Marginsplot in stata forex

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First, load the following dataset from the Stata webpage. This is a subset of the National Longitudinal Survey, and it contains socioeconomic variables from young women who were years old over the period The Stata code to perform this regression would be: logit collgrad age i.

Important note: in this dataset the variable age is defined as a discrete variable a discrete jump of one year. However, I will treat it as a continuous variable. I hope that anyone gets upset with that :. It makes sense that the predicted probability is higher at 40 years old than at In each case, the margins are computed at the value of the variable age indicated and the other covariates set to their observed values.

Also, one might be interested in knowing the predicted probability along with the age distribution; this is for several ages. Moreover, values from different independent variables can be indicated at the same time. Again, with the other covariates set to their observed values. Thus, the coefficient, which indicates the relationship between the dependent variable and the independent variable, may vary along with the distribution of the independent variable.

In our case, it might be interesting to get the partial derivative of the variable age or, in other words, the marginal effect. This allows understanding how a change in the variable age one more year affects the expected probability of having a college graduate. This average marginal effect is computed as the average of all the marginal effects from each observation in the sample and the code is as follows: margins, dydx age This output, 0.

This is, the marginal effect of increasing one year the age of a woman. More interesting, we can estimate the same model by OLS and perform the same exercise: reg collgrad age i. Suppose we only have two genders in our study, male and female.

To see why only one dummy code is needed for a binary variable, suppose you have a female participant. If we entered both dummy variables into our regression, it would result in what is known as perfect collinearity or redundancy in our estimates and most statistical software programs would simply drop one of the dummy codes from your model.

Now we are ready to fit our model, recalling that we only enter one of the dummy codes. We have to be careful when choosing which dummy code to omit because the omitted group is also known as the reference group.

Recall that we assigned value labels to the gender variable in the Requirements section in the beginning of the seminar. This step is recommended for categorical variables, and the tabulate command can help us see whether the labeling was effective. Percent Cum. Note that these are value labels we have assigned.

In order to see this, you can specify the option nolabel tab gender, nolabel gender Freq. The underlying numerical value is important for understanding how Stata handles dummy codes because Stata takes the lowest value and assigns it to the reference group for any linear model command like regress. This means that if we use the prefix i. Quiz: Write out the equation for the model above.

In order to change the reference group so that Females are omitted, we can use ib2. The results of the change of base is shown below. Answer: False. The code ib2. Another way to think about it is if we know the slope of Hours for females, this is the additional slope for males. The interaction is not significant, but we decide to probe the interaction anyway for demonstration purposes.

Go to top of page Obtaining simple slopes by each level of the categorical moderator Since our goal is to obtain simple slopes of Hours by gender we use the dydx hours option after margins. Since gender is a categorical variable, we specify it before the comma. Remember that continuous variables come after the comma usually specified at particular values with the at option and categorical variables usually come before the comma. Conceptually this may make more sense because we are obtaining the simple slopes of Hours over values of Gender.

The output is equivalent to the previous command. A common misconception is that since the simple slope of Hours is significant for females but not males, we should have seen a significant interaction. However, the interaction tests the difference of the Hours slope for males and females and not whether each simple slope is different from zero which is what we have from the output above.

The test of simple slopes is not the same as the test of the interaction, which tests the difference of simple slopes. The only difference is that the sign is flipped because we are taking female — males females have higher Hours slopes whereas the interaction takes male — female. Take a look a the shortened summary table below and verify the p-value and the sign of the coefficient highlighted in red. We are not obtaining the simple effect of Gender but simple slopes of Hours.

The statement dydx hours indicates the simple slope we are requesting. Since gender is categorical, it comes before the comma which means we want the simple slope of Hours by Gender. Quiz: True of False The command margins gender, dydx hours pwcompare effects requests pairwise differences in the predicted values of Hours for females versus males. Answer: False, this is the pairwise difference in the slope of Hours for females versus males.

Recall that dydx hours obtains simple slopes and at obtains predicted values. Exercise Relevel gender using ib. What does the naming convention in the coefficient table represent? Note you should get output from regress and margins that looks like this loss Coef. Go to top of page Optional Flipping the moderator MV and the independent variable IV An interaction is symmetric, which means we can also flip the moderator gender so that gender is now the categorical IV and Hours is now the MV.

The interaction model is exactly the same, but we decompose the interaction differently. Since Hours is continuous, it means we can hypothetically choose an unlimited number of values. The simple effect of Gender is the difference of two predicted values. In Stata, obtaining simple effects is the same as obtaining simple slopes, we can use the option dydx gender even if gender is binary. Answer: False, dydx gender requests simple effects of gender, which is the difference of the predicted value of males versus females at a particular level of Hours.

Note that in this case, 2. From our other simple effects we can see that as Hours increases, the male versus female difference becomes more negative females are losing more weight than males. If we specified ib1. Answer: True. By specifying ib1. Hint: look at the p-values and standard errors of each simple effect.

Answer: Although the simple effect of Gender change as Hours varies, the standard errors are so big that we cannot statistically conclude a difference. See the plot below for the large overlap in confidence intervals. Thankfully, this is easy to accomplish using marginsplot. First we specify the margins command. Since Gender is a categorical variable, it comes before the comma.

Stata will automatically know to use the categorical variable as the moderator that separates the lines. We confirm that the standard error of the interaction coefficient 1. From our previous analysis, we found that there are no gender differences in the relationship of time spent exercising and weight loss.

Perhaps females and males respond differently to different types of exercise here we make gender the IV and exercise type the MV. The question we ask is, does type of exercise W moderate the gender effect X? In other words, do males and females lose weight differently depending on the type of exercise they engage in?

Since this person is not in the jogging or swimming condition, we can conclude that this person is in the reading condition. We are now ready to set up the interaction of two categorical variables. How about for the second categorical variable prog. Not that in Stata i. Therefore we only need to put ib2. Note that Stata will automatically know to relevel the simple effects based on the interaction.

Without the i. From the syntax above we obtain the following shortened output: loss Coef. Also, the jogging effect jogging — reading for males versus the jogging effect for females. Also, the swimming effect swimming- reading for males versus the swimming effect for females. The last two coefficients are the most difficult to interpret. Quiz: Use the coefficients from the categorical by categorical interaction to derive the female female — male effect for the swimming group.

First we want to obtain the predicted values for each combination of Gender and Program. Typically, for continuous variables this would require the at option. However, recall that categorical variables come before the comma in margins and since both gender and prog are categorical, we omit the at option. Since gender and prog are both defined to be categorical with the corresponding ib. Expression : Linear prediction, predict Delta-method Margin Std. For example, females in the reading program have an estimated weight gain of 3.

Exercise Try to reproduce each predicted value from margins using the coefficient table alone. Do you notice a pattern for the coefficient terms? For females, the additional terms do not involve interaction terms, but for males it does. In order to understand the interaction, we need to obtain the simple effects which are differences of the predicted values. This can be accomplished using the dydx option after margins. The key is to know which independent variable IV you want to the make the moderator MV.

The hypothetical code is then margins mv, dydx iv. Note that both the MV and IV need to be categorical for this syntax to work. Recall that we specified ib2. We see that the male effect for jogging and swimming are significant at the 0. Additionally, males lose more weight in the jogging condition positive but females lose more weight in the swimming condition negative. Quiz: True or False The interaction is the male effect for a particular exercise type. See below. The male effect alone does not capture the interaction.

The interaction is the difference of simple effects. Going back to the output from regress loss ib2. In this case, we want the difference in the male effect males vs. From margins, recall that the gender effect for swimming is Then the difference of the two simple effects is We verify therefore that the interaction is the pairwise difference of the male effects male-female for swimming versus reading. It is essentially a difference of differences.

Exercise Find the interaction that is not automatically generated by the original regression output and obtain its effect by manually calculating the difference of differences using the output from margins. Confirm your answer with a regression Hint: you need to change the reference group. Running regress loss ib2. However, an interaction is symmetric which means we can also look at the effect of exercise type IV split by gender MV.

Obtain the same interaction term using margins with gender as the moderator. In the previous example, we treated Exercise as the MV so that the interpretation is the difference in the gender effect for jogging vs. Go to top of page Plotting the categorical by categorical interaction Finally, the best way to understand an interaction is to plot it. The marginsplot command follows margins and plots the independent variable IV on the x-axis and splits the lines by levels of the moderating variable MV.

For our case, we want prog to be our moderator, so we specify the following syntax margins gender prog marginsplot Quiz: True or False The code margins prog gender tells marginsplot that we want prog on the x-axis with lines corresponding to levels of gender. We obtain the following interaction plot: Here we see the results confirming the predicted values and simple effects we found before.

Each point on the plot is a predicted value and each line or connection of two points is a simple effect.