## Summary

Performs generalized linear regression (GLR) to generate predictions or to model a dependent variable in terms of its relationship to a set of explanatory variables. This tool can be used to fit continuous (OLS), binary (logistic), and count (Poisson) models.

## Usage

This tool can be used in two operation modes. You can evaluate the performance of different models as you explore different explanatory variables and tool settings. Once a good model has been found, you can fit the model to a new dataset.

Use the Input Features parameter with a field representing the phenomena you are modeling (the Dependent Variable parameter) and one or more fields representing the explanatory variables.

The Generalized Linear Regression tool also produces output features and diagnostics. Output feature layers are automatically added to the map with a rendering scheme applied to model residuals. A full explanation of each output is provided below.

It is important to use the correct model type (Continuous, Binary, or Count) for your analysis to obtain accurate results of your regression analysis.

Model summary results and diagnostics are written to the messages window, and charts will be created below the output feature class. The diagnostics reported depend on the Model Type parameter. The three model type options are as follows:

- Use the Continuous (Gaussian) model type if the dependent variable can accept a wide range of values such as temperature or total sales. Ideally, the dependent variable will be normally distributed.
Use a Binary (logistic) model type if the dependent variable can accept one of two possible values, such as success and failure or presence and absence. The field containing the dependent variable must be numeric and contain only ones and zeros. There must be variation of ones and zeros in your data.

Consider using a Count (Poisson) model type if the dependent variable is discrete and represents the number of occurrences of an event such as a count of crimes. Count models can also be used if the dependent variable represents a rate and the denominator of the rate is a fixed value such as sales per month or number of people with cancer per 10,000 in the population. A Count model assumes that the mean and variance of the dependent variable are equal, and the values of the dependent variable cannot be negative or contain decimals.

The Dependent Variable and Explanatory Variable parameters should be numeric fields, containing a range of values. This tool cannot solve when variables have the same values (if all the values for a field are 9.0, for example).

Features with one or more null values or empty string values in prediction or explanatory fields will be excluded from the output. You can modify values using the Calculate Field tool if necessary.

Review the over- and underpredictions evident in the regression residuals to see whether they provide information about potential missing variables from your regression model.

You can use the regression model that has been created to make predictions for other features. Creating these predictions requires that each prediction feature has values for each of the explanatory variables provided. If the field names from the input features and prediction locations parameters do not match, a variable matching the parameter is provided. When matching the explanatory variables, the fields from the Input Features and Input Prediction Features parameters must be of the same type (double fields must be matched with double fields, for example).

The GeoAnalytics implementation of GLR has the following limitations:

- It is a global regression model and does not take the spatial distribution of data into account.
- Analysis does not apply Moran's I test on the residuals.
- Feature datasets (points, lines, polygons, and tables) are supported as input; rasters are not supported.
- You cannot classify values into multiple classes.

This geoprocessing tool is powered by ArcGIS GeoAnalytics Server. Analysis is completed on your GeoAnalytics Server, and results are stored in your content in ArcGIS Enterprise.

When running GeoAnalytics Server Tools, the analysis is completed on the GeoAnalytics Server. For optimal performance, make data available to the GeoAnalytics Server through feature layers hosted on your ArcGIS Enterprise portal or through big data file shares. Data that is not local to your GeoAnalytics Server will be moved to your GeoAnalytics Server before analysis begins. This means that it will take longer to run a tool, and in some cases, moving the data from ArcGIS Pro to your GeoAnalytics Server may fail. The threshold for failure depends on your network speeds, as well as the size and complexity of the data. Therefore, it is recommended that you always share your data or create a big data file share.

Learn more about sharing data to your portal

Learn more about creating a big data file share through Server Manager

## Syntax

GeneralizedLinearRegression(input_features, dependent_variable, model_type, explanatory_variables, output_features_name, {generate_coefficient_table}, {input_features_to_predict}, {explanatory_variables_to_match}, {dependent_variable_mapping}, {data_store})

Parameter | Explanation | Data Type |

input_features | The layer containing the dependent and independent variables. | Record Set |

dependent_variable | The numeric field containing the observed values to be modeled. | Field |

model_type | Specifies the type of data that will be modeled. - CONTINUOUS — The dependent_variable is continuous. The Gaussian model will be used, and the tool will perform ordinary least squares regression. This is the default.
- BINARY — The dependent_variable represents presence or absence. This can be either conventional 1s and 0s, or string values mapped to 0 or 1s in the Match Explanatory Variables parameter. The Logistic Regression model will be used.
- COUNT —The dependent_variable is discrete and represents events, for example, crime counts, disease incidents, or traffic accidents. The Poisson regression model will be used.
| String |

explanatory_variables [explanatory_variables,...] | A list of fields representing independent explanatory variables in the regression model. | Field |

output_features_name | The name of the feature class that will be created containing the dependent variable estimates and residuals. | String |

generate_coefficient_table (Optional) | Specifies whether an output table with Boolean values will be generated. - CREATE_TABLE —A table with coefficient values will be generated.
- NO_TABLE —A table with coefficient values will not be generated. This is the default.
| Boolean |

input_features_to_predict (Optional) | A layer containing features representing locations where estimates should be computed. Each feature in this dataset should contain values for all the explanatory variables specified. The dependent variable for these features will be estimated using the model calibrated for the input layer data. | Record Set |

explanatory_variables_to_match [[Field from Prediction Locations, Field from Input Features],...] (Optional) | Matches the explanatory variables in the input_features_to_predict parameter to corresponding explanatory variables from the input_features parameter—for example, [["LandCover2000", "LandCover2010"], ["Income", "PerCapitaIncome"]] | Value Table |

dependent_variable_mapping [dependent_variable_mapping,...] (Optional) | Two strings representing the values used to map to 0 (absence) and 1 (presence) for binary regression. By default 0 and 1 will be used. For example, if you wanted to predict an arrest and had fields with values of Arrest and No Arrest, you would enter No Arrest for False Value (0) and Arrest for True Value (1). | Value Table |

data_store (Optional) | Specifies the ArcGIS Data Store where the output will be saved. The default is SPATIOTEMPORAL_DATA_STORE. All results stored in the SPATIOTEMPORAL_DATA_STORE will be stored in WGS84. Results stored in a RELATIONAL_DATA_STORE will maintain their coordinate system. - SPATIOTEMPORAL_DATA_STORE —Output will be stored in a spatiotemporal big data store. This is the default.
- RELATIONAL_DATA_STORE —Output will be stored in a relational data store.
| String |

#### Derived Output

Name | Explanation | Data Type |

output | The output feature service containing the dependent variable estimates for each input feature. | Record Set |

output_predicted_features | An output layer containing the input variables and predicted explanatory values. | Record Set |

coefficient_table | An output table with coefficient values. | Record Set |

## Code sample

The following Python window script demonstrates how to use the GeneralizedLinearRegression tool.

In this script, you create a model and predict if an arrest was made for given crimes.

```
#-------------------------------------------------------------------------------
# Name: GeneralizedLinearRegression.py
# Description: Run GLR on crime data and predict if an arrest was made for a crime reporting.
#
# Requirements: ArcGIS GeoAnalytics Server
# Import system modules
import arcpy
# Set local variables
trainingDataset = "https://analysis.org.com/server/rest/services/Hosted/old_crimes/FeatureServer/0"
predictionDataset = "https://analysis.org.com/server/rest/services/Hosted/new_crimes/FeatureServer/0"
outputTrainingName = "training"
# Execute GLR
arcpy.geoanalytics.GeneralizedLinearRegression(
trainingDataset, "ArrestMade", "BINARY", "CRIME_TYPE; WARD; DAY_OF_MONTH", outputTrainingName,
"NO_TABLE", predictionDataset, "CRIME_TYPE CRIME_TYPE;WARD WARD;DAY_OF_MONTH DAY_OF_MON",
"Arrest NoArrest", "SPATIOTEMPORAL_DATA_STORE")
```

## Environments

- Output Coordinate System
The coordinate system that will be used for analysis. Analysis will be completed in the input coordinate system unless specified by this parameter. For GeoAnalytics Tools, final results will be stored in the spatiotemporal data store in WGS84.

## Licensing information

- Basic: Requires ArcGIS GeoAnalytics Server
- Standard: Requires ArcGIS GeoAnalytics Server
- Advanced: Requires ArcGIS GeoAnalytics Server