# Spatial Lag Response Plot

## Contents

## Introduction

The response plot is a graph that shows plots between the response or dependent variable \(y\) and the predicted or fitted value \(\hat{y}\). It is used to check linearity and to detect influential cases and outliers of the spatial lag model. More discussion and explanation of spatial lag models can be found **here**.

## Inputs

To show the tool in action, we will run the tool looking at a spatial lag model of effect of income on rent across Adelaide. In doing so, we assume that the **Lagrange Multipliers** test has indicated that a spatial lag model is the appropriate treatment for this dataset, as opposed to the **Spatial Error Model**.

**Select***Adelaide GCCSA*as your area**Select***SA2-based T02 Selected Medians and Averages as at 2011-08-11*as your dataset, selecting*2011*as your time filter, and all attributes**Spatialise**the dataset**Generate a Contiguous Spatial Weights Matrix**for the spatialised dataset

Once you have done this, open the Spatial Lag Response Plot (*Tools → Charts → Spatial Lag Response Plot*) and enter the parameters as shown in the image below (these are explained in more detail after the image)

*Dataset Input:*Select the spatialised dataset for which you would like to generate the graph. In this instance we select*SPATIALISED SA2-based T02 Selected Medians and Averages as at 2011-08-11**Spatial Weights Matrix:*Select the spatial weights matrix that you generated which will be used to feed into the spatial lag model. In this instance we select*CONTIG SWM FOR SPATIALISED SA2-based T02 Selected Medians and Averages as at 2011-08-11**Key Column:*Select the column in the spatialised dataset which specifies the unique codes for your areas. In this instance we select*ASGS 2011**Dependent Variable:*Select the variable that you would like to be explained by the model (i.e. the Y variable). In this instance we select*Median rent ($/weekly*)*Independent Variables:*Select the variables that you would like to test as explanatory variables for the variation in Y (i.e. the X variables). You can select more than one, although in this instance, we are selecting only*Median total family income ($/weekly)**Chart Title:*Create a name for your graph. In this instance we have called the graph*SPATIAL LAG REPONSE PLOT Median Income vs Median Rent Adelaide SA2s**Grid:*Keep this checked if you want grid lines on the graph (default), or unchecked if you want it clear*Greyscale:*Keep this unchecked if you want a colour graph (default) or checked if you want it to be greyscale

Once you have added all the parameters, click *Add and Run *to execute the tool

## Outputs

Once your tool has run, click the *Display *button on the pop up dialogue box that appears. Your graph should look something like the image shown below

## References

- Cressie, N. A. C. (1991) Statistics for spatial data, New York: Wiley.
- Olive, D. J. (2013) Plots, Prediction and Testing for the Multivariate Linear Model, preprint, see (
**http://lagrange.math.siu.edu/Olive/ppmultreg.pdf**). - Hofe, R. (2010) Residual plot, N. Salkind (Ed.), Encyclopedia of research design, pp. 1263 – 1268, Thousand Oaks, CA: SAGE Publications, Inc.