WEBVTT 00:00:00.400 --> 00:00:04.000 Moderation and mediation are  concepts that are associated   00:00:04.800 --> 00:00:07.680 with the relationship of three variables. 00:00:07.680 --> 00:00:11.840 These concepts are very common in  empirical research in management. 00:00:11.840 --> 00:00:16.240 And moderation and mediation models are  typically estimated using regression analysis. 00:00:16.800 --> 00:00:19.040 Let's take a look at what  moderation and mediation are. 00:00:19.680 --> 00:00:23.360 Mediation basically refers to a scenario,   00:00:23.360 --> 00:00:29.680 where the effect of one variable x on another variable y goes through a third variable m. 00:00:29.680 --> 00:00:34.240 So we are saying that the  effect of x is mediated by y,   00:00:34.240 --> 00:00:37.920 so the causality goes from x to m, from m to y. 00:00:37.920 --> 00:00:44.400 For example studying causes learning, learning causes increased performance on the final exam. 00:00:45.520 --> 00:00:51.760 So mediation is about mechanisms, and Singleton & Straits use the term intervening variables,   00:00:51.760 --> 00:00:53.840 so it's a variable that sits in the middle. 00:00:54.560 --> 00:01:02.800 If x does not cause, if x causes m, and  m causes y, then if for some reason the  00:01:02.800 --> 00:01:07.600 level of m would not change even if  you change x, then y would not occur. 00:01:07.600 --> 00:01:13.520 For example, if you study but you don't  learn, then you can't expect to perform well. 00:01:13.520 --> 00:01:18.480 So studying must lead to learning, learning  leads to performing well on the exam. 00:01:19.280 --> 00:01:23.200 Moderation, on the other hand,  refers to a scenario, where a   00:01:23.200 --> 00:01:27.360 third variable determines the strength  of association between two variables. 00:01:28.160 --> 00:01:36.560 For example if x is the amount of weight training that you do, and y is the amount of gains that   00:01:36.560 --> 00:01:41.760 you have in muscle mass, then the mediator could be the amount of eating that you do. 00:01:41.760 --> 00:01:45.600 If you train and you eat a lot,  you gain muscle, if you train   00:01:45.600 --> 00:01:50.400 equally much but you don't eat as much,  then your muscle gains will not be as large. 00:01:50.960 --> 00:01:56.160 So moderation models are  useful for studying contexts. 00:01:56.160 --> 00:02:01.840 So we can do these moderation models to  understand, under which conditions something   00:02:01.840 --> 00:02:07.840 happens, and also, what determines the strength of effects, are there any contextual factors. 00:02:08.800 --> 00:02:13.760 Let's take a look at how these are estimated in the context of regression analysis. 00:02:14.480 --> 00:02:20.960 So our first example is Hekman's paper,  and Hekman is studying a moderation model. 00:02:20.960 --> 00:02:26.320 So moderation model, this is one  moderation effect, their hypothesis 3a. 00:02:26.960 --> 00:02:32.320 They are saying that because of  customer racial or gender bias,   00:02:32.960 --> 00:02:39.920 women or minorities are rewarded less  for performance, than white men. 00:02:40.480 --> 00:02:47.360 So the effect of service provider performance is assumed to be positive on rating of employees, but   00:02:47.360 --> 00:02:54.560 that positive relationship is assumed to be less for women and minorities compared to white men. 00:02:54.560 --> 00:02:55.920 So this is moderation. 00:02:55.920 --> 00:02:59.440 And how do we do moderation  in regression analysis? 00:02:59.440 --> 00:03:03.360 So the idea of moderation was, that  the regression coefficient of x   00:03:03.360 --> 00:03:06.400 beta 1 here depends on the value of m. 00:03:06.400 --> 00:03:11.120 So we can say that the regression  coefficient beta 1 is actually a function of   00:03:11.120 --> 00:03:13.920 'beta m1, beta m2 multiplied by m'. 00:03:13.920 --> 00:03:17.840 So it depends on m, it's not the constant  value that is same for everybody. 00:03:18.720 --> 00:03:24.640 We can do a little bit of math, and we plug  in the second equation in place of beta1. 00:03:25.360 --> 00:03:30.240 We get that kind of equation, and we  simplify it a bit by eliminating the   00:03:30.240 --> 00:03:36.880 parentheses and we can see that moderation can be studied by doing these interaction models. 00:03:36.880 --> 00:03:40.240 So interaction refers to  multiplying two things together. 00:03:40.240 --> 00:03:47.040 So we have x the main interesting variable  here quality, m the moderator here gender   00:03:47.040 --> 00:03:54.480 or minority race as the moderator, we multiply them together, and then we can see if the race 00:03:54.480 --> 00:04:01.760 or gender has an effect on how well, how much the person is rewarded for being high quality doctor. 00:04:02.720 --> 00:04:05.280 And here are the interaction terms, we can see 00:04:05.840 --> 00:04:11.280 in the Model 2 that female are  rewarded less for being high quality. 00:04:11.840 --> 00:04:19.280 So the overall effect of quality is positive,  but women are rewarded less than men. 00:04:19.280 --> 00:04:21.680 So this is how the table would be interpreted. 00:04:22.320 --> 00:04:28.320 In practice, interpreting the magnitude  of these effects is difficult because   00:04:28.320 --> 00:04:31.680 they are interactions, so  people will do plottings. 00:04:31.680 --> 00:04:35.040 In Hekman's paper, they have these four plots. 00:04:35.040 --> 00:04:38.320 So they show that, this is how  the regression lines would go,   00:04:38.320 --> 00:04:42.960 this is the line for male, this is for female,  this is for white, this is for non-whites. 00:04:43.840 --> 00:04:50.240 And they found something really interesting, they found that actually if you are non-white   00:04:50.240 --> 00:04:53.760 then, if you get better, you get more productive,   00:04:53.760 --> 00:04:56.880 then you are actually penalized in  the customer satisfaction scores. 00:04:57.600 --> 00:05:01.200 They explained that in the paper  and that is an unexpected finding. 00:05:02.240 --> 00:05:06.000 I'm 100 % sure that this is  actually just an analysis error. 00:05:06.720 --> 00:05:11.440 What actually is this, what kind of error  it is, it's beyond the scope of this   00:05:12.720 --> 00:05:20.960 video, but basically the right results would  be that all the lines go up, but the slope,   00:05:20.960 --> 00:05:27.520 or how steeply the line goes up for women and minorities is less than it goes up for men. 00:05:28.160 --> 00:05:30.960 So this is moderation. 00:05:30.960 --> 00:05:34.080 Let's take a look at mediation, and in  our example article Barron and Tang. 00:05:34.800 --> 00:05:39.120 They have a hypothesis or multiple  hypothesis, one of them is hypothesis 3   00:05:39.120 --> 00:05:44.960 and then hypothesis 3a is simply a  more precise variant of hypothesis 3. 00:05:44.960 --> 00:05:48.160 So they're basically saying that  entrepreneurs with good social skills   00:05:48.880 --> 00:05:52.800 are better at gathering essential resources. 00:05:53.440 --> 00:05:58.960 And if you have more essential resources then that allows your venture to perform better. 00:05:58.960 --> 00:06:06.160 So there is the mechanism, through which social skills allow an entrepreneur to venture,   00:06:06.160 --> 00:06:11.360 to perform better, is that social skills  allow you to get more resources and   00:06:11.360 --> 00:06:16.000 those resources are the ones that affect  performance, not the social skills per se. 00:06:16.640 --> 00:06:20.320 How is this kind of moral  testing with regression analysis? 00:06:20.320 --> 00:06:24.560 We have this a very simple approach  consisting of three regression analysis   00:06:25.120 --> 00:06:26.560 introduced by Barron and Kenny. 00:06:26.560 --> 00:06:31.120 And this is known as Barron and  Kenny method or causal steps method. 00:06:31.120 --> 00:06:37.600 So the idea first is that we regress y on x,  to see if there is a causal effect of x on y,   00:06:38.800 --> 00:06:40.640 that can be mediated. 00:06:40.640 --> 00:06:47.520 Then we regress m on x, so we regress the  mediator on the first independent variable,   00:06:47.520 --> 00:06:53.360 and then we regress both y on the  mediator and the original variable. 00:06:54.160 --> 00:07:00.000 If we ideally want to show that x  influences m and m influences y,   00:07:00.560 --> 00:07:05.360 but not necessarily that x influences  y, when we control four values of m. 00:07:06.080 --> 00:07:08.800 We can see these three models, three steps here. 00:07:08.800 --> 00:07:12.080 So this model number three  is the first step, it is   00:07:12.800 --> 00:07:16.880 sales, which is the y  variable regressed on all the   00:07:16.880 --> 00:07:22.880 interesting variables and controls except for the mediator variables, which are two in this case. 00:07:23.760 --> 00:07:29.440 Then we have Model 2, which is step number two, that is resource acquisition, a mediator variable. 00:07:29.440 --> 00:07:33.120 And then we have Model 3, where we  regress the final dependent variable   00:07:33.120 --> 00:07:35.680 on the mediators and the original x variables. 00:07:36.560 --> 00:07:42.080 Then we simply multiply the regression  coefficients together to get the mediation. 00:07:42.080 --> 00:07:45.840 So mediation involves testing a  series of regression analysis. 00:07:45.840 --> 00:07:50.080 There are, of course, other techniques for  testing mediation but this is the simplest one. 00:07:51.280 --> 00:07:55.360 Mediation can be of two different  kinds, if there is mediation. 00:07:55.360 --> 00:07:57.840 There is full mediation and partial mediation. 00:07:57.840 --> 00:08:02.080 Full mediation means that after we  control for the mediator in this case,   00:08:03.360 --> 00:08:07.600 resource acquisition, there is  no effect on expressiveness. 00:08:08.160 --> 00:08:16.000 So if there is a very expressive entrepreneur, if that expressiveness does not translate into better   00:08:17.040 --> 00:08:20.480 resource acquisition skills, then  there is no effect on the employment. 00:08:21.840 --> 00:08:27.520 Use another example, if a person studies  really really hard but does not learn anything,   00:08:28.400 --> 00:08:31.440 then they will not perform  well in an exam, because   00:08:31.440 --> 00:08:35.360 learning is a mediator between  studying and performing in an exam. 00:08:36.160 --> 00:08:40.160 If we look at the actual regression  results, we can see the full   00:08:40.160 --> 00:08:43.040 mediation and partial mediation evidence here. 00:08:43.040 --> 00:08:48.720 So this is partial mediation, we can see  that the effect of expressiveness here   00:08:48.720 --> 00:08:54.080 persists in Model 5, which contains the  original variables and the mediator,   00:08:54.080 --> 00:08:57.440 I've left out the controls just  to simplify the table a bit. 00:08:58.000 --> 00:09:04.960 And then when we look at this full mediation here, we can see that the effect of expressiveness   00:09:04.960 --> 00:09:12.320 is non-significant on employment growth  rate after a control for the mediator. 00:09:12.320 --> 00:09:16.720 So the effect, if we hold the  mediator in a constant, then   00:09:17.360 --> 00:09:20.080 increasing expressiveness  does not make a difference. 00:09:21.600 --> 00:09:25.040 Okay to summarize, mediation  and moderation are two ways   00:09:25.040 --> 00:09:29.440 of analyzing relationships  that are about three variables. 00:09:29.440 --> 00:09:34.320 Mediation is the study of mechanism, is  there a variable that sits in between   00:09:34.320 --> 00:09:37.040 this step in the causal path from x to y. 00:09:37.760 --> 00:09:40.160 And that allows us to study mechanisms. 00:09:40.160 --> 00:09:44.240 Singleton & Straits use the term intervening variable for these kind of models. 00:09:44.240 --> 00:09:45.840 Then we have moderation,   00:09:45.840 --> 00:09:50.240 and moderation means that the effect of  x and y depends on the third variable. 00:09:50.240 --> 00:09:54.960 This kind of model is useful because  it allows us to study context. 00:09:54.960 --> 00:09:58.640 When does an effect occur, when does it not occur.