25-Activity-Area-Data-IV.Rmd

---
title: "Activity 12: Area Data IV"
output: html_notebook
---

# Activity 12: Area Data IV

## Practice questions

Answer the following questions:

1. How are row-standardized and binary spatial weights interpreted?
2. What is the reason for using a Bonferroni correction for multiple tests?
3. What types of spatial patterns can the local version of Moran's I detect?
4. What types of spatial patterns can the $G_i(d)$ statistic detect?
5. What is the utility of detecting hot and cold spatial spots?

## Learning objectives

In this activity, you will:

1. Calculate Moran's I coefficient of autocorrelation for area data.
2. Create Moran's scatterplots.
2. Examine the results of the tests/scatterplots for further insights.
3. Think about ways to decide whether a landscape is random when working with area data.

## Suggested reading

O'Sullivan D and Unwin D (2010) Geographic Information Analysis, 2nd Edition, Chapter 7. John Wiley & Sons: New Jersey. 

## Preliminaries

For this activity you will need the following:

* An R markdown notebook version of this document (the source file).

* A package called `geog4ga3`.

It is good practice to clear the working space to make sure that you do not have extraneous items there when you begin your work. The command in R to clear the workspace is `rm` (for "remove"), followed by a list of items to be removed. To clear the workspace from _all_ objects, do the following:
```{r}
rm(list = ls())
```

Note that `ls()` lists all objects currently on the workspace.

Load the libraries you will use in this activity. 

In addition to `tidyverse`, you will need `sf`, a package that implements simple features in R (you can learn about `sf` [here](https://cran.r-project.org/web/packages/sf/vignettes/sf1.html)) and `spdep`, a package that implements several spatial statistical methods (you can learn more about it [here](https://cran.r-project.org/web/packages/spdep/index.html)):
```{r message=FALSE, warning=FALSE}
library(geog4ga3)
library(sf)
library(spdep)
library(tidyverse)
```

Begin by loading the data that you will use in this activity:
```{r}
data(Hamilton_CT)
```

This is a `sf` object with census tracts and selected demographic variables for the Hamilton CMA in Canada.
You can obtain new (calculated) variables as follows. For instance, to obtain the proportion of residents who are between 20 and 34 years old, and between 35 and 49:
```{r}
Hamilton_CT <- mutate(Hamilton_CT, Prop20to34 = (AGE_20_TO_24 + AGE_25_TO_29 + AGE_30_TO_34)/POPULATION, Prop35to49 = (AGE_35_TO_39 + AGE_40_TO_44 + AGE_45_TO_49)/POPULATION)
```

This function is used to create local Moran maps:
```{r}
localmoran.map <- function(p = p, listw = listw, VAR = VAR, by = by){
  require(tidyverse)
  require(spdep)
  require(plotly)
  
  df_msc <- transmute(p,
                      key = p[[by]],
                      Z = (p[[VAR]] - mean(p[[VAR]])) / var(p[[VAR]]),
                      SMA = lag.listw(listw, Z),
                      Type = case_when(Z < 0 & SMA < 0 ~ "LL",
                                       Z > 0 & SMA > 0 ~ "HH",
                                       TRUE ~ "HL/LH"))
  
  local_I <- localmoran(p[[VAR]], listw)
  
  df_msc <- left_join(df_msc, 
                  data.frame(key = p[[by]], local_I))
  df_msc <- rename(df_msc, p.val = Pr.z...0.)
  
  plot_ly(df_msc) %>%
    add_sf(split = ~(p.val < 0.05), color = ~Type, colors = c("red", "khaki1", "dodgerblue", "dodgerblue4")) 
}
```

This function is used to create $G_i^*$ maps:
```{r}
gistar.map <- function(p = p, listw = listw, VAR = VAR, by = by){
  require(tidyverse)
  require(spdep)
  require(sf)
  require(plotly)
  
  p <- mutate(p, key = p[[by]])
  
  df.lg <- localG(p[[VAR]], listw)
  df.lg <- as.numeric(df.lg)
  df.lg <- data.frame(Gstar = df.lg, p.val = 2 * pnorm(abs(df.lg), lower.tail = FALSE))
  
  df.lg <- mutate(df.lg, 
              Type = case_when(Gstar < 0 & p.val <= 0.05 ~ "Low Concentration",
                               Gstar > 0 & p.val <= 0.05 ~ "High Concentration",
                               TRUE ~ "Not Signicant"))

  p <- left_join(p, 
                  data.frame(key = p[[by]], df.lg))
  
  plot_ly(p) %>%
    add_sf(split = ~(p.val < 0.05), color = ~Type, colors = c("red", "dodgerblue", "gray"))
}
```

Create spatial weights.

1) By contiguity:
```{r}
Hamilton_CT.w <- nb2listw(poly2nb(pl = Hamilton_CT.sp))
```

2) Binary, by distance (3 km threshold) _including self_.
```{r}
Hamilton_CT.3knb <- Hamilton_CT.sp %>% coordinates() %>% dnearneigh(d1 = 0, d2 = 3)
Hamilton_CT.3kw <- nb2listw(include.self(Hamilton_CT.3knb), style = "B")
```

You are now ready for the next activity.

## Activity

**NOTE**: Activities include technical "how to" tasks/questions. Usually, these ask you to organize data, create a plot, and so on in support of analysis and interpretation. These tasks are indicated by a star (*).

1. (*)Create local Moran maps for the population in age group 20-34 and _proportion_ of population in age group 20-34. 

2. (\*) Use the $G_i^*$ statistic to analyze the population _and_ proportion of population in the age group 20-34.

3. (*)Now create local Moran maps for the population and _population density_ in the age group 20-34. 

4. Concerning the analysis in point 1: What is the difference between using population (absolute) and population density (rate)?

5. Concerning the analysis in point 2: What is the difference between using population (absolute) and proportion of population (rate)? Is there a reason to prefer either variable in analysis? Discuss.

6. More generally, what do you think should guide the decision of whether to analyze variables as absolute values or rates?