IRIII.2 Quantitative Methods in the Study of International Relations
Model Presentation
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# = o_o =_______ \ \ -Model Presentation-
# __^ __( \.__) )
# (@)<_____>__(_____)____/
If it’s not installed, install it.
library(tidyverse)
#> ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
#> ✔ dplyr 1.1.1 ✔ readr 2.1.4
#> ✔ forcats 1.0.0 ✔ stringr 1.5.0
#> ✔ ggplot2 3.4.2 ✔ tibble 3.2.1
#> ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
#> ✔ purrr 1.0.1
#> ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
#> ✖ dplyr::filter() masks stats::filter()
#> ✖ dplyr::lag() masks stats::lag()
#> ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(modelsummary)
# library(kableExtra) # for extra formatting options, in this format.
options("modelsummary_factory_default" = "kableExtra")
^ Note: “tinytable” (c.f. {tinytable}) is now default, though previous
versions of this were written around “kableExtra” (c.f. {kableExtra}).
As you develop your skills here (and importantly move away from
copy-pasting stuff into Word), you may want to more fully transition
into {modelsummary}’s default settings. However, we should keep this
tractable here. Also note that anyone viewing this on the public course
website will note that there are additional formatting things we should
be doing to make this presentable in that particular format. However,
what’s offered here is fine for the intended format. We’ll be doing
copy-pasting from RStudio into Word.
Load the data
WVS <- readRDS("~/Dropbox/teaching/eh1903-ir3/2/data/wv6-sweden-v20201117.rds")
^ Note: you have access to this, but I won’t know where you put it on your hard drive. You need to download it and load it.
Let’s grab the information I used in the example paper I wrote for you. Here’s where I have to emphasize you need to read the codebook. The codebook describes the variables included and tells you the basic information they are communicating. You have to read the codebook, whatever the codebook is.
WVS %>%
select(
#importance of democracy, justifiability of divorce
V140, V205,
# age, sex, scale of incomes,
V242, V240, V239,
# how often you pray, age completed education
V146, V249) -> Data
^ read the codebook. It’ll tell you what you want.
Optional, but renames columns to be more informative. In most cases, you should seriously think about doing this because a lot of variable names in standing data sets are either vague or obscene to look at.
colnames(Data) <- c("impdem", "justdiv", "age", "sex", "inc", "pray", "educ")
Surveys typically make men to be 1 and women to be 2, but I’ve always hated this practice. This makes women to be 1 and men to be 0.
Data %>% mutate(sex = ifelse(sex == 2, 1, 0)) -> Data
Data
#> # A tibble: 1,206 × 7
#> impdem justdiv age sex inc pray educ
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 10 10 38 1 5 8 31
#> 2 10 4 51 1 5 3 29
#> 3 8 10 70 0 7 3 23
#> 4 6 1 21 1 6 2 6
#> 5 10 10 65 1 5 6 21
#> 6 10 10 51 1 5 2 32
#> 7 10 10 48 1 5 8 38
#> 8 10 10 81 0 7 8 27
#> 9 8 10 19 0 4 8 18
#> 10 10 10 61 0 8 8 18
#> # ℹ 1,196 more rows
Let’s run the linear models I described in the paper.
# First model
M1 <- lm(impdem ~ justdiv, Data)
# Full model
M2 <- lm(impdem ~ justdiv + age + sex + inc + pray + educ, Data)
summary(M1)
#>
#> Call:
#> lm(formula = impdem ~ justdiv, data = Data)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -8.4876 0.5124 0.5124 0.5993 1.2948
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 8.61826 0.15757 54.696 < 2e-16 ***
#> justdiv 0.08694 0.01807 4.811 1.7e-06 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 1.428 on 1161 degrees of freedom
#> (43 observations deleted due to missingness)
#> Multiple R-squared: 0.01955, Adjusted R-squared: 0.0187
#> F-statistic: 23.15 on 1 and 1161 DF, p-value: 1.697e-06
summary(M2)
#>
#> Call:
#> lm(formula = impdem ~ justdiv + age + sex + inc + pray + educ,
#> data = Data)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -8.0004 -0.1078 0.3590 0.7373 2.0805
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 6.992661 0.267222 26.168 < 2e-16 ***
#> justdiv 0.095031 0.018053 5.264 1.70e-07 ***
#> age 0.018337 0.002236 8.202 6.59e-16 ***
#> sex 0.180965 0.084742 2.135 0.03294 *
#> inc 0.056494 0.022731 2.485 0.01309 *
#> pray -0.006103 0.019008 -0.321 0.74820
#> educ 0.013148 0.005088 2.584 0.00989 **
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 1.365 on 1091 degrees of freedom
#> (108 observations deleted due to missingness)
#> Multiple R-squared: 0.1064, Adjusted R-squared: 0.1015
#> F-statistic: 21.65 on 6 and 1091 DF, p-value: < 2.2e-16
Prepare a table of descriptive statistics of your data.
Papers make routine use of the table of descriptive statistics to
communicate some basic features about the data. this is easily done in
{modelsummary} with the datasummary_skim() function. The
datasummary() function in the same package has more flexibility but
this is easier to explain and its default format actually looks nicer.
Data %>%
# setNames(c("Imp. Dem.", "Justif. Divorce",
# "Age", "Female", "Income", "Prayer Frequency",
# "Age at End of Schooling")) %>%
# na.omit %>%
datasummary_skim(title = "Summary Statistics of the Data Used in this Analysis",
align = c("lcccccccc"),
histogram = TRUE,
# output = "tinytable",
notes = "You can put a footnote here.")
| Unique | Missing Pct. | Mean | SD | Min | Median | Max | Histogram | |
|---|---|---|---|---|---|---|---|---|
| impdem | 11 | 1 | 9.3 | 1.5 | 1.0 | 10.0 | 10.0 |  |
| justdiv | 11 | 3 | 8.4 | 2.3 | 1.0 | 10.0 | 10.0 |  |
| age | 68 | 0 | 47.3 | 19.4 | 18.0 | 47.0 | 85.0 |  |
| sex | 2 | 0 | 0.5 | 0.5 | 0.0 | 1.0 | 1.0 |  |
| inc | 11 | 3 | 5.4 | 1.8 | 1.0 | 5.0 | 10.0 |  |
| pray | 9 | 1 | 6.4 | 2.3 | 1.0 | 8.0 | 8.0 |  |
| educ | 54 | 2 | 24.1 | 8.3 | 5.0 | 22.0 | 83.0 |  |
Be mindful that the data I supplied here are all numeric and the data has only what I want to summarize. This will try to (want to) summarize everything, so be mindful what you are asking it to do.
The histogram = TRUE is nice but often doesn’t print well to documents
(and it won’t in Word as I’m going to show you to do it). So, you can
use this (as a beginner) to get an idea of what your data look like and
what issues you may have, but you should disable it for use.
Now, we’re going to do a few things. First, we’re going to “uncomment”
that setNames() comment, which is going to quickly rename our
variables to be something that would be insane for an analysis but easy
for formatting a table. Next, we’re going to disable that
(histogram = FALSE) and knock off a “c” from the align argument.
Data %>%
setNames(c("Imp. Dem.", "Justif. Divorce",
"Age", "Female", "Income", "Prayer Frequency",
"Age at End of Schooling")) %>%
# na.omit %>%
datasummary_skim(title = "Summary Statistics of the Data Used in this Analysis",
align = c("lccccccc"),
histogram = F,
notes = "You can put a footnote here.")
| Unique | Missing Pct. | Mean | SD | Min | Median | Max | |
|---|---|---|---|---|---|---|---|
| Imp. Dem. | 11 | 1 | 9.3 | 1.5 | 1.0 | 10.0 | 10.0 |
| Justif. Divorce | 11 | 3 | 8.4 | 2.3 | 1.0 | 10.0 | 10.0 |
| Age | 68 | 0 | 47.3 | 19.4 | 18.0 | 47.0 | 85.0 |
| Female | 2 | 0 | 0.5 | 0.5 | 0.0 | 1.0 | 1.0 |
| Income | 11 | 3 | 5.4 | 1.8 | 1.0 | 5.0 | 10.0 |
| Prayer Frequency | 9 | 1 | 6.4 | 2.3 | 1.0 | 8.0 | 8.0 |
| Age at End of Schooling | 54 | 2 | 24.1 | 8.3 | 5.0 | 22.0 | 83.0 |
Looks nice, right? Let’s copy-paste it into a Word document. Some cosmetic things you’ll have to do yourself (e.g. potential centering and what-not). All you need is Ctrl-A, Ctrl-C, Ctrl-V (Cmd equivalent for you Mac users).
Make a plot or two or three
For what it’s worth, this descriptive statistics table is pointing you to potential issues you can encounter in your data. In this particular example, I see several things I’ll want to consider. For one, I see an överliggare there who said they finished schooling at 83 (which, fam…). I see that there is huge problems of left-skew. Most Swedes maximally value democracy, are maximally permissive about divorce, and don’t pray at all (per the codebook). I can already anticipate these are going to be issues I should at least acknowledge because I can suspect they’re going to point me to problems in my linear model.
At the least, I can offer a visual display of these. A bar chart should suffice.
Data %>%
select(impdem) %>%
na.omit %>%
ggplot(.,aes(factor(impdem))) +
geom_bar(fill="#9bb2ce", alpha=.8, color='black') +
geom_text(stat='count', aes(label=..count..), vjust=-.5) +
# theme_steve(style = 'generic') +
theme_minimal() +
labs(caption = "Data: World Values Survey in Sweden (2011, Wave 6)",
x = "Values of the Importance of Democracy",
y = "Count of Observations") +
scale_y_continuous(limits = c(0,1000))
Issues in the dependent variable will typically be the ones you should think about first and the most, but you can see these issues manifest elsewhere.
Data %>%
select(justdiv) %>%
na.omit %>%
ggplot(.,aes(factor(justdiv))) +
geom_bar(fill="#9bb2ce", alpha=.8, color='black') +
geom_text(stat='count', aes(label=..count..), vjust=-.5) +
# theme_steve(style = 'generic') +
theme_minimal() +
labs(caption = "Data: World Values Survey in Sweden (2011, Wave 6)",
x = "Values of the Justifiability of Divorce",
y = "Count of Observations") +
scale_y_continuous(limits = c(0,750))
Now that you’ve created a graph that summarizes important features about your data, save it (in Rstudio) to a PNG file. Then, in your Word document, grab it and move it in. You can also—if it pleases and sparkles—zoom into the plot, right-click, copy image, and paste it into your Word document. Choice is yours.
Create a regression table
To really impress me, you’ll need to have a regression table that
summarizes the results, and that summary cannot (well, really, really
should not) be a PrtScrn job. You should get comfortable with the
modelsummary() function in R.
Its basic form looks something like this.
modelsummary(list(M1, M2))
| (Intercept) | 8.618 | 6.993 |
| (0.158) | (0.267) | |
| justdiv | 0.087 | 0.095 |
| (0.018) | (0.018) | |
| age | 0.018 | |
| (0.002) | ||
| sex | 0.181 | |
| (0.085) | ||
| inc | 0.056 | |
| (0.023) | ||
| pray | -0.006 | |
| (0.019) | ||
| educ | 0.013 | |
| (0.005) | ||
| Num.Obs. | 1163 | 1098 |
| R2 | 0.020 | 0.106 |
| R2 Adj. | 0.019 | 0.101 |
| AIC | 4132.9 | 3808.4 |
| BIC | 4148.1 | 3848.4 |
| Log.Lik. | -2063.469 | -1896.218 |
| RMSE | 1.43 | 1.36 |
Notice here that modelsummary() works best with list types, and lists
are just super-flexible ways of corralling a diverse set of object types
in R. Here, we have two regression summaries (M1, M2). We’re
wrapping them in a list(). modelsummary() will do what it does with
them.
There’s a lot we should really think about doing here. First, it may be
useful to so-called “name” your regressions. In my sample paper, M1 is a
simple bivariate linear model and M2 adds the control variables. I can
name them within list() like this.
modelsummary(list("Bivariate Regression" = M1,
"Full Model" = M2))
| Bivariate Regression | Full Model | |
|---|---|---|
| (Intercept) | 8.618 | 6.993 |
| (0.158) | (0.267) | |
| justdiv | 0.087 | 0.095 |
| (0.018) | (0.018) | |
| age | 0.018 | |
| (0.002) | ||
| sex | 0.181 | |
| (0.085) | ||
| inc | 0.056 | |
| (0.023) | ||
| pray | -0.006 | |
| (0.019) | ||
| educ | 0.013 | |
| (0.005) | ||
| Num.Obs. | 1163 | 1098 |
| R2 | 0.020 | 0.106 |
| R2 Adj. | 0.019 | 0.101 |
| AIC | 4132.9 | 3808.4 |
| BIC | 4148.1 | 3848.4 |
| Log.Lik. | -2063.469 | -1896.218 |
| RMSE | 1.43 | 1.36 |
Next—and really important—thing I want to do is add asterisks to help me
identify so-called statistical significance. There are some
customization options here, but just add stars = TRUE here.
modelsummary(list("Bivariate Regression" = M1,
"Full Model" = M2),
stars = TRUE)
| Bivariate Regression | Full Model | |
|---|---|---|
| (Intercept) | 8.618*** | 6.993*** |
| (0.158) | (0.267) | |
| justdiv | 0.087*** | 0.095*** |
| (0.018) | (0.018) | |
| age | 0.018*** | |
| (0.002) | ||
| sex | 0.181* | |
| (0.085) | ||
| inc | 0.056* | |
| (0.023) | ||
| pray | -0.006 | |
| (0.019) | ||
| educ | 0.013** | |
| (0.005) | ||
| Num.Obs. | 1163 | 1098 |
| R2 | 0.020 | 0.106 |
| R2 Adj. | 0.019 | 0.101 |
| AIC | 4132.9 | 3808.4 |
| BIC | 4148.1 | 3848.4 |
| Log.Lik. | -2063.469 | -1896.218 |
| RMSE | 1.43 | 1.36 |
|
||
Next, and also really important, thing I want to do is rename the
variables to be something intuitive. This is the coef_map argument in
modelsummary(). Of note: it will help you to build the simple version
above so you know what you’re looking at. In coef_map, there’s a c()
function that takes arguments effectively communicating that “what the
thing is called in the model, on the left, is going to be called this
new thing, on the right”. justdiv is my main independent variable, but
“Justifiability of Divorce” is what I want to call it.
modelsummary(list("Bivariate Regression" = M1,
"Full Model" = M2),
stars = TRUE,
coef_map = c("justdiv" = "Justifiability of Divorce",
"age" = "Age",
"educ" = "Age at End of Schooling",
"sex" = "Female",
"pray" = "Frequency of Prayer",
"inc" = "Scale of Incomes",
"(Intercept)" = "Intercept"))
| Bivariate Regression | Full Model | |
|---|---|---|
| Justifiability of Divorce | 0.087*** | 0.095*** |
| (0.018) | (0.018) | |
| Age | 0.018*** | |
| (0.002) | ||
| Age at End of Schooling | 0.013** | |
| (0.005) | ||
| Female | 0.181* | |
| (0.085) | ||
| Frequency of Prayer | -0.006 | |
| (0.019) | ||
| Scale of Incomes | 0.056* | |
| (0.023) | ||
| Intercept | 8.618*** | 6.993*** |
| (0.158) | (0.267) | |
| Num.Obs. | 1163 | 1098 |
| R2 | 0.020 | 0.106 |
| R2 Adj. | 0.019 | 0.101 |
| AIC | 4132.9 | 3808.4 |
| BIC | 4148.1 | 3848.4 |
| Log.Lik. | -2063.469 | -1896.218 |
| RMSE | 1.43 | 1.36 |
|
||
Just as an FYI, this works in order you specify them (i.e. the justdiv
variable is displayed first here) and if you don’t specify it, it gets
dropped from the summary (i.e. check for typos!).
Finally, it’s worth clarifying that modelsummary() returns almost all
goodness of fit statistic for the model (contingent on the model type)
and there are often lots of these. You don’t need all of them. In the
simple linear model, you really just want information about the number
of observations at a minimum, and maybe one or both of the R-squares.
Use the gof_map argument to specify what you want. If you don’t know
what they’re called, use broom::glance() to see what they’re called
internally.
broom::glance(M2)
#> # A tibble: 1 × 12
#> r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.106 0.101 1.37 21.7 3.89e-24 6 -1896. 3808. 3848.
#> # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>
# I want, in order, "nobs", "r.squared", and "adj.r.squared".
modelsummary(list("Bivariate Regression" = M1,
"Full Model" = M2),
stars = TRUE,
coef_map = c("justdiv" = "Justifiability of Divorce",
"age" = "Age",
"educ" = "Age at End of Schooling",
"sex" = "Female",
"pray" = "Frequency of Prayer",
"inc" = "Scale of Incomes",
"(Intercept)" = "Intercept"),
gof_map = c("nobs", "adj.r.squared", "r.squared"))
| Bivariate Regression | Full Model | |
|---|---|---|
| Justifiability of Divorce | 0.087*** | 0.095*** |
| (0.018) | (0.018) | |
| Age | 0.018*** | |
| (0.002) | ||
| Age at End of Schooling | 0.013** | |
| (0.005) | ||
| Female | 0.181* | |
| (0.085) | ||
| Frequency of Prayer | -0.006 | |
| (0.019) | ||
| Scale of Incomes | 0.056* | |
| (0.023) | ||
| Intercept | 8.618*** | 6.993*** |
| (0.158) | (0.267) | |
| Num.Obs. | 1163 | 1098 |
| R2 Adj. | 0.019 | 0.101 |
| R2 | 0.020 | 0.106 |
|
||
Finally, you may want to add a caption that explains that this a regression table. You’ll want to call it something better than what I call it here.
modelsummary(list("Bivariate Regression" = M1,
"Full Model" = M2),
stars = TRUE,
coef_map = c("justdiv" = "Justifiability of Divorce",
"age" = "Age",
"educ" = "Age at End of Schooling",
"sex" = "Female",
"pray" = "Frequency of Prayer",
"inc" = "Scale of Incomes",
"(Intercept)" = "Intercept"),
gof_map = c("nobs", "adj.r.squared", "r.squared"),
caption = "Hi Mom!")
| Bivariate Regression | Full Model | |
|---|---|---|
| Justifiability of Divorce | 0.087*** | 0.095*** |
| (0.018) | (0.018) | |
| Age | 0.018*** | |
| (0.002) | ||
| Age at End of Schooling | 0.013** | |
| (0.005) | ||
| Female | 0.181* | |
| (0.085) | ||
| Frequency of Prayer | -0.006 | |
| (0.019) | ||
| Scale of Incomes | 0.056* | |
| (0.023) | ||
| Intercept | 8.618*** | 6.993*** |
| (0.158) | (0.267) | |
| Num.Obs. | 1163 | 1098 |
| R2 Adj. | 0.019 | 0.101 |
| R2 | 0.020 | 0.106 |
|
||
Dope, let’s put it in our Word document. In Rstudio, click on that viewer of the table. Then: Ctrl-A, Ctrl-C, Ctrl-V into your Word document. For you Mac users, this should be Cmd instead of Ctrl.