# 8 Lab 4 (Stata)

## 8.1 Lab Goals & Instructions

We’re using a new dataset today. This is from the World Health Organization, containing various measures related to health outcomes.

Research Question: What measures are associated with a country’s life expectancy?

#### Goals

• Transform variables in your dataset in a few new ways
• Predict marginal effects from your regression
• Visualize marginal effects to communicate your regression results

#### Instructions

1. Download the data and the script file from the lab files below.
2. Run through the script file and reference the explanations on this page if you get stuck.
3. If you have time, complete the challenge activity on your own.

## 8.2 Generating Related Variables

At various point in your data cleaning, you will want to create related variables, something that shows the same information but in a different form. By related variables, I mean you are using some variables in your dataset to calculate or configure a new variable.

For these related variables, we will rely on the mutate() function and various calculations.

### Example 1: New variables with simple calculations

You can always manipulate numeric variables in your dataset with basic math operations (adding, subtracting, multiplying, and so on). This is a relatively simple process, you just need to do it carefully.

For our first example, let’s say we want to know the percent population change between years. This data set contains measures from 2010, but it also has a variable for the 2005 population.

A) Lets take a look at our two population variables for an example country, say Lebanon…

list population if country == "Lebanon"
list pop_2005 if country == "Lebanon"
• 2010: 4337141
• 2005: 3986852

We could calculate the percent change manually

display 4337141 - 3986852
display 350289 / 4337141 * 100
350289

8.0764956

B) You can generate a simple variable based on a basic calculation

generate pop_change = (population - pop_2005) / population * 100

C) Let’s check out our new variable

summarize pop_change
Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
pop_change |        143   -1416.076    8407.399  -97846.89   99.89945

And for extra measure, the percent change for Lebanon…

tab pop_change if country == "Lebanon"
pop_change |      Freq.     Percent        Cum.
------------+-----------------------------------
8.076495 |          1      100.00      100.00
------------+-----------------------------------
Total |          1      100.00

There are clearly some funky populations in this dataset we would need to look closer at, but right now I want you to focus on knowing how to calculate the new variable.

### Example 2: Logging variables

This next example is really an extension of the last. We’re just explicitly using the log function to address nonlinearity in our model.

Let’s take a closer look at GDP and life expectancy.

A) Scatter plot of life expectency vs gdp

scatter lifeexpectancy gdp || lowess lifeexpectancy gdp

There is a clear nonlinear relationship between these two variables

B) Create a new logged version of the variable to deal with the nonlinearity

gen log_gdp = log(gdp)

C) Now let’s look at the scatter plot again

scatter lifeexpectancy log_gdp || lowess lifeexpectancy log_gdp

It’s not perfectly linear, but it’s a lot better!

### Example 3: From continuous to categorical via quantiles

There are other ways to deal with nonlinearity besides logging the variable. In this case we are going to divide a continuous variables into categories based on the quantiles. Essentially, we will now be asking in our regression–does it matter whether someone is in the bottom quantile vs the second, third, or top quantile?

But first, let’s learn how to go from continuous to quantile categories.

A) Scatterplot of life expectancy vs infant death rate

scatter lifeexpectancy infantdeaths
summarize infantdeaths, detail
Number of Infant Deaths per 1000 population
-------------------------------------------------------------
Percentiles      Smallest
1%            0              0
5%            0              0
10%            0              0       Obs                 183
25%            0              0       Sum of wgt.         183

50%            3                      Mean           27.92896
Largest       Std. dev.      104.0253
75%           21            239
90%           54            372       Variance       10821.26
95%           79            521       Skewness       8.770086
99%          521           1200       Kurtosis       92.69153

We can see that the infant death rate has a huge positive skew. Now let’s turn it into a categorical variable with quantiles. Quantiles refer to the values from 0-25%, 26-50%, 51-75%, and 76-100% of the range.

B) Use egen and xtile to make quantiles
Use “egen” and a command from the egenmore package, which automatically sorts the values into quantile ranges and assigns a category number 1-4.

First download the package and the ‘xtiles’ command

ssc install egenmore

Then generate the new variable

egen infant_quantiles = xtile(infantdeaths), nq(4)
label variable infant_quantiles "Infant death rate quantile"

C) Let’s take a look at the new variable

tab infant_quantiles
Infant |
death rate |
quantile |      Freq.     Percent        Cum.
------------+-----------------------------------
1 |         54       29.51       29.51
2 |         46       25.14       54.64
3 |         38       20.77       75.41
4 |         45       24.59      100.00
------------+-----------------------------------
Total |        183      100.00
scatter lifeexpectancy infant_quantiles || lowess lifeexpectancy infant_quantiles

And just like that we are linear!
Now we have a categorical variable for infant deaths where the bottom part of the range (0-25%) is category 1, the second quantile (25-49%) is category 2, and so on. You can see where each value fell into the range. It has a much more linear relationship

### 8.2.1 A note on gen vs egen

gen and egen are the two commands in Stata to calculate new variables based on other variables. Why are there two different commands? There’s not a good answer. The two commands a relic of how stata code has evolved over the years. Here’s what each command can do.

Here are some common math operations and functions that generate or gen can be used with:

• subtraction
• multiplication
• / division
• ^ power
• abs(x) absolute value of x
• exp(x) antilog of x
• ln(x), log(x) natural logarithm of x
• sqrt(x)square root of x
• round(x) rounds to the nearest integer of x
• round(x,y) x rounded in units of y (i.e., round(x,.1) rounds to one decimal place)

egen is often used with more complex functions like:

• xtile() to create quantiles
• std()
• anycount() to help you sum counts across variables
• rank() to assign a rank value to every observation based on a variable
• rowmean() to calculate the mean across variables in a row
• rowmiss() to calculate the total number of missing variables across a row

This is just a sample of what each command can do. If you need to do some type of calculation or transformation across variables, google the options you can do with each command.

## 8.3 Interpreting Results with Margins

How does the outcome change when a specific independent variable changes or is at a specific value?

This is what the margins command tells us. “Marginal effects” refer to the average predicted values for groups of observations, the groups being defined by levels of some variable(s) in the model, or for certain values of continuous variables (like the average). Marginal values will give us a lot of ways to visualize the results of our linear regression model.

### Margins for Categorical Variables

‘Margins’ is easy for categorical variables: as long as you told STATA it was a categorical/binary variable (used the i.), you can just write ‘margins [var]’ to see predicted variables for each category.

Run the regression first

regress lifeexpectancy i.infant_quantiles
Source |       SS           df       MS      Number of obs   =       183
-------------+----------------------------------   F(3, 179)       =     37.95
Model |  6123.27377         3  2041.09126   Prob > F        =    0.0000
Residual |  9627.92326       179  53.7872808   R-squared       =    0.3887
-------------+----------------------------------   Adj R-squared   =    0.3785
Total |   15751.197       182  86.5450386   Root MSE        =     7.334

-------------------------------------------------------------------------------
lifeexpecta~y | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
infant_quan~s |
2  |  -2.468357   1.471513    -1.68   0.095    -5.372101    .4353864
3  |  -8.218129   1.552906    -5.29   0.000    -11.28249   -5.153772
4  |  -14.71667   1.480315    -9.94   0.000    -17.63778   -11.79555
|
_cons |   75.99444   .9980284    76.14   0.000     74.02503    77.96386
-------------------------------------------------------------------------------

Predict the marginal effects for x (infant_quantiles).

margins infant_quantiles
Adjusted predictions                                       Number of obs = 183
Model VCE: OLS

Expression: Linear prediction, predict()

-------------------------------------------------------------------------------
|            Delta-method
|     Margin   std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
infant_quan~s |
1  |   75.99444   .9980284    76.14   0.000     74.02503    77.96386
2  |   73.52609   1.081337    68.00   0.000     71.39228    75.65989
3  |   67.77632   1.189729    56.97   0.000     65.42862    70.12401
4  |   61.27778   1.093285    56.05   0.000     59.12039    63.43516
-------------------------------------------------------------------------------

In a bivariate regression, the regression tells us the predicted values of people who are in each infant death rate quantile.

Interpretation: Countries in the lowest infant death quantile have an average life expectancy of 76 years whereas countries in the highest infant death quantile have an average life expectancy of 61 years.

### Margins for Continuous Variables

When you are using the margins command for continuous variables, you have to tell it more information. You have to specify the specific value of x you want to predict the outcome for.

Run the regression first (not displaying the results this time for brevity)

regress lifeexpectancy total_hlth

With this command you specify the values that you want to calculate the marginal effects for inside the brackets. You can specify a single value, a range of values, or more.

Margins for 5% total health expenditures.

margins, at(total_hlth = 5)
Adjusted predictions                                       Number of obs = 180
Model VCE: OLS

Expression: Linear prediction, predict()
At: total_hlth = 5

------------------------------------------------------------------------------
|            Delta-method
|     Margin   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
_cons |   69.12835   .7166116    96.47   0.000      67.7142    70.54249
------------------------------------------------------------------------------

Interpretation: Countries who spend 5% of total government expenditures on health are associated with a life expectancy of 69 years.

Margins for a range of total health expenditure levels. This code reads:

• calculate margins (GGPREDICT)
• for the model (FIT2)
• with the variable total_hlth (TERMS = "total_hlt …)
• starting from 0
• to a maximum of 15
• by increments of 5 I chose these cut points based on the range of total_hlth
margins, at(total_hlth = (0(5)15))
Adjusted predictions                                       Number of obs = 180
Model VCE: OLS

Expression: Linear prediction, predict()
1._at: total_hlth =  0
2._at: total_hlth =  5
3._at: total_hlth = 10
4._at: total_hlth = 15

------------------------------------------------------------------------------
|            Delta-method
|     Margin   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
_at |
1  |   64.31708   1.628695    39.49   0.000     61.10305    67.53112
2  |   69.12835   .7166116    96.47   0.000      67.7142    70.54249
3  |   73.93961   1.141811    64.76   0.000     71.68638    76.19283
4  |   78.75087    2.24126    35.14   0.000     74.32801    83.17373
------------------------------------------------------------------------------

Interpretation: As health expenditure increases, the life expectancy in that country also increases. At a 5% health expenditure, the associated life expectancy is 69 years, where as at a 15% health expenditure, the associated life expectancy is 79 years.

### Margins for regressions with more than one X variable

Run the regression first

regress lifeexpectancy i.infant_quantiles total_hlth

Calculate the margins for the infant death rate quantiles

margins infant_quantiles
Predictive margins                                         Number of obs = 180
Model VCE: OLS

Expression: Linear prediction, predict()

-------------------------------------------------------------------------------
|            Delta-method
|     Margin   std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
infant_quan~s |
1  |   75.54355   .9861075    76.61   0.000     73.59736    77.48975
2  |   73.41128   1.057689    69.41   0.000     71.32382    75.49875
3  |   68.22427    1.18852    57.40   0.000     65.87859    70.56995
4  |   61.90537   1.096809    56.44   0.000      59.7407    64.07005
-------------------------------------------------------------------------------

Like the previous example, we are asking Stata to generate the predicted values for the variable infant death rate quantiles (coded as 1, 2, 3, 4). But when calculating the predicted value for a person in each quantile, we now have to take into account our other x variable - total health expenditures. So what does this function do?

The function makes an assumption: that the other x values are being held at their mean (for continuous variables) or the “reference category” (for categorical variables). When you put just one variable, what the function actually calculates is the predicted value for each value of x when age is at its mean in the dataset.

mean total_hlth
Mean estimation                            Number of obs = 180

--------------------------------------------------------------
|       Mean   Std. err.     [95% conf. interval]
-------------+------------------------------------------------
total_hlth |   6.151222   .2038742      5.748916    6.553528
--------------------------------------------------------------

Interpretation: Countries in the lowest infant death quantile have an average life expectancy of 75 years whereas countries in the highest infant death quantile have an average life expectancy of 61 years, holding total health expenditures constant at the average.

### Other variations of margins

We can do a lot with ggpredict() and the margins it produces. For example, Let’s say we want to know…

A) The predicted life expectancy for at various levels of health expenditure, but only for countries in the first infant death quantile:

margins, at(total_hlth = (0(5)15) infant_quantiles = 1)
Adjusted predictions                                       Number of obs = 180
Model VCE: OLS

Expression: Linear prediction, predict()
1._at: infant_quantiles =  1
total_hlth       =  0
2._at: infant_quantiles =  1
total_hlth       =  5
3._at: infant_quantiles =  1
total_hlth       = 10
4._at: infant_quantiles =  1
total_hlth       = 15

------------------------------------------------------------------------------
|            Delta-method
|     Margin   std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
_at |
1  |    71.6689   1.686734    42.49   0.000     68.33994    74.99786
2  |    74.8184   1.044886    71.60   0.000      72.7562     76.8806
3  |    77.9679   1.160133    67.21   0.000     75.67824    80.25755
4  |   81.11739   1.899327    42.71   0.000     77.36886    84.86593
------------------------------------------------------------------------------

Interpretation: For countries in with the lowest infant death rate, at a 5% health expenditure, the associated life expectancy is 74 years, where as at a 15% health expenditure, the associated life expectancy is 81 years.

B) The predicted values for each quantile at different levels of health expenditure.

margins infant_quantiles, at(total_hlth = (0(5)15))
Adjusted predictions                                       Number of obs = 180
Model VCE: OLS

Expression: Linear prediction, predict()
1._at: total_hlth =  0
2._at: total_hlth =  5
3._at: total_hlth = 10
4._at: total_hlth = 15

-------------------------------------------------------------------------------
|            Delta-method
|     Margin   std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
_at#|
infant_quan~s |
1 1  |    71.6689   1.686734    42.49   0.000     68.33994    74.99786
1 2  |   69.53663   1.651616    42.10   0.000     66.27698    72.79628
1 3  |   64.34962   1.598282    40.26   0.000     61.19523      67.504
1 4  |   58.03072   1.583146    36.66   0.000     54.90621    61.15524
2 1  |    74.8184   1.044886    71.60   0.000      72.7562     76.8806
2 2  |   72.68613   1.090304    66.67   0.000     70.53429    74.83797
2 3  |   67.49911   1.181185    57.15   0.000     65.16791    69.83032
2 4  |   61.18022   1.102643    55.49   0.000     59.00403    63.35641
3 1  |    77.9679   1.160133    67.21   0.000     75.67824    80.25755
3 2  |   75.83563   1.287284    58.91   0.000     73.29503    78.37623
3 3  |   70.64861   1.497765    47.17   0.000      67.6926    73.60462
3 4  |   64.32972   1.390216    46.27   0.000     61.58597    67.07347
4 1  |   81.11739   1.899327    42.71   0.000     77.36886    84.86593
4 2  |   78.98513   2.032941    38.85   0.000     74.97289    82.99736
4 3  |   73.79811   2.258056    32.68   0.000     69.34158    78.25464
4 4  |   67.47922   2.158006    31.27   0.000     63.22015    71.73828
-------------------------------------------------------------------------------

Interpretation: (Choosing one example from these margins) In countries with the highest level of health expenditure (15%), those with the highest infant death rates have an associated life expectancy of 67 years whereas those with the lowest infant death rates have a life expectancy of 81 years.

NOTE: This is a good example of why you have to be precise with ggpredict() margins. By changing our specification of infant_quantiles, we can find out the predicted life expectancy for a) only the first quantile at different levels of health expenditure OR b) each quantile at different levels of health expenditure.

## 8.4 Graphing Results with Margins

Knowing the margins can help you translate your findings into comprehensible statements. Displaying them is a great visual way to communicate those findings.

marginsplot is a command that can be used after margins to visualize our predicted values. Let’s visualize the margins from the last section.

#### Plot A

Predict your margins first, then add a marginsplot command.

regress lifeexpectancy i.infant_quantiles total_hlth
margins, at(total_hlth = (0(5)15) infant_quantiles = 1)
marginsplot

#### Plot B

Predict your margins first, then add a marginsplot command.

margins infant_quantiles, at(total_hlth = (0(5)15))
marginsplot

Plotting the margins allows us to actually make easier the visualization of what we are trying to describe with the predicted results. There are also some fun things we can do while visualizing relationships.

#### Here is an option with a bar graph

margins infant_quantiles
marginsplot, recast(bar)

#### Here is an option with the lines split to multiple graphs

margins infant_quantiles, at(total_hlth = (0(5)15))
marginsplot, by(infant_quantiles)

## 8.5 BONUS: Saving and Improving your Graphs

You may be manually saving your plots or taking screenshots, but here is some other helpful code to save a graph in code. If you tweak anything in your previous code that would affect the graph, your new graph will be saved when you rerun your code. It saves times as you are iterating your findings

FIRST: Create the graph

margins infant_quantiles, at(total_hlth = (0(5)15))
marginsplot

SECOND: Save the most recent graph

graph export "figs_output/infantdeath_plot.png", replace

## 8.6 Challenge Activity

Run a regression of life expectancy (lifeexpectancy) and child HIV/AIDS death rate (child_hivaids).

1. Create a new variable that addresses the skew of the HIV/AIDS variable. There are multiple ways to do this.

2. Produce a margins plot that clearly communicates the effect of the child HIV/AIDS death rate on life expectancy.

This activity is not in any way graded, but if you’d like me to give you feedback email me your script file and a few sentences interpreting your results.