# Chapter 8 Manipulating Vectors and Matrices12

### Motivation

Nunn and Wantchekon (2011) -- "The Slave Trade and the Origins of Mistrust in Africa"13 -- argues that across African countries, the distrust of co-ethnics fueled by the slave trade has had long-lasting effects on modern day trust in these territories. They argued that the slave trade created distrust in these societies in part because as some African groups were employed by European traders to capture their neighbors and bring them to the slave ships.

Nunn and Wantchekon use a variety of statistical tools to make their case (adding controls, ordered logit, instrumental variables, falsification tests, causal mechanisms), many of which will be covered in future courses. In this module we will only touch on their first set of analysis that use Ordinary Least Squares (OLS). OLS is likely the most common application of linear algebra in the social sciences. We will cover some linear algebra, matrix manipulation, and vector manipulation from this data.

### Where are we? Where are we headed?

Up till now, you should have covered:

• R basic programming
• Data Import
• Statistical Summaries.

Today we'll cover

• Matrices & Dataframes in R
• Manipulating variables
• And other R tips

## 8.1 Read Data

library(haven)
nunn_full <- read_dta("data/input/Nunn_Wantchekon_AER_2011.dta")

Nunn and Wantchekon's main dataset has more than 20,000 observations. Each observation is a respondent from the Afrobarometer survey.

head(nunn_full)
## # A tibble: 6 x 59
##   respno ethnicity murdock_name isocode region district townvill location_id
##   <chr>  <chr>     <chr>        <chr>   <chr>  <chr>    <chr>          <dbl>
## 1 BEN00… fon       FON          BEN     atlna… KPOMASSE TOKPA-D…          30
## 2 BEN00… fon       FON          BEN     atlna… KPOMASSE TOKPA-D…          30
## 3 BEN00… fon       FON          BEN     atlna… OUIDAH   3ARROND           31
## 4 BEN00… fon       FON          BEN     atlna… OUIDAH   3ARROND           31
## 5 BEN00… fon       FON          BEN     atlna… OUIDAH   PAHOU             32
## 6 BEN00… fon       FON          BEN     atlna… OUIDAH   PAHOU             32
## # … with 51 more variables: trust_relatives <dbl>, trust_neighbors <dbl>,
## #   intra_group_trust <dbl>, inter_group_trust <dbl>,
## #   trust_local_council <dbl>, ln_export_area <dbl>, export_area <dbl>,
## #   export_pop <dbl>, ln_export_pop <dbl>, age <dbl>, age2 <dbl>, male <dbl>,
## #   urban_dum <dbl>, occupation <dbl>, religion <dbl>, living_conditions <dbl>,
## #   education <dbl>, near_dist <dbl>, distsea <dbl>, loc_murdock_name <chr>,
## #   loc_ln_export_area <dbl>, local_council_performance <dbl>,
## #   council_listen <dbl>, corrupt_local_council <dbl>, school_present <dbl>,
## #   electricity_present <dbl>, piped_water_present <dbl>, sewage_present <dbl>,
## #   health_clinic_present <dbl>, district_ethnic_frac <dbl>,
## #   frac_ethnicity_in_district <dbl>, townvill_nonethnic_mean_exports <dbl>,
## #   district_nonethnic_mean_exports <dbl>, region_nonethnic_mean_exports <dbl>,
## #   country_nonethnic_mean_exports <dbl>, murdock_centr_dist_coast <dbl>,
## #   centroid_lat <dbl>, centroid_long <dbl>, explorer_contact <dbl>,
## #   railway_contact <dbl>, dist_Saharan_node <dbl>, dist_Saharan_line <dbl>,
## #   malaria_ecology <dbl>, v30 <dbl+lbl>, v33 <dbl+lbl>, fishing <dbl>,
## #   exports <dbl>, ln_exports <dbl>, total_missions_area <dbl>,
## #   ln_init_pop_density <dbl>, cities_1400_dum <dbl>
colnames(nunn_full)
##  [1] "respno"                          "ethnicity"
##  [3] "murdock_name"                    "isocode"
##  [5] "region"                          "district"
##  [7] "townvill"                        "location_id"
##  [9] "trust_relatives"                 "trust_neighbors"
## [11] "intra_group_trust"               "inter_group_trust"
## [13] "trust_local_council"             "ln_export_area"
## [15] "export_area"                     "export_pop"
## [17] "ln_export_pop"                   "age"
## [19] "age2"                            "male"
## [21] "urban_dum"                       "occupation"
## [23] "religion"                        "living_conditions"
## [25] "education"                       "near_dist"
## [27] "distsea"                         "loc_murdock_name"
## [29] "loc_ln_export_area"              "local_council_performance"
## [31] "council_listen"                  "corrupt_local_council"
## [33] "school_present"                  "electricity_present"
## [35] "piped_water_present"             "sewage_present"
## [37] "health_clinic_present"           "district_ethnic_frac"
## [39] "frac_ethnicity_in_district"      "townvill_nonethnic_mean_exports"
## [41] "district_nonethnic_mean_exports" "region_nonethnic_mean_exports"
## [43] "country_nonethnic_mean_exports"  "murdock_centr_dist_coast"
## [45] "centroid_lat"                    "centroid_long"
## [47] "explorer_contact"                "railway_contact"
## [49] "dist_Saharan_node"               "dist_Saharan_line"
## [51] "malaria_ecology"                 "v30"
## [53] "v33"                             "fishing"
## [55] "exports"                         "ln_exports"
## [57] "total_missions_area"             "ln_init_pop_density"
## [59] "cities_1400_dum"

First, let's consider a small subset of this dataset.

nunn <- read_dta("data/input/Nunn_Wantchekon_sample.dta")
nunn
## # A tibble: 10 x 5
##    trust_neighbors exports ln_exports export_area ln_export_area
##              <dbl>   <dbl>      <dbl>       <dbl>          <dbl>
##  1               3   0.388      0.328     0.00407        0.00406
##  2               3   0.631      0.489     0.0971         0.0926
##  3               3   0.994      0.690     0.0125         0.0124
##  4               0 183.         5.21      1.82           1.04
##  5               3   0          0         0              0
##  6               2   0          0         0              0
##  7               2 666.         6.50     14.0            2.71
##  8               0   0.348      0.298     0.00608        0.00606
##  9               3   0.435      0.361     0.0383         0.0376
## 10               3   0          0         0              0

## 8.2 data.frame vs. matricies

This is a data.frame object.

class(nunn)
## [1] "tbl_df"     "tbl"        "data.frame"

But it can be also consider a matrix in the linear algebra sense. What are the dimensions of this matrix?

nrow(nunn)
## [1] 10

data.frames and matrices have much overlap in R, but to explicitly treat an object as a matrix, you'd need to coerce its class. Let's call this matrix X.

X <- as.matrix(nunn)

What is the difference between a data.frame and a matrix? A data.frame can have columns that are of different types, whereas --- in a matrix --- all columns must be of the same type (usually either "numeric" or "character").

You can think of data frames maybe as matrices-plus, because a column can take on characters as well as numbers. As we just saw, this is often useful for real data analyses.

Another way to think about data frames is that it is a type of list. Try the str() code below and notice how it is organized in slots. Each slot is a vector. They can be vectors of numbers or characters.

# enter this on your console
str(cen10)

## 8.3 Handling matricies in R

You can easily transpose a matrix

X
##       trust_neighbors     exports ln_exports  export_area ln_export_area
##  [1,]               3   0.3883497  0.3281158  0.004067405    0.004059155
##  [2,]               3   0.6311236  0.4892691  0.097059444    0.092633367
##  [3,]               3   0.9941893  0.6902376  0.012524694    0.012446908
##  [4,]               0 182.5891266  5.2127004  1.824284434    1.038255095
##  [5,]               3   0.0000000  0.0000000  0.000000000    0.000000000
##  [6,]               2   0.0000000  0.0000000  0.000000000    0.000000000
##  [7,]               2 665.9652100  6.5027380 13.975566864    2.706419945
##  [8,]               0   0.3476418  0.2983562  0.006082553    0.006064130
##  [9,]               3   0.4349871  0.3611559  0.038332380    0.037615947
## [10,]               3   0.0000000  0.0000000  0.000000000    0.000000000
t(X)
##                        [,1]       [,2]       [,3]       [,4] [,5] [,6]
## trust_neighbors 3.000000000 3.00000000 3.00000000   0.000000    3    2
## exports         0.388349682 0.63112360 0.99418926 182.589127    0    0
## ln_exports      0.328115761 0.48926911 0.69023758   5.212700    0    0
## export_area     0.004067405 0.09705944 0.01252469   1.824284    0    0
## ln_export_area  0.004059155 0.09263337 0.01244691   1.038255    0    0
##                       [,7]        [,8]       [,9] [,10]
## trust_neighbors   2.000000 0.000000000 3.00000000     3
## exports         665.965210 0.347641766 0.43498713     0
## ln_exports        6.502738 0.298356235 0.36115587     0
## export_area      13.975567 0.006082553 0.03833238     0
## ln_export_area    2.706420 0.006064130 0.03761595     0

What are the values of all rows in the first column?

X[, 1]
##  [1] 3 3 3 0 3 2 2 0 3 3

What are all the values of "exports"? (i.e. return the whole "exports" column)

X[, "exports"]
##  [1]   0.3883497   0.6311236   0.9941893 182.5891266   0.0000000   0.0000000
##  [7] 665.9652100   0.3476418   0.4349871   0.0000000

What is the first observation (i.e. first row)?

X[1, ]
## trust_neighbors         exports      ln_exports     export_area  ln_export_area
##     3.000000000     0.388349682     0.328115761     0.004067405     0.004059155

What is the value of the first variable of the first observation?

X[1, 1]
## trust_neighbors
##               3

Pause and consider the following problem on your own. What is the following code doing?

X[X[, "trust_neighbors"] == 0, "export_area"]
## [1] 1.824284434 0.006082553

Why does it give the same output as the following?

X[which(X[, "trust_neighbors"] == 0), "export_area"]
## [1] 1.824284434 0.006082553

Some more manipulation

X + X
##       trust_neighbors      exports ln_exports  export_area ln_export_area
##  [1,]               6    0.7766994  0.6562315  0.008134809     0.00811831
##  [2,]               6    1.2622472  0.9785382  0.194118887     0.18526673
##  [3,]               6    1.9883785  1.3804752  0.025049388     0.02489382
##  [4,]               0  365.1782532 10.4254007  3.648568869     2.07651019
##  [5,]               6    0.0000000  0.0000000  0.000000000     0.00000000
##  [6,]               4    0.0000000  0.0000000  0.000000000     0.00000000
##  [7,]               4 1331.9304199 13.0054760 27.951133728     5.41283989
##  [8,]               0    0.6952835  0.5967125  0.012165107     0.01212826
##  [9,]               6    0.8699743  0.7223117  0.076664761     0.07523189
## [10,]               6    0.0000000  0.0000000  0.000000000     0.00000000
X - X
##       trust_neighbors exports ln_exports export_area ln_export_area
##  [1,]               0       0          0           0              0
##  [2,]               0       0          0           0              0
##  [3,]               0       0          0           0              0
##  [4,]               0       0          0           0              0
##  [5,]               0       0          0           0              0
##  [6,]               0       0          0           0              0
##  [7,]               0       0          0           0              0
##  [8,]               0       0          0           0              0
##  [9,]               0       0          0           0              0
## [10,]               0       0          0           0              0
t(X) %*% X
##                 trust_neighbors    exports ln_exports export_area
## trust_neighbors       62.000000   1339.276   18.61181    28.40709
## exports             1339.276369 476850.298 5283.76294  9640.42990
## ln_exports            18.611811   5283.763   70.50077   100.46202
## export_area           28.407085   9640.430  100.46202   198.65558
## ln_export_area         5.853106   1992.047   23.08189    39.72847
##                 ln_export_area
## trust_neighbors       5.853106
## exports            1992.046502
## ln_exports           23.081893
## export_area          39.728468
## ln_export_area        8.412887
cbind(X, 1:10)
##       trust_neighbors     exports ln_exports  export_area ln_export_area
##  [1,]               3   0.3883497  0.3281158  0.004067405    0.004059155  1
##  [2,]               3   0.6311236  0.4892691  0.097059444    0.092633367  2
##  [3,]               3   0.9941893  0.6902376  0.012524694    0.012446908  3
##  [4,]               0 182.5891266  5.2127004  1.824284434    1.038255095  4
##  [5,]               3   0.0000000  0.0000000  0.000000000    0.000000000  5
##  [6,]               2   0.0000000  0.0000000  0.000000000    0.000000000  6
##  [7,]               2 665.9652100  6.5027380 13.975566864    2.706419945  7
##  [8,]               0   0.3476418  0.2983562  0.006082553    0.006064130  8
##  [9,]               3   0.4349871  0.3611559  0.038332380    0.037615947  9
## [10,]               3   0.0000000  0.0000000  0.000000000    0.000000000 10
cbind(X, 1)
##       trust_neighbors     exports ln_exports  export_area ln_export_area
##  [1,]               3   0.3883497  0.3281158  0.004067405    0.004059155 1
##  [2,]               3   0.6311236  0.4892691  0.097059444    0.092633367 1
##  [3,]               3   0.9941893  0.6902376  0.012524694    0.012446908 1
##  [4,]               0 182.5891266  5.2127004  1.824284434    1.038255095 1
##  [5,]               3   0.0000000  0.0000000  0.000000000    0.000000000 1
##  [6,]               2   0.0000000  0.0000000  0.000000000    0.000000000 1
##  [7,]               2 665.9652100  6.5027380 13.975566864    2.706419945 1
##  [8,]               0   0.3476418  0.2983562  0.006082553    0.006064130 1
##  [9,]               3   0.4349871  0.3611559  0.038332380    0.037615947 1
## [10,]               3   0.0000000  0.0000000  0.000000000    0.000000000 1
colnames(X)
## [1] "trust_neighbors" "exports"         "ln_exports"      "export_area"
## [5] "ln_export_area"

## 8.4 Variable Transformations

exports is the total number of slaves that were taken from the individual's ethnic group between Africa's four slave trades between 1400-1900.

What is ln_exports? The article describes this as the natural log of one plus the exports. This is a transformation of one column by a particular function

log(1 + X[, "exports"])
##  [1] 0.3281158 0.4892691 0.6902376 5.2127003 0.0000000 0.0000000 6.5027379
##  [8] 0.2983562 0.3611559 0.0000000

Question for you: why add the 1?

Verify that this is the same as X[, "ln_exports"]

## 8.5 Linear Combinations

In Table 1 we see "OLS Estimates". These are estimates of OLS coefficients and standard errors. You do not need to know what these are for now, but it doesn't hurt to getting used to seeing them.

A very crude way to describe regression is through linear combinations. The simplest linear combination is a one-to-one transformation.

Take the first number in Table 1, which is -0.00068. Now, multiply this by exports

-0.00068 * X[, "exports"]
##  [1] -0.0002640778 -0.0004291640 -0.0006760487 -0.1241606061  0.0000000000
##  [6]  0.0000000000 -0.4528563428 -0.0002363964 -0.0002957912  0.0000000000

Now, just one more step. Make a new matrix with just exports and the value 1

X2 <- cbind(1, X[, "exports"])

name this new column "intercept"

colnames(X2)
## NULL
colnames(X2) <- c("intercept", "exports")

What are the dimensions of the matrix X2?

dim(X2)
## [1] 10  2

Now consider a new matrix, called B.

B <- matrix(c(1.62, -0.00068))

What are the dimensions of B?

dim(B)
## [1] 2 1

What is the product of X2 and B? From the dimensions, can you tell if it will be conformable?

X2 %*% B
##           [,1]
##  [1,] 1.619736
##  [2,] 1.619571
##  [3,] 1.619324
##  [4,] 1.495839
##  [5,] 1.620000
##  [6,] 1.620000
##  [7,] 1.167144
##  [8,] 1.619764
##  [9,] 1.619704
## [10,] 1.620000

What is this multiplication doing in terms of equations?

## 8.6 Matrix Basics

Let's take a look at Matrices in the context of R

cen10 <- read_csv("data/input/usc2010_001percent.csv")
head(cen10)
## # A tibble: 6 x 4
##   state         sex      age race
##   <chr>         <chr>  <dbl> <chr>
## 1 New York      Female     8 White
## 2 Ohio          Male      24 White
## 3 Nevada        Male      37 White
## 4 Michigan      Female    12 White
## 5 Maryland      Female    18 Black/Negro
## 6 New Hampshire Male      50 White

What is the dimension of this dataframe? What does the number of rows represent? What does the number of columns represent?

dim(cen10)
## [1] 30871     4
nrow(cen10)
## [1] 30871
ncol(cen10)
## [1] 4

What variables does this dataset hold? What kind of information does it have?

colnames(cen10)
## [1] "state" "sex"   "age"   "race"

We can access column vectors, or vectors that contain values of variables by using the $sign head(cen10$state)
## [1] "New York"      "Ohio"          "Nevada"        "Michigan"
## [5] "Maryland"      "New Hampshire"
head(cen10$race) ## [1] "White" "White" "White" "White" "Black/Negro" ## [6] "White" We can look at a unique set of variable values by calling the unique function unique(cen10$state)
##  [1] "New York"             "Ohio"                 "Nevada"
##  [4] "Michigan"             "Maryland"             "New Hampshire"
##  [7] "Iowa"                 "Missouri"             "New Jersey"
## [10] "California"           "Texas"                "Pennsylvania"
## [13] "Washington"           "West Virginia"        "Idaho"
## [16] "North Carolina"       "Massachusetts"        "Connecticut"
## [19] "Arkansas"             "Indiana"              "Wisconsin"
## [22] "Maine"                "Tennessee"            "Minnesota"
## [25] "Florida"              "Oklahoma"             "Montana"
## [28] "Georgia"              "Arizona"              "Colorado"
## [31] "Virginia"             "Illinois"             "Oregon"
## [34] "Kentucky"             "South Carolina"       "Kansas"
## [37] "Louisiana"            "Alabama"              "District of Columbia"
## [40] "Mississippi"          "Utah"                 "Delaware"
## [43] "Nebraska"             "Alaska"               "New Mexico"
## [46] "South Dakota"         "Hawaii"               "Vermont"
## [49] "Rhode Island"         "Wyoming"              "North Dakota"

How many different states are represented (this dataset includes DC as a state)?

length(unique(cen10$state)) ## [1] 51 Matrices are rectangular structures of numbers (they have to be numbers, and they can't be characters). A cross-tab can be considered a matrix: table(cen10$race, cen10$sex) ## ## Female Male ## American Indian or Alaska Native 142 153 ## Black/Negro 2070 1943 ## Chinese 192 162 ## Japanese 51 26 ## Other Asian or Pacific Islander 587 542 ## Other race, nec 877 962 ## Three or more major races 37 51 ## Two major races 443 426 ## White 11252 10955 cross_tab <- table(cen10$race, cen10$sex) dim(cross_tab) ## [1] 9 2 cross_tab[6, 2] ## [1] 962 But a subset of your data -- individual values-- can be considered a matrix too. # First 20 rows of the entire data # Below two lines of code do the same thing cen10[1:20, ] ## # A tibble: 20 x 4 ## state sex age race ## <chr> <chr> <dbl> <chr> ## 1 New York Female 8 White ## 2 Ohio Male 24 White ## 3 Nevada Male 37 White ## 4 Michigan Female 12 White ## 5 Maryland Female 18 Black/Negro ## 6 New Hampshire Male 50 White ## 7 Iowa Female 51 White ## 8 Missouri Female 41 White ## 9 New Jersey Male 62 White ## 10 California Male 25 White ## 11 Texas Female 23 White ## 12 Pennsylvania Female 66 White ## 13 California Female 57 White ## 14 Texas Female 73 Other race, nec ## 15 California Male 43 White ## 16 Washington Male 29 White ## 17 Texas Male 8 White ## 18 Missouri Male 78 White ## 19 West Virginia Male 10 White ## 20 Idaho Female 9 White cen10 %>% slice(1:20) ## # A tibble: 20 x 4 ## state sex age race ## <chr> <chr> <dbl> <chr> ## 1 New York Female 8 White ## 2 Ohio Male 24 White ## 3 Nevada Male 37 White ## 4 Michigan Female 12 White ## 5 Maryland Female 18 Black/Negro ## 6 New Hampshire Male 50 White ## 7 Iowa Female 51 White ## 8 Missouri Female 41 White ## 9 New Jersey Male 62 White ## 10 California Male 25 White ## 11 Texas Female 23 White ## 12 Pennsylvania Female 66 White ## 13 California Female 57 White ## 14 Texas Female 73 Other race, nec ## 15 California Male 43 White ## 16 Washington Male 29 White ## 17 Texas Male 8 White ## 18 Missouri Male 78 White ## 19 West Virginia Male 10 White ## 20 Idaho Female 9 White # Of the first 20 rows of the entire data, look at values of just race and age # Below two lines of code do the same thing cen10[1:20, c("race", "age")] ## # A tibble: 20 x 2 ## race age ## <chr> <dbl> ## 1 White 8 ## 2 White 24 ## 3 White 37 ## 4 White 12 ## 5 Black/Negro 18 ## 6 White 50 ## 7 White 51 ## 8 White 41 ## 9 White 62 ## 10 White 25 ## 11 White 23 ## 12 White 66 ## 13 White 57 ## 14 Other race, nec 73 ## 15 White 43 ## 16 White 29 ## 17 White 8 ## 18 White 78 ## 19 White 10 ## 20 White 9 cen10 %>% slice(1:20) %>% select(race, age) ## # A tibble: 20 x 2 ## race age ## <chr> <dbl> ## 1 White 8 ## 2 White 24 ## 3 White 37 ## 4 White 12 ## 5 Black/Negro 18 ## 6 White 50 ## 7 White 51 ## 8 White 41 ## 9 White 62 ## 10 White 25 ## 11 White 23 ## 12 White 66 ## 13 White 57 ## 14 Other race, nec 73 ## 15 White 43 ## 16 White 29 ## 17 White 8 ## 18 White 78 ## 19 White 10 ## 20 White 9 A vector is a special type of matrix with only one column or only one row # One column cen10[1:10, c("age")] ## # A tibble: 10 x 1 ## age ## <dbl> ## 1 8 ## 2 24 ## 3 37 ## 4 12 ## 5 18 ## 6 50 ## 7 51 ## 8 41 ## 9 62 ## 10 25 cen10 %>% slice(1:10) %>% select(c("age")) ## # A tibble: 10 x 1 ## age ## <dbl> ## 1 8 ## 2 24 ## 3 37 ## 4 12 ## 5 18 ## 6 50 ## 7 51 ## 8 41 ## 9 62 ## 10 25 # One row cen10[2, ] ## # A tibble: 1 x 4 ## state sex age race ## <chr> <chr> <dbl> <chr> ## 1 Ohio Male 24 White cen10 %>% slice(2) ## # A tibble: 1 x 4 ## state sex age race ## <chr> <chr> <dbl> <chr> ## 1 Ohio Male 24 White What if we want a special subset of the data? For example, what if I only want the records of individuals in California? What if I just want the age and race of individuals in California? # subset for CA rows ca_subset <- cen10[cen10$state == "California", ]

ca_subset_tidy <- cen10 %>% filter(state == "California")

all_equal(ca_subset, ca_subset_tidy)
## [1] TRUE
# subset for CA rows and select age and race
ca_subset_age_race <- cen10[cen10$state == "California", c("age", "race")] ca_subset_age_race_tidy <- cen10 %>% filter(state == "California") %>% select(age, race) all_equal(ca_subset_age_race, ca_subset_age_race_tidy) ## [1] TRUE Some common operators that can be used to filter or to use as a condition. Remember, you can use the unique function to look at the set of all values a variable holds in the dataset. # all individuals older than 30 and younger than 70 s1 <- cen10[cen10$age > 30 & cen10$age < 70, ] s2 <- cen10 %>% filter(age > 30 & age < 70) all_equal(s1, s2) ## [1] TRUE # all individuals in either New York or California s3 <- cen10[cen10$state == "New York" | cen10$state == "California", ] s4 <- cen10 %>% filter(state == "New York" | state == "California") all_equal(s3, s4) ## [1] TRUE # all individuals in any of the following states: California, Ohio, Nevada, Michigan s5 <- cen10[cen10$state %in% c("California", "Ohio", "Nevada", "Michigan"), ]
s6 <- cen10 %>% filter(state %in% c("California", "Ohio", "Nevada", "Michigan"))
all_equal(s5, s6)
## [1] TRUE
# all individuals NOT in any of the following states: California, Ohio, Nevada, Michigan
s7 <- cen10[!(cen10\$state %in% c("California", "Ohio", "Nevada", "Michigan")), ]
s8 <- cen10 %>% filter(!state %in% c("California", "Ohio", "Nevada", "Michigan"))
all_equal(s7, s8)
## [1] TRUE

## Checkpoint

### 1

Get the subset of cen10 for non-white individuals (Hint: look at the set of values for the race variable by using the unique function)

# Enter here

### 2

Get the subset of cen10 for females over the age of 40

# Enter here

### 3

Get all the serial numbers for black, male individuals who don't live in Ohio or Nevada.

# Enter here

## Exercises

### 1

Let $\mathbf{A} = \left[\begin{array} {rrr} 0.6 & 0.2\\ 0.4 & 0.8\\ \end{array}\right]$

Use R to write code that will create the matrix $$A$$, and then consecutively multiply $$A$$ to itself 4 times. What is the value of $$A^{4}$$?

## Enter yourself

Note that R notation of matrices is different from the math notation. Simply trying X^n where X is a matrix will only take the power of each element to n. Instead, this problem asks you to perform matrix multiplication.

### 2

Let's apply what we learned about subsetting or filtering/selecting. Use the nunn_full dataset you have already loaded

1. First, show all observations (rows) that have a "male" variable higher than 0.5
## Enter yourself
1. Next, create a matrix / dataframe with only two columns: "trust_neighbors" and "age"
## Enter yourself
1. Lastly, show all values of "trust_neighbors" and "age" for observations (rows) that have the "male" variable value that is higher than 0.5
## Enter yourself

### 3

Find a way to generate a vector of "column averages" of the matrix X from the Nunn and Wantchekon data in one line of code. Each entry in the vector should contain the sample average of the values in the column. So a 100 by 4 matrix should generate a length-4 matrix.

### 4

Similarly, generate a vector of "column medians".

### 5

Consider the regression that was run to generate Table 1:

form <- "trust_neighbors ~ exports + age + age2 +  male + urban_dum + factor(education) + factor(occupation) + factor(religion) + factor(living_conditions) + district_ethnic_frac + frac_ethnicity_in_district + isocode"
lm_1_1 <- lm(as.formula(form), nunn_full)

# The below coef function returns a vector of OLS coefficiants
coef(lm_1_1)
##                (Intercept)                    exports
##               1.619913e+00              -6.791360e-04
##                        age                       age2
##               8.395936e-03              -5.473436e-05
##                       male                  urban_dum
##               4.550246e-02              -1.404551e-01
##         factor(education)1         factor(education)2
##               1.709816e-02              -5.224591e-02
##         factor(education)3         factor(education)4
##              -1.373770e-01              -1.889619e-01
##         factor(education)5         factor(education)6
##              -1.893494e-01              -2.400767e-01
##         factor(education)7         factor(education)8
##              -2.850748e-01              -1.232085e-01
##         factor(education)9        factor(occupation)1
##              -2.406437e-01               6.185655e-02
##        factor(occupation)2        factor(occupation)3
##               7.392168e-02               3.356158e-02
##        factor(occupation)4        factor(occupation)5
##               7.942048e-03               6.661126e-02
##        factor(occupation)6        factor(occupation)7
##              -7.563297e-02               1.699699e-02
##        factor(occupation)8        factor(occupation)9
##              -9.428177e-02              -9.981440e-02
##       factor(occupation)10       factor(occupation)11
##              -3.307068e-02              -2.300045e-02
##       factor(occupation)12       factor(occupation)13
##              -1.564540e-01              -1.441370e-02
##       factor(occupation)14       factor(occupation)15
##              -5.566414e-02              -2.343762e-01
##       factor(occupation)16       factor(occupation)18
##              -1.306947e-02              -1.729589e-01
##       factor(occupation)19       factor(occupation)20
##              -1.770261e-01              -2.457800e-02
##       factor(occupation)21       factor(occupation)22
##              -4.936813e-02              -1.068511e-01
##       factor(occupation)23       factor(occupation)24
##              -9.712205e-02               1.292371e-02
##       factor(occupation)25      factor(occupation)995
##               2.623186e-02              -1.195063e-03
##          factor(religion)2          factor(religion)3
##               5.395953e-02               7.887878e-02
##          factor(religion)4          factor(religion)5
##               4.749150e-02               4.318455e-02
##          factor(religion)6          factor(religion)7
##              -1.787694e-02              -3.616542e-02
##         factor(religion)10         factor(religion)11
##               6.015041e-02               2.237845e-01
##         factor(religion)12         factor(religion)13
##               2.627086e-01              -6.812813e-02
##         factor(religion)14         factor(religion)15
##               4.673681e-02               3.844555e-01
##        factor(religion)360        factor(religion)361
##               3.656843e-01               3.416413e-01
##        factor(religion)362        factor(religion)363
##               8.230393e-01               3.856565e-01
##        factor(religion)995 factor(living_conditions)2
##               4.161301e-02               4.395862e-02
## factor(living_conditions)3 factor(living_conditions)4
##               8.627372e-02               1.197428e-01
## factor(living_conditions)5       district_ethnic_frac
##               1.203606e-01              -1.553648e-02
## frac_ethnicity_in_district                 isocodeBWA
##               1.011222e-01              -4.258953e-01
##                 isocodeGHA                 isocodeKEN
##               1.135307e-02              -1.819556e-01
##                 isocodeLSO                 isocodeMDG
##              -5.511200e-01              -3.315727e-01
##                 isocodeMLI                 isocodeMOZ
##               7.528101e-02               8.223730e-02
##                 isocodeMWI                 isocodeNAM
##               3.062497e-01              -1.397541e-01
##                 isocodeNGA                 isocodeSEN
##              -2.381525e-01               3.867371e-01
##                 isocodeTZA                 isocodeUGA
##               2.079366e-01              -6.443732e-02
##                 isocodeZAF                 isocodeZMB
##              -2.179153e-01              -2.172868e-01

First, get a small subset of the nunn_full dataset. This time, sample 20 rows and select for variables exports, age, age2, male, and urban_dum. To this small subset, add (bind_cols() in tidyverse or cbind() in base R) a column of 1's; this represents the intercept. If you need some guidance, look at how we sampled 10 rows selected for a different set of variables above in the lecture portion.

# Enter here

Next let's try calculating predicted values of levels of trust in neighbors by multiplying coefficients for the intercept, exports, age, age2, male, and urban_dum to the actual observed values for those variables in the small subset you've just created.

# Hint: You can get just selected elements from the vector returned by coef(lm_1_1)

# For example, the below code gives you the first 3 elements of the original vector
coef(lm_1_1)[1:3]
##  (Intercept)      exports          age
##  1.619913146 -0.000679136  0.008395936
# Also, the below code gives you the coefficient elements for intercept and male
coef(lm_1_1)[c("(Intercept)", "male")]
## (Intercept)        male
##  1.61991315  0.04550246

1. Module originally written by Shiro Kuriwaki and Yon Soo Park