# Multiple regression testing and interpreting interactions pdf aiken

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- Multiple Regression: Testing and Interpreting Interactions
- Leona S. Aiken
- Decomposing, Probing, and Plotting Interactions in Stata
- Understating and Overstating Interaction Results in International Business Research

*Because the book is always talking about people.*

## Multiple Regression: Testing and Interpreting Interactions

This seminar will show you how to decompose , probe, and plot two-way interactions in linear regression using the margins command in Stata. We can probe or decompose each of these interactions by asking the following research questions:.

Proceed through the seminar in order or click on the hyperlinks below to go to a particular section:. Before beginning the seminar, please make sure you have Stata installed. The dataset used in the seminar can be found here as a Stata file exercise. You can also import the data directly into Stata via the URL using the following code:.

Suppose you are doing a simple study on weight loss and notice that people who spend more time exercising lose more weight. Upon further analysis you notice that those who spend the same amount of time exercising lose more weight if they are more effortful. The more effort people put into their workouts, the less time they need to spend exercising. This is popular in workouts like high intensity interval training HIIT. You know that hours spent exercising improves weight loss, but how does it interact with effort?

Here are three questions you can ask based on hypothetical scenarios. Additionally, we can visualize the interaction to help us understand these relationships. This is a hypothetical study of weight loss for participants in a year-long study of 3 different exercise programs, a jogging program, a swimming program, and a reading program which serves as a control activity.

Variables include. What exactly do I mean by decomposing , probing , and plotting an interaction? For a more thorough explanation of multiple regression look at Section 1. For example, suppose we want to know the predicted weight loss after putting in two hours of exercise. We fit the main effects model,. Using the command regress , we specify the following syntax where the dependent variable comes before the independent variables:. The predicted weight loss is This is an example that we can work by hand, but we can also ask margins to help us.

The margins command introduced in Stata 11 is a post-estimation command to obtain marginal means, predicted values and simple slopes. Post-estimation means that you must run a type of linear model before running margins by first running the regress command. In our example, we are requesting predicted values using the at option.

In Stata, command options follow after a comma. We get a predicted value of Losing 10 pounds of weight for 2 hours of exercise seems a little unrealistic. Maybe this study was conducted on the moon.

Now that we understand predicted values how do you obtain a slope? Well a slope is defined as. Going back to our original equation,. In our case, for a one hour increase in time put in, we achieve 2. We obtain 2. However, instead of using the at option, we use the option dydx which stands for the partial derivative. Without going into calculus, you can think of the partial derivative in this case as the slope of hours. We are telling margins to calculate the partial derivative or the slope for the variable Hours.

Since this is a main effect or slope , the slope does not vary as we vary the value of hours. In the Continuous by Continuous section, we will see how the slope can change in the presence of an interaction. Quiz: True or False In the margins command, the option dydx is used to estimate predicted values and at is used to estimate simple slopes. How do the results compare with dydx? Visualizing is always a good thing.

The command marginsplot allows us to easily plot this. Note that marginsplot must always follow margins. First, decide a range of values of Hours so that we have enough points on the x-axis to create a line. Recall that to obtain predicted values of Weight Loss at specific Hours we need the at option.

Follow this code by marginsplot to generate the graph; Stata automatically knows to put Hours on the x-axis and Weight Loss on the y-axis. The plot look like the following, and can be interpreted as for every one unit increase in Hours, there is a 2.

In the next section we will discuss how to estimate and interpret slopes that vary with levels of another variable i. We know that amount of exercise is positively related with weight loss.

Given the recent news about the efficacy of high intensity interval training HIIT , perhaps we can achieve the same weight loss goals in a shorter time interval if we increase our exercise intensity. The model to address the research question is. Two things to note. Here we have two continuous variables, so we specify c. Second, the between the two variables specifies a two way interaction and is equivalent to adding the lower order terms to the interaction term specified by a single.

Although we may think that the slope of Hours should be positive at levels of Effort, remember that in this case, Effort is zero. As we see in our data, this is improbable as the minimum value of effort is Suppose we want to find the predicted weight loss given two hours of exercise and an effort of As before, use the at option after margins to specify 2 for Hours and 30 for Effort:.

The results show that predicted weight loss is This is demonstration of the fact that we are extrapolating, which means we are making predictions about our data beyond what the data can support.

This is why we should always choose reasonable values of our predictors in order to interpret our data properly. Extrapolation then becomes a non-issue. We know to choose reasonable values when predicting values. The same concept applies when decomposing an interaction. Our output suggests that Hours varies by levels of Effort. Since effort is continuous, we can choose an infinite set of values with which to fix effort.

For ease of presentation, some researchers pick three representative values of Effort with which to estimate the slope of Hours. Traditional spotlight analysis was made for a continuous by categorical variable but we will borrow the same concept here. What three values should we choose? Aiken and West recommend plotting three lines for Hours, one at the mean level of Effort, a second at one standard deviation about the mean level of Effort, and finally a third at one standard deviation below the mean level of effort.

In symbols, we have. In Stata, we can use summarize to store the mean and standard deviation of effort into a list. The command return then invokes invoke the objects in the list,. The object r mean gives us the mean and r sd gives us the standard deviation. We can then store these values into what is known as a global variable , which allows the user to recall the value of that variable for future use.

For ease of presentation in the plot we will create later, the function round x,0. The mean of effort is about A quick way to check the values of one standard deviation above and one standard deviation below is to make sure that the former The command display allows us to view the values of the newly created global variables. First, we need to specify three values of effort we found above in preparation for spotlight analysis using the at option.

The margins command is a post-estimation command that follows regress loss c. Note that our global and return commands do not interfere with regress because only the latter is an estimation command. Looking at the output, we get three separate simple slopes for hours. As we increase levels of Effort, the relationship of hours on weight loss seems to increase. If it the interval contains zero, then the simple slope is not significant.

Here it seems that the simple slope of Hours is significant only for mean Effort levels and above. For the x-axis, we need to create a sequence of values to span a reasonable range of Hours, but we need only three values of Effort for spotlight analysis.

First, use that at option to create a sequence of Hours values from 0 to 4, incremented by 1 and Effort is assigned one standard deviation below the mean, at the mean and one standard deviation above the mean.

The code and output is listed below. We advise checking the margins output to confirm whether you specified the list correctly. Then we can follow margins with marginsplot.

Stata knows to plot Hours on the x-axis and separate lines by Effort because of the order by which we specified the at option. The results suggest that hours spent exercising is only effective for weight loss if we put in more effort, which supports the rationale for high intensity interval training.

At the highest levels of Effort, we achieve higher weight loss for a given time input. In case you prefer confidence bands over confidence bars, you can modify the marginsplot code using the option recast.

The option and sub-option recast line draws the predicted regression line but removes the points associated with each value on the x-axis. This allows us to draw a continuous line which will look more aesthetically pleasing when we overlay the confidence band.

Note that transparency is available to Stata 15 or higher.

## Leona S. Aiken

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PDF DESIGNING TESTING AND. INTERPRETING INTERACTIONS. AIKEN L S AND WEST S G MULTIPLE. REGRESSION. MULTIPLE REGRESSION.

## Decomposing, Probing, and Plotting Interactions in Stata

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*Multiple regression is a commonly used analytic method in the behavioral, educational, and social sciences because it provides a way to model a quantitative outcome variable from regressor variables. Unable to display preview.*

### Understating and Overstating Interaction Results in International Business Research

Abstract Schadenfreude is a compound word of the word Schaden, which means loss, and Freude, which means joy. It shows that envy plays an important role in generating Schadenfreude; People are pleased with the misfortune of others when this misfortune gives them a social comparison that increases the feeling of their selfesteem or removes the basic feelingof hurtful jealousy. This research method isexperiments with factorial design. The Sampling techniques uses RandomSampling. Analysis techniques are used with the correlation technique of PearsonProduct moment. The results of this study complement these opposing findings, indicating that envy is the Schadenfreude predictor when the target has the same gender. This research was conducted at one of the universities in Salatiga.

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Aiken and Stephen G. West do an excellent job of structuring, testing, and interpreting multiple regression models containing interactions, curvilinear effects, or a.

#### At the library

This seminar will show you how to decompose , probe, and plot two-way interactions in linear regression using the margins command in Stata. We can probe or decompose each of these interactions by asking the following research questions:. Proceed through the seminar in order or click on the hyperlinks below to go to a particular section:. Before beginning the seminar, please make sure you have Stata installed. The dataset used in the seminar can be found here as a Stata file exercise. You can also import the data directly into Stata via the URL using the following code:.