WEBVTT Kind: captions Language: en 00:00:00.544 --> 00:00:04.204 Interaction models allow us to  study the effect of a third variable 00:00:04.204 --> 00:00:07.264 on the strength of the relationship  between two other variables. 00:00:07.689 --> 00:00:13.068 Or alternatively nonlinear effects  of one variable on another, 00:00:13.068 --> 00:00:15.528 where the effect first goes up and then goes down, 00:00:15.528 --> 00:00:16.733 or vice versa. 00:00:17.143 --> 00:00:19.050 So why are this kind of models interesting? 00:00:19.050 --> 00:00:22.770 This is the normal way of  drawing a moderation model. 00:00:22.952 --> 00:00:25.142 And we have the M here, 00:00:25.142 --> 00:00:28.623 which influences the strength of  the relationship between X and Y. 00:00:28.957 --> 00:00:31.950 And this kind of model allows us to 00:00:31.950 --> 00:00:33.090 answer the question 00:00:33.090 --> 00:00:36.090 under which conditions the  effect of X and Y works, 00:00:36.090 --> 00:00:37.890 and under which conditions it does not. 00:00:37.890 --> 00:00:42.420 So let's say X is the amount of  weights that you lift through the week, 00:00:42.420 --> 00:00:44.416 how many times a week you go to the gym, 00:00:44.492 --> 00:00:46.472 and Y is your weight gain, 00:00:46.472 --> 00:00:48.212 so how much muscle mass you gain. 00:00:48.531 --> 00:00:52.129 That relationship could be moderated  by the amount of food that you eat. 00:00:52.175 --> 00:00:55.535 If you eat a lot while at the  same time going to the gym, 00:00:55.550 --> 00:00:57.230 then you will gain muscle mass. 00:00:57.473 --> 00:01:00.783 If you go to a gym a lot and you don't eat much, 00:01:00.783 --> 00:01:02.538 then there is no muscle gain. 00:01:02.538 --> 00:01:03.545 So you need both, 00:01:03.545 --> 00:01:08.165 and the effect of one variable depends  on the presence of another variable, 00:01:08.302 --> 00:01:09.707 on the third variable. 00:01:10.224 --> 00:01:14.460 So these models allow us to  study the effects of context 00:01:14.460 --> 00:01:19.429 and the effects of two variables  influencing the dependent variable together. 00:01:20.067 --> 00:01:23.970 Moderation models come in two typical variants 00:01:24.684 --> 00:01:27.720 that are both presented in the Deephouse's  paper and in the Hekman's paper. 00:01:27.720 --> 00:01:29.405 Let's start with the Hekman paper. 00:01:29.542 --> 00:01:33.185 So the Hekman paper has a pretty  traditional moderation hypothesis. 00:01:33.185 --> 00:01:36.870 They're saying that the relationship  between customer performance, 00:01:36.870 --> 00:01:38.370 sorry, the provider performance, 00:01:38.370 --> 00:01:46.920 and customer satisfaction  depends on the provider's race. 00:01:47.452 --> 00:01:52.620 So for example minorities are rewarded  less for their good performance, 00:01:52.620 --> 00:01:56.280 than whites, in this particular scenario. 00:01:56.280 --> 00:01:59.640 So that's the traditional  case of moderation effect, 00:01:59.640 --> 00:02:02.400 you have a third variable, called the moderator, 00:02:02.400 --> 00:02:05.340 which influences the relationship  between these two variables. 00:02:05.933 --> 00:02:10.140 Then we also have this another  type of interaction effect, 00:02:10.140 --> 00:02:12.422 called a U-shaped effect. 00:02:12.860 --> 00:02:16.730 And Deephouse says that there's a  curvilinear concave down relationship, 00:02:16.730 --> 00:02:21.100 which basically means that the  effect of strategic deviation on ROA 00:02:21.100 --> 00:02:22.359 is first positive, 00:02:22.359 --> 00:02:24.470 but once you get too deviant, 00:02:24.470 --> 00:02:26.570 then it starts to go down, so it's negative. 00:02:26.570 --> 00:02:29.960 So it's positive first then it turns negative, 00:02:29.960 --> 00:02:32.750 so it looks like a U, that is drawn upside down. 00:02:33.343 --> 00:02:36.743 Why this is an interaction effect is because 00:02:36.865 --> 00:02:41.635 the effect of strategic deviation  on ROA depends on itself, 00:02:41.635 --> 00:02:43.929 so that initially it's positive, 00:02:43.929 --> 00:02:46.794 but when strategic deviation value increases, 00:02:46.794 --> 00:02:49.103 then this relationship turns negative. 00:02:49.103 --> 00:02:53.210 So that's a way of making U-shaped effects using interactions. 00:02:54.714 --> 00:02:57.620 A typical way of drawing  these models is to draw boxes 00:02:57.620 --> 00:02:58.960 and then you have an arrow, 00:02:58.960 --> 00:03:01.074 which presents a causal relationship, 00:03:01.363 --> 00:03:03.013 or a regression relationship, 00:03:03.013 --> 00:03:06.650 and then you have these arrows from the third box, 00:03:06.650 --> 00:03:08.814 that go to the middle of this arrow. 00:03:09.133 --> 00:03:11.540 And this particular paper studies 00:03:11.540 --> 00:03:15.000 the effect of service provider  performance on rating, 00:03:15.000 --> 00:03:19.030 and then there is a customer gender/racial bias, 00:03:19.030 --> 00:03:22.250 that acts as a moderator for this relationship. 00:03:22.250 --> 00:03:25.190 So the strength of these relationships depends on 00:03:25.190 --> 00:03:29.240 the customers' possible bias  against the service provider. 00:03:31.367 --> 00:03:34.720 How we estimate these kinds of models 00:03:34.720 --> 00:03:38.450 can be understood by writing  the model in this kind of form. 00:03:38.450 --> 00:03:44.349 So we're saying here that the effect  of X has some base value beta1, 00:03:44.471 --> 00:03:47.381 and then it depends also on the value of M, 00:03:47.381 --> 00:03:50.033 so it's beta1 + beta2m. 00:03:50.185 --> 00:03:52.045 If beta 2 is a large number, 00:03:52.045 --> 00:03:56.720 then it means that the M has  a strong moderating effect, 00:03:56.720 --> 00:03:59.180 if it's a value that is close to zero, 00:03:59.180 --> 00:04:00.980 then there is no moderation effect. 00:04:02.300 --> 00:04:05.660 We can't estimate that kind of model  directly in the regression analysis, 00:04:05.660 --> 00:04:08.240 but if you write it differently then we can. 00:04:08.240 --> 00:04:11.725 So we can rewrite it without the parentheses, 00:04:11.893 --> 00:04:17.753 and it becomes beta0 + beta1x + beta2mx + beta3m. 00:04:17.935 --> 00:04:25.580 So the idea of, how we estimate these  kinds of moderation models is that, 00:04:25.580 --> 00:04:29.781 we multiply the moderator and the  interesting variable together, 00:04:29.781 --> 00:04:33.120 and then we add all two  variables and their product 00:04:33.120 --> 00:04:36.693 as independent variables  to the regression analysis. 00:04:37.301 --> 00:04:44.478 Here this equation shows that the  effect of X on Y is no longer constant. 00:04:44.675 --> 00:04:46.590 So it's not a constant effect, 00:04:46.590 --> 00:04:48.798 like we had in a regression analysis, 00:04:48.889 --> 00:04:51.079 because it depends on the value of M. 00:04:51.079 --> 00:04:54.900 And to understand, how we interpret these effects 00:04:54.900 --> 00:04:57.750 that is not constant but  depend on another variable, 00:04:57.750 --> 00:05:00.420 we need to introduce the  concept of marginal effect. 00:05:00.420 --> 00:05:07.920 So the marginal effect is the idea that  the effect of one variable on another 00:05:07.920 --> 00:05:10.950 depends on other variables, 00:05:10.950 --> 00:05:15.600 and it's constant at a certain point  but it can vary between points. 00:05:15.949 --> 00:05:19.260 So let's take a look at  regression analysis example. 00:05:19.260 --> 00:05:22.341 So normal regression analysis gives you a line, 00:05:22.508 --> 00:05:25.088 and the marginal effect is, 00:05:25.088 --> 00:05:29.190 how much Y changes, when X changes a little. 00:05:29.190 --> 00:05:32.670 So it's a derivative or a tangent for this line. 00:05:33.000 --> 00:05:34.890 And because this is a line, 00:05:34.890 --> 00:05:38.970 the derivative or the direction  of the line is always constant. 00:05:39.365 --> 00:05:43.948 And the marginal effect is a line. 00:05:44.632 --> 00:05:46.512 So marginal effect is, 00:05:46.512 --> 00:05:51.000 how much Y changes when X changes a little, 00:05:51.000 --> 00:05:54.088 or a very small amount at a particular point. 00:05:54.817 --> 00:05:57.686 When we have nonlinear effects, 00:05:57.792 --> 00:06:01.032 for example a log-transformed dependent variable, 00:06:01.032 --> 00:06:04.052 then the marginal effect is no longer constant. 00:06:04.052 --> 00:06:07.562 We can see here that the direction  of the line is different, 00:06:07.562 --> 00:06:12.430 it goes up but less strongly as it goes here. 00:06:12.430 --> 00:06:15.220 So the regression line here, if we draw it here, 00:06:15.220 --> 00:06:18.040 then it's much steeper than here. 00:06:18.040 --> 00:06:22.741 So the marginal effect for  nonlinear effects depends on, 00:06:22.833 --> 00:06:25.210 which part of the curve we are looking at. 00:06:25.529 --> 00:06:27.970 And typically when we do interactions, 00:06:27.970 --> 00:06:30.790 we are interested in interpreting  the marginal effects.