Election analysis workflow

Workflow using ArcGIS Pro

メモ:

The steps below are based on the 2.1.0 release of ArcGIS Pro but should work fine for later software releases as well. To follow the steps below, you may download the data in the data package provided, or improvise using your own data.

This tutorial covers key components of the political analyst's workflow. It reviews what she did to download and prepare the data, then provides step-by-step instructions for examining broad spatial correlations at a national level and finding properly specified regression models for a three-state region (Arizona, Colorado, and New Mexico). While in this example the methods are used to analyze election results, you can apply these methods in many other applications where you want to explore the relationships between variables.

Collect the data

The analyst's initial dataset included every county in the continental United States.

Using tools such as Enrich Layer, Add Field, Calculate Field, and Add Join the analyst added the 2016 presidential vote percentages (Republican and Democratic) to the counties layer attribute table, along with about 30 socioeconomic explanatory variables.

Later, for the regional analysis, she used the same tools to add a number of additional variables, including Tapestry LifeMode and Urbanization categories. She also used the Near tool to calculate the distance each county in the region lies from the United States - Mexico border and from a major city.

The downloadable dataset includes layers containing fewer explanatory variables for both the national analysis and the Southwestern regional analysis, to speed up the processing as you work through the analysis.

Since your analysis will be composed of fewer explanatory variables, the reports you generate will look slightly different than the ones the analyst created. However, your results will be essentially the same as the analyst's.

Determine which explanatory variables are consistent predictors of the percentage Trump vote

To get a feeling for which variables were consistently good predictors of Trump support, the political analyst used Exploratory Regression. Using Exploratory Regression with a number of relevant explanatory variables is a quick way to see which variables you've collected are consistently good predictors of another variable (the dependent variable). You can complete the steps below using the provided data.

1. Run Exploratory Regression with these parameters.
   • Input features: CountyData_EnrichLayer
   • Dependent Variable: PCT_GOP
   • Candidate Explanatory Variables:
     • 2016 Ave HH Income
     • 2016 Diversity Index
     • 2016 Population Density
     • % Seniors (Age 65+)
     • % Republican
     • % Blue Collar Workers
     • % Never Married
     • % College Degree
   • Output Report File: CountyData_ERNational.txt (or another name of your choosing)

Since at this point you are only trying to identify significant variables, and not looking for properly specified models, you can run Exploratory Regression with the default parameters.

2. Navigate to the folder containing the report and open the report.
While the report generated by Exploratory Regression contains a lot of information, at this stage you are interested in identifying the explanatory variables having the strongest relationship with the dependent variable (the Trump vote, in this example). These appear at the top of the Summary of Variable Significance section, which tells you about variable relationships and how consistent those relationships are. The % Significant column indicates the proportion of times a variable was statistically significant. The % Negative and % Positive columns indicate the stability of a variable. That is, how consistently a variable had either a negative or positive relationship with the dependent variable. The variables that are the strongest predictors of the dependent variable have a high value in the % Significant column (100% or close to it) and will be primarily positive or primarily negative.



In the next section you'll explore how the relationships change across the country for two of the variables—PBLUECOLLAR (% Blue Collar Workers), which has a positive relationship with the Trump vote, and PCOLLEGEDEG (% College Degree), which has a negative relationship

ヒント:

When choosing variables for your own analyses, you should be able to justify each explanatory variable you include (based on research, knowledge of the subject matter, common sense, and so on). You should also be able to state whether you expect the relationship between an explanatory variable and the dependent variable to be positive or negative. In other words, avoid the temptation to just throw in everything under the sun and see what bubbles up to the top. Here are some additional cautions about using Exploratory Regression.

Analyze correlations and how they change across the nation

The steps to look at the variation across the nation in the correlation between the percentage of votes for Trump and the percentage of blue collar workers are shown below. The analyst used the same steps to analyze the correlation for percent of people with a college or professional degree. You can analyze these or any of the other explanatory variables in the counties layer. In fact, this same workflow could be used to examine the correlation between any two variables .
1. Run Geographically Weighted Regression (GWR) using the percent Trump vote as the dependent variable and the percent blue collar workers as the only explanatory variable. Each county will get a coefficient value indicating how strong the correlation between these two variables is.
   • Input features: CountyData_EnrichLayer
   • Dependent variable: PCT_GOP
   • Explanatory variable: % Blue Collar Workers
   • Output feature class: GWR_BlueCollar
   • Kernel type: Fixed
   • Bandwidth method: Akaike Information Criterion
2. Examine the output feature class.
   • GWR creates an output feature class of counties with a number of fields. The default map displays the values for the standard residuals field (Std. Residuals). However, the field of interest for this analysis is the one labeled Coefficient #1 pBlueCollar (the field will always be labeled Coefficient #1, followed by the name of the explanatory variable). Open the layer's attribute table to view the field.
   • A positive value for the coefficient indicates a positive relationship between the explanatory variable and the dependent variable—as the percentage of blue collar workers in a county increases, the percent GOP vote also increases.
   • The absolute magnitude of the coefficient indicates the strength of the relationship. For example, for % Blue Collar Workers, a coefficient of 3.0 for a county means that a one percent increase in the percentage of blue collar workers is associated with a three percent increase in the GOP vote. .
   • To see the pattern of where the relationship is strongest, map the coefficient field (for example, Coefficient #1 pBlueCollar) using graduated colors.

     

     注意:

     If the map does not display when you change the symbology, remove the GWR_BlueCollar layer from the Contents pane. Then add the feature class back to the map by dragging it from the Catalog, and change the symbology.

3. Run GWR again using % College Degree as the explanatory variable, or experiment with some of the other available variables, and examine the output feature class.
   • For % College Degree, the relationship is primarily negative—as the percentage of people with a college degree in a county increases, the percent GOP vote decreases. A coefficient of -1.5 indicates that a one percent increase in the percentage of people with a college degree in a county results in a decrease of 1.5 percent in the GOP vote.

ヒント:

Using a Quantile classification method for your map, with five or seven classes, will make the patterns more apparent. Quantile classification is useful when you want to see relative rankings (high, medium, low). However, when comparing maps be aware that the strength of the relationship between the explanatory and dependent variable (as indicated by the coefficient values) may vary between maps, even though the classes are rendered the same on both maps. For example, the largest coefficient value for % blue-collar workers is 3.07 (a one percent increase in the percentage of blue-collar workers in a county resulted in a 3.07 percent increase in the vote for Trump), while for the percent seniors variable the largest coefficient is 0.04, indicating a much weaker relationship.

Add explanatory variables and Identify battleground counties

To prepare for finding a properly specified model for counties at a state or regional level the analyst added more explanatory variables to the counties layer, including several distance variables to account for spatial trends or underlying spatial processes associated with Trump voting patterns. The chances of finding a properly specified model increase with more explanatory variables—as long as they are relevant and justifiable. She then identified battleground counties to focus her analysis.

Once the analyst had added the additional explanatory variables, she set about finding and selecting a subset of counties for her regional analysis. You can perform these steps with the continental United States counties layer.

1. In Fields View, add a new field to the CountyData_EnrichLayer layer. Name the field pGOP_minus_pDEM, and assign a Data Type of Float.
2. Use Calculate Field to calculate the values for the new field by subtracting the percentage 2016 Democratic vote (PCT_DEM) from the percentage 2016 GOP (PCT_GOP) vote.

   

3. Use Select Layer by Attribute to select the counties where the pGOP_minus_pDEM value is between -0.2 and 0.2.
4. Use Copy Features to copy the selected counties to a new data layer.
5. Using the new layer, create the map of battleground counties using Graduated Colors and specifying the pGOP_minus_pDEM field with a Manual Interval and two categories: values between 0 and 0.2 (an Upper value of 0.2) were counties that Trump won by less than 20 percent; values between 0 and -0.2 (an Upper value of 0.0) were counties that Clinton won by less than 20 percent. Select a red color for the former and a blue color for the latter, and update the labels.

   

   

Modeling the regional vote

The analyst's goal was to find at least one properly specified model that explained the GOP vote in the area of focus, the Southwestern United States (specifically, the three-state region composed of Arizona, Colorado, and New Mexico). When you are lucky enough to find more than one properly specified model, you can look for consistency in the variables that appear. When a variable shows up in multiple passing models you have confidence it is an important predictor. You should also look at the coefficient magnitude. Large differences from zero (either positive or negative) indicate a bigger influence on the dependent variable.

In the steps below, you will generate several properly specified models for the Arizona-Colorado-New Mexico region. You will then examine the model results and select the explanatory variables that appear in multiple passing models and have the largest (absolute value) coefficients. These variables could then be used to construct potential political messaging.

1. Run Exploratory Regression using the following parameters.
   • Input Features: AZ_CO_NM_EnrichLayer
   • Dependent Variable: PCT_GOP
   • Candidate Explanatory Variables:
     • 2016 Ave HH Income
     • 2016 Total Population
     • Median Age
     • % Republican
     • per HH Cash Contributions to Churches/Rel Org
     • % White
     • % Hispanic
     • % HH w Children
     • % Savvy Suburbs 1D
     • % RustBelt 5D
     • % Southern Sat 10A
     • % Rooted Rural 10B
     • % College Degree
     • MedYearMovedIn
   • Output Report File: AZ_CO_NM_ER3vars.txt (or a name of your choosing)
   • Under Search Criteria specify the following (models that meet these criteria are considered properly specified, and deemed "passing" models).
     • Maximum Number of Explanatory Variables: 3
     • Minimum Number of Explanatory Variables: 1
     • Minimum Acceptable Adj R Squared: 0.8 (model must explain at least 80% of variation in the vote totals)
     • Maximum Coefficient p value Cutoff: 0.01 (there must be 99% certainty that any variables in a given model were not included due to chance)
     • Maximum VIF Value Cutoff: 5 (reduces the acceptable level of redundancy between variables, termed multicollinearity)
     • Minimum Acceptable Jarque Bera p value: 0.1 (default)
     • Minimum Acceptable Spatial Autocorrelation p value: 0.1 (default)
2. Examine the report created by Exploratory Regression to see if there are any passing models (the report should show that there aren't any) and to identify poorly correlated variables.

   

   The Exploratory Regression report using one, two, and three variable models. While the best-scoring variables are shown, none of the combinations meet the analyst's stringent criteria for a passing model (the Passing Models header appears, but no models are listed, as indicated by the circled areas).

   Exploratory Regression runs Ordinary Least Squares (OLS) regression for every combination of candidate explanatory variables up to the number of variables you specify to include in the model (so if you specify that models include three variables, Exploratory Regression tries every possible combination of variables, three at a time). This can take time to process, especially for models with five or more variables. To speed up the processing, examine the report created by Exploratory Regression to look for variables that can be excluded from the analysis. (While not required with the small number of variables included here, these techniques are useful if you have many features and many candidate explanatory variables. Excluding poorly correlated variables is an effective strategy to speed up the Exploratory Regression process.)

   1. In the Summary of Mutlicollinearity section of the report, identify for exclusion any variables having high multicollinearity, say over 85% or 90%. These are variables that are redundant with one or more other variables. Having redundancy in a model can make the results more suspect.

      

      Two variables—AVEHHINC16 (average household income) and PHHCCCHURCHREL (percent of households contributing to churches or religious organizations)—are redundant with each other.

      Locate the variables in the Summary of Variable Significance section. Note the variable that is significant in more models—the other variable(s) exhibiting high multicollinearity with this variable can be excluded.

      

      The variable that is significant in more models—AVEHHINC16—can be kept for the analysis while the other (PHHCCCHURCHREL) is excluded.

   2. Also in the Summary of Variable Significance section identify any variables that are significant in less than 1% of the models tested. This means they are not likely factors in predicting the dependent variable. They appear at the bottom of the Summary of Variable Significance.

      

      Some of the variables show up as significant in less than 1% of the models tested, so can be removed from the analysis.

3. Exclude these poor performers from the next run of Exploratory Regression by unchecking them in the Visible column in Fields View in the AZ_CO_NM_EnrichLayer layer's attribute table. That way, they won't appear in the Exploratory Regression dialog. (Alternatively, you can uncheck the variables in the Exploratory Regression dialog. However, it's much easier to keep track of what you're doing in Fields View. Plus, if you need to run Exploratory Regression again with the same data layer at a later time, the variables will still be turned off and you won't have to uncheck them again in the dialog.) Uncheck the Visible checkbox for the variables below, and click Save.
   • per HH Cash Contributions to Churches/Rel Org
   • % Rooted Rural 10B
   • % Savvy Suburbs 1D
   • 2016 Total Population
   • % RustBelt 5D
   • % Southern Sat 10A
4. Run Exploratory Regression using 4 as the Maximum and Minimum number of explanatory variables. Use the same parameters as before, but include the remaining eight explanatory variables from the original list, and change the name of the report to AZ_CO_NM_ER4vars.txt. Examine the report to see if there are any passing models.
5. Repeat Step 4, using 5 for the Maximum and Minimum number of explanatory variables and changing the report name to AZ_CO_NM_ER5vars.txt.

At this point, since there were still no passing models the analyst looked for additional explanatory variables her analysis might be missing, and identified the change in percent Hispanic population and the percent Identifying American Indian variables. She added these to the layer of counties for the region.

These variables are included in the provided data layer, so you don't need to run Enrich Layer to add them — you simply need to make them visible in Fields View in the layer's attribute table.

6. In the AZ_CO_NM_EnrichLayer attribute table, in the Visible column in Fields View, click the checkbox next to % Identifying American Indian and Change in % Hispanic 2010 to 2016. Since you are adding new variables to the analysis you should also include any variables that were excluded previously because they were significant in less than 1% of models tested. There is a chance that in combination with the new variables they will now be significant in more models—and perhaps even appear in a passing model. So in the Visible column check the boxes for the five variables you previously unchecked (see above). When you have checked all the necessary boxes, click Save.

   

7. Re-run Exploratory Regression using the same parameters as in Step 5 above (again specifying 5 as the Maximum and Minimum number of explanatory variables). There should be a total of 15 candidate explanatory variables: the two new variables; the eight variables from the previous run; and the five variables that were excluded earlier as being significant in less than 1% of models tested. You can use the same name for the report file and overwrite the existing file. When you examine the report, it should show one passing model. Note that some variables have a positive relationship with the Trump vote while others have a negative relationship.

   

ヒント:

When doing your own analyses, if you are finding that Exploratory Regression takes a long time to complete you could once again check the Summary of Variable Significance section to see if any of the variables are significant in less than 1% of models tested. You could then exclude them from subsequent runs by unchecking them in the Visible column, as you did earlier, to speed up the completion of the tool. (This is not necessary in this example since the analysis includes a relatively small number of explanatory variables and completes quickly.) Keep in mind that the 1% figure is a guideline. If you have many candidate explanatory variables (a hundred or more) and many features, you may want to use a higher figure (even 5% or 10%) and exclude more variables to speed up the processing. Remember though that whenever you include new variables in the analysis you will need to also include any of the variables you previously excluded because they were not showing up as significant.
8. Run Exploratory Regression, specifying 6 for the Maximum and Minimum number of explanatory variables, and changing the name of the report to AZ_CO_NM_ER6vars.txt. There should be three passing models. The analyst did this to find additional passing models in order to identify explanatory variables that occur in several properly specified ("passing") models.

   

9. Using the two reports with the passing models, identify the variables that occur in at least half the passing models. They are:

   • % Republican (PREPPARTY)
   • % White (PWHITE)
   • % Hispanic (PHISPANIC)
   • % HH w Children (PHHWCHILDREN)
   • % College Degree (PCOLLEGEDEG)
   • Change in % Hispanic 2010 to 2016 (PHISP_DELTA_2010_2016)
10. Identify the model that contains all six variables and has the highest AdjR2 value—the top six-variable model.
11. Run Ordinary Least Squares (OLS) to identify the two variables having the strongest relationship with the dependent variable (PCT_GOP). While Exploratory Regression shows you whether a variable has a positive or negative relationship with the dependent variable, it doesn't tell you how strong the relationship is. The report generated by OLS includes a coefficient for each explanatory variable indicating the strength of the relationship with the dependent variable.
    • Input Feature Class: AZ_CO_NM_EnrichLayer
    • Unique ID Field: COMBINED_FIPS
    • Output Feature Class: AZ_CO_NM_EnrichLayer_OLS
    • Dependent Variable: PCT_GOP
    • Explanatory Variables:
      • % Republican
      • % White
      • % Hispanic
      • % HH w Children
      • % College Degree
      • Change in % Hispanic 2010 to 2016
    • Output Report File: AZ_CO_NM_EnrichLayer_OLS.pdf (or a name of your choosing)

メモ:

You can ignore the warning message regarding Spatial Autocorrelation. You already know from running Exploratory Regression that this model meets your stringent criteria.
12. Examine the report file generated by OLS. The report shows that % Change in Hispanic Population (PCTHISP_DELT) has the largest coefficient at 1.77—a positive relationship with the dependent variable—while % College Degree (PCOLLEGEDEG) has the next largest, in absolute terms, at -1.02, a negative relationship. These are variables that would likely be the most effective for use in creating campaign messages.

    

ヒント:

• When whittling down the number of candidate explanatory variables to include when you run Exploratory Regression, there is some risk that you might be removing a variable that would be significant down the road in models that include more variables. You will need to decide if it is worth the tradeoff to ensure any passing models provide accurate results while also speeding up the processing. In many cases, the poorly correlated variables can be winnowed out early in the process—there are likely to be fewer of these variables in subsequent runs of Exploratory Regression for models using more variables.
• If you are unable to find any passing models after several attempts using increasing numbers of explanatory variables, look for additional variables that might be missing from the analysis. Search the literature (again) or create maps of the area of interest to look for spatial phenomena you might have missed.
• If you are finding properly specified models, how do you know which is the best one (the one that does the best job of predicting the dependent variable), and when to stop looking for better models? Here are some guidelines:
  • The adjusted R² value indicates how good a job the model does at predicting the dependent variable. An R² of 0.9, for example, tells 90 percent of the story. So the higher the R², the better the model.
  • If you are comparing models, the one with the higher R² and the lower AICc value does the better job of predicting the dependent variable. However, if a model has a slightly higher R² than another model, but the AICc value is lower by less than three, the models can be considered comparable.
  • As you create models using more and more explanatory variables be wary, especially if you see a dramatic change in the R² value and/or AICc value—you may be overfitting, where the models are describing random error in the data rather than the relationships between variables. You are better off rejecting these models and relying on passing models comprised of fewer explanatory variables.
  • When to stop looking for a better model depends in part on the purpose of your analysis. In this case study, the analyst was looking for several explanatory variables she could be confident in developing campaign messaging around. Her approach was to find several properly specified models and then identify the most commonly occurring variables in those models. So she stopped looking for better models once she achieved this goal. In your analysis, it may be that you want to find the best possible properly specified model—it may make sense to use the guidelines above to keep adding explanatory variables to find the best model you can. At some point, it's possible (likely, even) that the R² value will stop increasing, or will start to decrease. That is definitely the time to stop looking.