Lab 05

[sunaynagoel]

Question #4 on Lab 05

Average Salary of Minority female, there are two ways I can calculate it. Not sure which one is accurate

1. Mean salary of minority women = a0+ a1 (female)+ a2(minority)+ a3 (female*minority)
   When I use dummy variable in this equation, the last part with a3 becomes confusing because both female and minority end up having significant value of 1.

or should I use this solution

2. Mean salary of minority women = a0+ a1 (female)+ a2(minority)+ a3 (female*minority)
   since a3 is significant
   the slope in this case would be a0+a3

The answer is very different in both cases. Logically second one make sense to me because I feel like in first one I double counting some numbers.

Am I reading too much in this?

[lecy]

Yeah this is the tricky part about interactions.

The intuition is that we have four groups: white men, minority men, white women, minority women. The model is created to measure group means - the average salary of each group, and also to test differences in group means which is how we would detect program impact or in this case detect discrimination. To do this, we need four coefficients.

The interactions make it a little more confusing, but think about it as average home prices in four neighborhoods, with a dummy variable for each neighborhood (D1 represents neighborhood 1, etc). If we ran the model:

home price = b0 + b1(D1) + b2(D2) + b3(D3)

Then b0 would represent the average home value for neighborhood 4, and neighborhoods 1-3 can be calculated by b0 + b1, b0 + b2, b0 + b3.

If we ran the model:

home price = b0 + b1(D1) + b2(D2)

Then b0 now represents the average of homes from neighborhoods 3 and 4 combined. With only three coefficients there is no way to know the average price in all 4 neighborhoods. We can't separate the prices in 3 and 4.

Similarly, we need all four coefficients here to know the mean salary of each group. It's just harder to think about because we don't have one categorical variable with four levels that was split into 4 distinct dummy variables. We have 2 categorical variables with 2 levels, so they are interacted to create the four distinct groups.

salary = a0+ a1 (female)+ a2(minority)+ a3 (female*minority)

In this model:

home price = b0 + b1(D1) + b2(D2)

b0 represents the mean of neighborhoods 3 and 4 combined.

In the salary model, if you calculate the mean salary of minority women as (a0 + a1 + a2) then you are saying the salary for minority women MUST be the average salary of the combined group of white women, minority women, and minority men. You are pooling groups in the same way that b0 pools neighborhoods 3 and 4 in the example above.

What the interaction female x minority does is essentially allow you to separate minority women from minority men, and minority women from white women and pool them into a 4th independent group.

You do need all coefficients, though. If you plug in female=1 and minority=1 to the equation, you get:

salary minority women = a0 + a1(1) + a2(1) + a3(1)(1) = a0 + a1 + a2 + a3

What this model tells us is that the group starts at the baseline salary of the model a0, then receives the salary benefits of being a woman a1, the salary benefits of being a minority a2, and the synergy of being both a woman and a minority a3.

If a3 is not significant, then we could in fact calculate the salary as a0 + a1 + a2. There is nothing unique about being a minority woman that is distinct from the gains of just being a minority and just being a woman.

This is analogous to the example in the lecture notes where we interact the slope with male to see if men have different returns to years of experience than women. If the interaction is not significant it means a single slope is sufficient to describe the data.

y = b0 + b1(male) + b2(years_of_experience)

VS

y = b0 + b1(male) + b2(years_of_experience) + b3(male)(years_of_experience)

[sunaynagoel]

Thank you it makes more sense now. Making a table with dummy variables for model 2 as well made so much more sense to me.

[castower]

Hello all,

I have been using the values in the table to manually respond to the questions and then I was planning to type them into my RMD file, but I'm curious if there is a data set that we are supposed to enter to create our own regression table?

Thanks!
Courtney

[lecy]

You don't need to include tables or code in the lab. You can answer all of the questions with the info in the regression table.

If you want to play with the data, though, here it is:

URL <- "https://raw.githubusercontent.com/DS4PS/cpp-523-fall-2019/master/labs/data/engineer-salaries.csv"
dat <- read.csv( URL, stringsAsFactors=F )

m1 <- lm( salary ~ female + minority + female*minority )
m2 <- lm( salary ~ male + white + male*white )
m3 <- lm( salary ~ white.male + white.female + minority.male + minority.female -1, data=dat )
           
stargazer( m1, m2, type="text", digits=0,
           intercept.bottom = FALSE,
           omit.stat = c("ser","f","rsq","adj.rsq"),
           covariate.labels = c("a0/b0: Constant",
                                "a1: female",
                                "a2: minority",
                                "a3: female x minority",
                                "b1: male",
                                "b2: white",
                                "b3: male x white") )

stargazer( m3, type="text", digits=0,
           intercept.bottom = FALSE,
           omit.stat = c("ser","f","rsq","adj.rsq") )

[castower]

You don't need to include tables or code in the lab. You can answer all of the questions with the info in the regression table.

If you want to play with the data, though, here it is:

URL <- "https://raw.githubusercontent.com/DS4PS/cpp-523-fall-2019/master/labs/data/engineer-salaries.csv"
dat <- read.csv( URL, stringsAsFactors=F )

m1 <- lm( salary ~ female + minority + female*minority )
m2 <- lm( salary ~ male + white + male*white )
m3 <- lm( salary ~ white.male + white.female + minority.male + minority.female -1, data=dat )
           
stargazer( m1, m2, type="text", digits=0,
           intercept.bottom = FALSE,
           omit.stat = c("ser","f","rsq","adj.rsq"),
           covariate.labels = c("a0/b0: Constant",
                                "a1: female",
                                "a2: minority",
                                "a3: female x minority",
                                "b1: male",
                                "b2: white",
                                "b3: male x white") )

stargazer( m3, type="text", digits=0,
           intercept.bottom = FALSE,
           omit.stat = c("ser","f","rsq","adj.rsq") )

Thank you! I've tried to load the data, but I keep getting the following error:

Error in eval(predvars, data, env) : object 'salary' not found

[castower]

I was able to resolve the error and realized that I needed to add data=dat to m1 and m2. However, now when the table is produced, I get this error:

length of NULL cannot be changedlength of NULL cannot be changedlength of NULL cannot be changedlength of NULL cannot be changedlength of NULL cannot be changed

[lecy]

Add data=dat to the regression models. lm()