLM's form a back one of our and its predecessor s the original authors of these languages often use LM s these functions allow us to easily access some parts of models thus rather than needing to manually interrogate an extract model outputs are gives helpful shortcuts these shortcuts allow us to see model outputs with functions like print and also makes statistical inferences with functions like summary when we were running at G L M model outputs automatically appear just like an LM alternatively we can explicitly print model outputs using the print function this output tells us several useful things including what model was fit or called the estimated coefficients the degrees of freedom which can be thought of as how many extra observations we have the null deviance and residual deviance which is the GLM version of residuals and the AIC score for the model in contrast to print summary provides more detail the first part of a summary output is the same as print and I did not include it here to save space the next portion of the GLM summary includes the Assembly of the deviance residuals which can be helpful for understanding a model fit next summary displays coefficients as well as your standard errors z-scores and p-values these can tell us if coefficients explain more variability than will be expected by chance alone next summary tells us about dispersion although not covered in this course some data can be over dispersed and neither have more variants or zeros than the model suggests these models require special over dispersion parameters next the model provides us similar deviance and degree of freedom information as the output last summary provides us with the Fischer scoring iterations which can be helpful if R has trouble fitting a model the tidy version also provides a standardized model output the tidy function in the broom package if we only want to look at the regression coefficients we can extract them using the couette function this provides us with the coefficient estimates for a model we might want to extract coefficients to either plot them or use them in future analysis similar to the coefficient function we can also estimate and display coefficient intervals using the confident function this function could take a while to run an R for larger models we can also change which intervals we estimate using the level option and only estimate the confidence interval for select parameters using the param option as a data scientist we often want to use models to predict future events like linear models the predict function can be used with g lms to use a fitted model with new data and make predictions if no new data file is specified then the predict function returns predictions based on the data used to fit the model if new data is specified the data from the prediction function is a vector that corresponds to the new data data frame you will get to apply these functions on GL and outputs that examine daily civilian non firefighter injuries this data is from Louisville Kentucky the data needs to be modeled using a Poisson distribution because it is count data with many zeros now let's look at the fire data and learn how to explore Geowelcome back during the previous exercises you learned about Poisson regressions now you will learn how L M functions can be applied to GL ends these functions help us understand and use GLM outputs besar has many functions for interacting with linear models and by extension GL ends in fact both lms and GLM's form a back one of our and its predecessor s the original authors of these languages often use LM s these functions allow us to easily access some parts of models thus rather than needing to manually interrogate an extract model outputs are gives helpful shortcuts these shortcuts allow us to see model outputs with functions like print and also makes statistical inferences with functions like summary when we were running at G L M model outputs automatically appear just like an LM alternatively we can explicitly print model outputs using the print function this output tells us several useful things including what model was fit or called the estimated coefficients the degrees of freedom which can be thought of as how many extra observations we have the null deviance and residual deviance which is the GLM version of residuals and the AIC score for the model in contrast to print summary provides more detail the first part of a summary output is the same as print and I did not include it here to save space the next portion of the GLM summary includes the Assembly of the deviance residuals which can be helpful for understanding a model fit next summary displays coefficients as well as your standard errors z-scores and p-values these can tell us if coefficients explain more variability than will be expected by chance alone next summary tells us about dispersion although not covered in this course some data can be over dispersed and neither have more variants or zeros than the model suggests these models require special over dispersion parameters next the model provides us similar deviance and degree of freedom information as the output last summary provides us with the Fischer scoring iterations which can be helpful if R has trouble fitting a model the tidy version also provides a standardized model output the tidy function in the broom package if we only want to look at the regression coefficients we can extract them using the couette function this provides us with the coefficient estimates for a model we might want to extract coefficients to either plot them or use them in future analysis similar to the coefficient function we can also estimate and display coefficient intervals using the confident function this function could take a while to run an R for larger models we can also change which intervals we estimate using the level option and only estimate the confidence interval for select parameters using the param option as a data scientist we often want to use models to predict future events like linear models the predict function can be used with g lms to use a fitted model with new data and make predictions if no new data file is specified then the predict function returns predictions based on the data used to fit the model if new data is specified the data from the prediction function is a vector that corresponds to the new data data frame you will get to apply these functions on GL and outputs that examine daily civilian non firefighter injuries this data is from Louisville Kentucky the data needs to be modeled using a Poisson distribution because it is count data with many zeros now let's look at the fire data and learn how to explore Geo\n"
