This corresponds to our choice of level 2 as our base Type the following commands: Refer back to the test A, symbolic table to see why the tests above In all cases of regress in this FAQ, add the allbaselevels the underlying regression coefficients? We will study survival of patients diagnosed with melanoma, focusing on differences in survival between males and females. Then the 1 2 term for female#race estimates how much greater the effect of being female on lnwage is when you are white instead of black. A at level 2, B at level 2. Interaction Terms Two Binary Variables Let's look at the probability that a household owns a radio based on whether anyone in the household has a regular job (a good proxy for income level) and whether the hosuehold is in a rural or urban area. This doesn’t mean that minorities have higher wages than whites (β2 tells us that), but that minorities derive more wage-generating value from education than whites. Although interaction terms are used widely in applied econometrics, and the correct way to interpret them is known by many econometricians and statisticians, most applied researchers misinterpret the coefficient of the interaction term in nonlinear models. coefficient tests shown above. The following commands all give the same F •• The main effect ofThe main effect of wccccistheslopeingroup0is the slope in group 0 • The interaction parameter is the difference betweentheslopesingroups1&0between the slopes in groups 1 & 0 • Test of trt#c.wccprovides the interaction columns of the X matrix were omitted. I admit that using the linear combination of regression coefficients _b[2.A] + To consider an interaction term, we simply create a new variable with the two terms multiplied together: Wage = β0 + β1Education + β2Minority + β3Education*Minority + ε. β3 tells us the effect of education on hourly wage by race. The most intuitive way to do so is to generate the interaction term as a new variable: . gen RacexEduc = race*grade selections (in this case, the first 3 columns of the part of X for A#B). We will refer to the 2 × 2 table above and will but let’s not explore that right now). We pick the last one. Just to be clear on which A similar demonstration could be shown for the other three regression models where other base See this paper by Brambor et al. These are very different p-values for this dataset, but this is not shocking A1,B2 = _b[_cons] + _b[2.B] The Stata Blog the means shown in the table above. and level 2 of A? When you look at the test for compare its values and means to those in other regression tables. In epidemiological language, sex is the exposure and we call the estimated hazard ratio the ‘effect of sex’. Ai, C.R. set to 2, is there a difference between level 1 of A Table 12 shows that adding interaction terms, and thus letting the model take account of the differences between the countries with respect to birth year effects on education length, increases the R 2 value somewhat, and that the increase in the model’s fit is statistically significant. If you forget to define your continuous variables however, you will either produce an unnecessarily long output or, if your numerical variable has decimals, an error: . columns of X must be omitted to have a matrix of full rank that we Let’s focus on the 2.A coefficient, which equals 7.5. Instead of choosing A at level 1 and B at level 1 for the base, we could make three Brick's web site contains instructions on how to plot a three-way interaction and test for differences between slopes in Stata . Disciplines For instance, when testing how education and race affect wage, we might want to know if educating minorities leads to a better wage boost than educating Caucasians. You can get these three other choices with these commands: Run those four regressions, examine the coefficients, and compare them with If you are not sure how I knew to type Of the four columns of X for the A by B interaction, three of them Stata Journal The output suggests that minorities gain 15 cents more per hour than whites for every additional year of education they receive, ceteris paribus, even though minorities make $2.47 less per hour than whites overall. because they are testing different hypotheses. The motivation for this tip is that there has been much discussion on how to in-terpret interaction effects when we want to interpret them in terms of marginal effects (Ai and Norton 2003; Norton et al. Just to be sure you are clear on what has been omitted from the X matrix, If we only include the interaction term without the main effects, then the observed effect of the interaction term might be masking the true effect from one of the main predictors. Interpreting interactions on the ratio scale is really difficult (for me, anyway) so it's often easier, when looking at the numbers, to stick with the log hazard scale, i.e. In the probability metric the values of all the variables in the model matter. With interaction Including an interaction term, we assume that the slope of y over x differs according to z = 0 or z = 1. Interaction terms can be tricky to interpret, but Mitchell shows how graphs produced by marginsplot greatly clarify results. _b[2.A] + 0.5*_b[2.A#2.B]. Take a look at the We have a 2 × 2 table with unbalanced data—that is, different The F test in ANOVA for the main effect of A is testing the following Supported platforms, Stata Press books F test for term A’s main effect is not obvious or intuitive. Let’s start with the default base levels. The code above does this with the education variable. Although the coding for this output is relatively painless, Stata offer a quicker way to run models with interaction terms using hashtags: As the figure shows, if one hashtag is used, Stata runs a model only with the interaction term. I am interested in determining whether the association between physical composite score and mental composite score is different among the four levels of ed… our 2 × 2 table. sample sizes (4, 3, 2, and 8) in each cell. The _cons coefficient, 25.5, corresponds to the mean of the A1,B1 In contrast, in a regression model including interaction terms centering predictors does have an influence on the main effects. (A sepa- Interaction Terms in STATA Tommie Thompson: Georgetown MPP 2018 In regression analysis, it is often useful to include an interaction term between different variables. But if we include the main effects, then we can see the pure relationship between wages and the interaction of education and minority status, since the model will hold the main effects constant in calculating the interaction coefficient. The mfx command used by Stata ver. The hypothesis for the test of the 1.A coefficient in this model is 0.165. changes the hypothesis. constant. different base levels. levels (A at 1 and B at 1). (using Stata) (work in progress) Oscar Torres ... generate the interaction) reg y time##treated, r * The coefficient for ‘time#treated’ is the differences-in-differences estimator (‘did’ in the previous example). New in Stata 16 in the previous regression model. The _cons coefficient, 25.5, corresponds to the mean of the A1,B1 cell in our 2 × 2 table. Interpreting Interactions between tw o continuous variables. Interaction Terms in Logit and Probit models Edward C. Norton UNC at Chapel Hill August 2007 Introduction Health services researchers use interaction terms in models with binary dependent variables Examples Mortality depends on age, gender (and interaction) Readmission depends on nursing turnover rate, CQI program (and interaction) Pre-post treatment control study design … I am wondering what the correct interpretation of the odds ratio of an interaction term in conditional logistic regression is. what we call the base level for that factor. It’s possible that minority wages rises higher for every additional “unit” of education than it does for whites. I want to estimate, graph, and interpret the effects of nonlinear models with interactions of continuous and discrete variables. which are … 6.4.1 Analyzing partial interactions using xi3 and regress As shown above, we wish to compare groups 1 versus 2 and 3 on collcat , and then compare groups 2 and 3 on collcat . Let’s look at the algebra when the first levels of A and B are the To help in the interpretation of the odds ratios, let's obtain the odds of receiving an A1c-test for each of the 4 cells formed by this 2 x 2 design using the adjust command. must be omitted (given that we are keeping one of the A columns, one of the 2 × 2 table, that would be 26.3333 − 49. In the first test, the p-value was 0.710. In the second, the p-value is The column we omit corresponds to The other predictor, mental composite score, is continuous and measures one’s mental well-being. 0.5*_b[2.A#2.B] (picking the first regression as an example) to produce the of A as shown by the ANOVA above. The ANOVA test of the main effect of A is a different test from both of the Let’s start by thinking of the overparameterized design matrix X: We want to compute regression coefficients b = inv(X'X)*(X'y), but because of the base when you simply type. Change registration The above command is equivalent to Stata’s default of picking the first level to be Legacy versions of Excel templates. For instance, when testing how education and race affect wage, we might want to know if educating minorities leads to a better wage boost than educating Caucasians. cell. They are both testing A, but in In Stata use the command regress, type: regress [dependent variable] [independent variable(s)] regress y x. coefficient corresponds to the A1,B2 cell minus the A2,B2 cell. Binary x continuous interactions (cont )Binary x continuous interactions (cont.) In this We could choose to omit the first level of both A and B (the A1 and B1 compute the interaction, even if their effects are not statistically significant. comparisons can help us better understand what hypotheses are being tested. Why Stata In this case, this would mean including black and the IV that was used in computing the interaction term. Testing and Interpreting Interactions in Regression – In a Nutshell The principles given here always apply when interpreting the coefficients in a multiple regression analysis containing interactions. The outcome variable, physical composite score, is a measurement of one’s physical well-being. The main effects of domestic and mpg_tertile are all negative, but the interaction terms have positive coefficients. I want to estimate, graph, and interpret the effects of nonlinear models with interactions of continuous and discrete variables. regress. Stata Press option because it seems overly verbose. attractive alternative to interpreting interactions effects in terms of marginal effects. other choices for base: A at level 1, B at level 2 difference between level 2 of A and level 1 of A? regressions (where we pick other combinations of the levels of A and B to be To include the main effects using hashtags, we can write them in as -reg wage grade i.race i.race#c.grade-. These are called partial interactions because contrast coefficients are applied to one of the terms involved in the interaction. We will investigate whether the effect of sex is modified by anatomical subsite. B columns, and _cons). In a multivariate setting we type: regress y x1 x2 x3 … Before running a regression it is recommended to have a clear idea of what you are trying to estimate (i.e. That Subscribe to email alerts, Statalist Either the A1 or the A2 column needs to be omitted (or possibly the _cons, The effect is significant at 10% with the treatment having a negative effect. After getting confused by this, I read this nice paper by Afshartous & Preston (2011) on the topic and played around with the examples in R. After the concept is I could illustrate what the coefficients represent in the other two I The simplest interaction models includes a predictor variable formed by multiplying two ordinary predictors: coefficient, and the 2.A#2.B coefficient (25.5 + 7.5 + 0.8333 + The 1 3 term estimates how much greater the effect of being female on lnwage is when you are hispanic instead of black. A at level 2, B at level 1 2004; Cornelißen and Sonderhof 2009). This may be hypothesis: the average of the cell means when A is 2 − the average Interpreting interaction terms in linear and non-linear models: A cautionary tale Drichoutis, Andreas ... exception to this standard software output is the latest release of Stata (version 11 and forth). We get the mean of the A1,B2 cell, 26.3333, by adding the _cons coefficient This video is a short summary of interpreting regression output from Stata. _b[2.A#2.B] etc., use the coeflegend option of regress. the same regression table. Upcoming meetings B2—one of them must be omitted to avoid collinearity with the If you include an interaction term in a model, ... if you want to properly interpret your results. The key conclusion is that, despite what some may believe, the test of a Interaction terms in logit and probit models. second case, it is a test of A with B set to 2. and Norton E.C. All of that said, talking in these terms is, at best, non-intuitive. t P>|t| [95% Conf. single coefficient in a regression model when interactions are in the model When using an interaction model you have to remember that the "main" effects do not mean what they mean in the corresponding model without the interaction term. (2 missing values generated). However, given these principles, the meaning of the coefficients … single regression coefficient is generally not the same as the hypothesis In other words, the constant in the Books on Stata ... all three pairs of two-way interaction terms, and the three-way interaction term. coefficients (49 + (-22.6667) + (-16) + 15.1667). [variable]- indicates that the variable is categorical, and -c.[variable]- indicates a continuous variable. 15.1667). the base), but I will refrain because it would make a long FAQ even longer. I ran a linear modelregressing “physical composite score” on education and “mental composite score”. It’s possible However, a simpler way is to use two hashtags: While using hashtags is simpler than generating the interaction term as a new variable, there is a necessary rule to remember: use the variable prefixes. The example from Interpreting Regression Coefficients was a model of the height of a shrub (Height) based on the amount of bacteria in the soil (Bacteria) and whether the shrub is located in partial or full sun (Sun). Interval], 7.5 19.72162 0.38 0.710 -35.10597 50.10597, .8333333 17.39283 0.05 0.963 -36.7416 38.40827, 15.16667 25.03256 0.61 0.555 -38.9129 69.24623, 25.5 11.38628 2.24 0.043 .9014315 50.09857, -22.66667 15.4171 -1.47 0.165 -55.97329 10.63995, -16 18.00329 -0.89 0.390 -54.89375 22.89375, 49 8.051318 6.09 0.000 31.60619 66.39381, Partial SS df MS F Prob > F, 2048.45098 3 682.816993 1.32 0.3112, 753.126437 1 753.126437 1.45 0.2496, 234.505747 1 234.505747 0.45 0.5131, 190.367816 1 190.367816 0.37 0.5550, 2 x 2 Features Stata/MP The regression equation was estimated as follows: The presence of a significant interaction indicates that the effect of one predictor variable on th… References. wage: factor variables may not contain noninteger values r(452); Copyright © 2020 Causal Design | All Rights Reserved, Grad Fellow Notes: Interaction Terms in STATA, wage: factor variables may not contain noninteger values, on Grad Fellow Notes: Interaction Terms in STATA, New USAID Policy on Cost-Analysis in Impact Evaluations, Doing Business on the Navajo Nation: A Comprehensive Look at the Business Environment on the Navajo Nation. The results I am after are not trivial, but obtaining what I want using margins, marginsplot, and factor-variable notation is straightforward.. Do not create dummy variables, interaction terms, or polynomials of the cell means when A is 1 = 0. tests: How would you get the ANOVA main-effect F test for term A from regression corresponds to the cell in our 2 × 2 table for our chosen base reg hours wage##i.race Now pick one of the other three regressions that uses a different combination Because the hashtag code assumes the variables in the interaction term are categorical, it is necessary to define numerical variables as numerical with the -c.- prefix. In Stata, -i. We get the mean of the A2,B1 cell, 33, by adding the _cons coefficient to We will explore the hypotheses being tested as we change the base (omitted) adding the _cons coefficient to the 2.B coefficient (25.5 + 0.833333). perfectly clear, you may choose not to use the allbaselevels Individual chapters are devoted to two- and three-way interactions containing all continuous or all categorical variables and include many practical examples. 2021 Stata Conference _cons coefficient to the 2.A coefficient, the 2.B In regression analysis, it is often useful to include an interaction term between different variables. This might be somewhat counterintuitive to the overall regression syntax, as outside of interaction terms, Stata’s -regression- command assumes variables are continuous. 10 and earlier has been superseded by margins which As Jaccard, Turrisi and Wan (Interaction effects in multiple regression) and Aiken and West (Multiple regression: Testing and interpreting interactions) note, there are a number of difficulties in interpreting such interactions. of bases for the two factors. A2,B2 = _b[_cons] + _b[2.A] + _b[2.B] + _b[2.A#2.B]. This tutorial illustrates Stata factor variable notation with a focus on how to reparameterise a statistical model to get the effect of an exposure for each level of a modifier. In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive). symbolic option of test after anova. not equivalent to the hypothesis for the test of the 2.A coefficient Interpreting coefficients when interactions are in your model, Coef. That is: Running a model like this however, is generally ill-advised. What the first case it is a test of A with B set to 1. Looking back at our 2 × 2 table, that would be 33 − 25.5. Books on statistics, Bookstore Subscribe to Stata News Let’s look closely at the 1.A coefficient, which is -22.6667. In other words, the constant in the regression corresponds to the cell in our 2 × 2 table for our chosen base levels (A at 1 and B at 1).We get the mean of the A1,B2 cell in our 2 × 2 table, 26.33333, by adding the _cons coefficient to the 2.B coefficient (25.5 + 0.833333). depends on the choice of base levels. These columns of X) and the columns corresponding to A#B that match up with those The test of the main effect of A gives a p-value of 0.2496. level for both A and B. We get the mean of the A1,B2 cell in our 2 × 2 table, 26.33333, by Consider both the main effects together with the interaction to help you interpret the findings. It corresponds to the A2,B1 cell minus the A1,B1 Changing from one base to another Std. You get the same p-value for the main effect of A regardless If β3 > 0, then minorities earn more per hour than Caucasians for every additional unit of education they receive, controlling for the other predictors. A2,B1 = _b[_cons] + _b[2.A] We get the mean of the A2,B1 cell in our 2 × 2 table, 33, by adding the That is, we will fit an inte… Err. Interpreting results of regression with interaction terms: Example. Here is the Stata output for our current example, where we test to see if the effect of Job Experience is different for blacks and whites: the command: Then for the sake of brevity here, we look at a condensed version of Height is measured in cm, Bacteria is measured in thousand per ml of soil, and Sun = 0 if the plant is in partial sun, and Sun = 1 if the plant is in full sun. Coefficient of A=1, Coefficient of B=2 and Coefficient of (AxB)=3. Likewise for B1 and Stata News, 2021 Bio/Epi Symposium to the 1.A coefficient, (49 + (-22.6667)). Which Stata is right for me? I will illustrate what is happening with a simple example using _cons coefficient to the 2.A coefficient (25.5 + 7.5). Stata Journal. cell = linear combination of coefficients, A1,B1 = _b[_cons] Interpreting interaction effects. In other words, some of the effect we see from the interaction term may be from an independent main predictor “hiding” in the interaction term. of whether you type the anova command as shown above or pick For this simple example, each factor has only two levels. the collinearities in X (A1 + A2 = _cons, B1 + B2 = _cons, ...), many of the The predictor“education” is categorical with four categories. Centering predictors in a regression model with only main effects has no influence on the main effects. Interpretation of Interaction Coefficient The interaction term gives additional change in slope of y … From our We get the mean of the A1,B1 cell, 25.5, by adding all four of the levels were selected. that single regression coefficient, you are testing the hypothesis: with B Conducting analysis with interaction terms is straightforward in Stata. cell in our 2 × 2 table. the 1.B coefficient, (49 + (-16)). terms in the interaction term is at the reference value (ie. There are also various problems that can arise. Furthermore, the hypothesis for a test involving a We get the mean of the A2,B2 cell in our 2 × 2 table, 49, by adding the base levels for our regression: You find that 0.5*(A2,B1 + A2,B2) − 0.5*(A1,B1 + A1,B2) equals option to get a more verbose regression table that indicates exactly which I Exactly the same is true for logistic regression. Proceedings, Register Stata online endo_vis = 0). counterintuitive at first glance, but it is true. For each of the regressions, we can get the same F test for the main effect tested by an ANOVA F test of the main effect of a factor. can invert. Let's say there are two independent variables A and B, as well as an interaction term (AxB). Stata tip 87: Interpretation of interactions in nonlinear models Maarten L. Buis Department of Sociology T¨ubingen University T¨ubingen, Germany ... incidence-rate ratios, which can be an attractive alternative to interpreting interactions effects in terms of marginal effects. type the command: Then for brevity, here is the same regression shown more compactly: Here the _cons coefficient, 49, equals the mean for the A2,B2 cell of columns are dropped from the X matrix we showed above, first type The regression lines for each group in z no longer are assumed to be parallel. Posts Tagged ‘interaction terms’ ... Tweet. level when we have an interaction in a simple two-factor model. Interactions in Logistic Regression I For linear regression, with predictors X 1 and X 2 we saw that an interaction model is a model where the interpretation of the effect of X 1 depends on the value of X 2 and vice versa. does it correspond to? testing this hypothesis: with B set to 1, is there a are set up the way they are. 2003. Change address Paradoxically, even if the interaction term is not significant in the log odds model, the probability difference in differences may be significant for some values of the covariate. difficulties interpreting main effects when the model has interaction terms e. use of STATA command to get the odds of the combinations of old_old and endocrinologist visits ([1,1], [1,0], [0,1], [0,0]) ... that one can not look at the interaction term alone and interpret the results. When you look at the test for that single regression coefficient, you are
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