Categorical weight loss

In our case, our factor variable is gender. We can verify that by the following:. Factor variables in R have an attribute attached to them known as levels. Here we have two levels, male and female, and we know that the output of this command is a character vector with two elements, where Element 1 is male and Element 2 is female. The order of the elements is important for understanding dummy codes because R internally takes the first element and omits it from the model.

Introduction

The naming of the variable genderfemale means that R is including the dummy code for females and omitting the dummy group for males. Now that we understand how R handles factor variables in lm models, we will go back to our original interaction model. How would we do this in R? This can be accomplished by the function relevel :. After re-leveling, we replace the re-coded gender into our data so that now female is our reference group. Finally, we are ready to fit our original model into lm :. The interaction is not significant, but we decide to probe the interaction anyway for demonstration purposes.

Since our goal is to obtain simple slopes of Hours by gender we use emtrends. We do not use emmeans because this function gives us the predicted values rather than slopes. We pass in contcat as our lm object from our continuous by categorical interaction model. The output we obtain is:. The simple slope for females is 3. 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. Answer: False. What do we notice about the p -value and the estimate? 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. By default, pairwise emtrends takes all differences from the reference group.

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. Answer: False, this is the pairwise difference in the slope of Hours for females versus males. Recall that emtrends obtains simple slopes and emmeans obtains predicted values. Relevel gender so that male is now the reference group, refit the lm model, store again it as a contcont object and use emtrends to obtain the simple effects.

What does the naming convention in summary contcont represent?

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. Be aware that the order of the factor variables in the list matters. The simple effect is the difference of two predicted values. 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. Hint: look at the p -values and standard errors of each simple effect.

Thankfully, this is easy to accomplish using emmip. Again we want the x-axis to indicate ranges of Hours between 0 and 4 by increments of 0. The only difference is we swap the moderator from effort to gender with two levels, female and male. The order matters for the legend, here female is on top.

We confirm that the standard error of the interaction coefficient 1. Plot the same interaction using ggplot by following the instructions for the continuous by continuous interaction.

The resulting plot should look like the figure below. Notice the large overlap of the confidence intervals between males and females. 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. Here is the exhaustive list of all membership categories using just jogging and swimming dummy codes:. We are now ready to set up the interaction of two categorical variables. Including the product terms and the lower order terms in our model we have:.

Before fitting this model in R, we have to make sure we tell R which category to make the reference or omitted group. R does not distinguish between a binary and categorical variable with more than two categories. Therefore, re-leveling Gender and re-leveling Exercise just requires one step.

There are two interaction terms, one for male by jogging and the other for male by swimming, and both of them are significant. The last two coefficients are the most difficult to interpret. Quiz: Use the coefficients from the categorical by categorical interaction to derive the fe male female — male effect for the swimming group.

Hint: flip the sign of the coefficient. Although the coefficients in the categorical by categorical regression model are a bit difficult to interpret, it is surprisingly easy to obtain predicted values from a software package like emmeans.

Publications

These are the predicted values of weight loss for all combinations of Gender and Exercise. For example, females in the reading program have an estimated weight gain of 3. Try to reproduce each predicted value from emcatcat using the summary 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 contrast function as part of emmeans. Since we previously stored our emmeans object in emcatcat , we can call it back and pass it as a parameter into the contrast function. We use "revpairwise" rather than "pairwise" because by default the reference group female would come first.

Finally we request no adjustment to the p -value. In practice however, it may be advisable to correct for multiple comparisons to guard against Type I error the probability of making a false rejection of the null hypothesis , or false positives.

1. Background.
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7. Decomposing, Probing, and Plotting Interactions in R.

If you do not specify anything, Tukey is the default, and the end of the output would show the following which varies depending on the number of estimates in your model:. Going back to the output from the contrast statement, we see that the male effect for jogging and swimming are significant at the 0.