WEBVTT
Kind: captions
Language: en
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Interaction models allow us to
study the effect of a third variable
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on the strength of the relationship
between two other variables.
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Or alternatively nonlinear effects
of one variable on another,
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where the effect first goes up and then goes down,
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or vice versa.
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So why are this kind of models interesting?
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This is the normal way of
drawing a moderation model.
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And we have the M here,
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which influences the strength of
the relationship between X and Y.
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And this kind of model allows us to
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answer the question
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under which conditions the
effect of X and Y works,
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and under which conditions it does not.
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So let's say X is the amount of
weights that you lift through the week,
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how many times a week you go to the gym,
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and Y is your weight gain,
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so how much muscle mass you gain.
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That relationship could be moderated
by the amount of food that you eat.
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If you eat a lot while at the
same time going to the gym,
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then you will gain muscle mass.
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If you go to a gym a lot and you don't eat much,
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then there is no muscle gain.
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So you need both,
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and the effect of one variable depends
on the presence of another variable,
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on the third variable.
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So these models allow us to
study the effects of context
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and the effects of two variables
influencing the dependent variable together.
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Moderation models come in two typical variants
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that are both presented in the Deephouse's
paper and in the Hekman's paper.
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Let's start with the Hekman paper.
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So the Hekman paper has a pretty
traditional moderation hypothesis.
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They're saying that the relationship
between customer performance,
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sorry, the provider performance,
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and customer satisfaction
depends on the provider's race.
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So for example minorities are rewarded
less for their good performance,
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than whites, in this particular scenario.
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So that's the traditional
case of moderation effect,
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you have a third variable, called the moderator,
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which influences the relationship
between these two variables.
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Then we also have this another
type of interaction effect,
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called a U-shaped effect.
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And Deephouse says that there's a
curvilinear concave down relationship,
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which basically means that the
effect of strategic deviation on ROA
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is first positive,
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but once you get too deviant,
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then it starts to go down, so it's negative.
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So it's positive first then it turns negative,
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so it looks like a U, that is drawn upside down.
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Why this is an interaction effect is because
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the effect of strategic deviation
on ROA depends on itself,
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so that initially it's positive,
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but when strategic deviation value increases,
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then this relationship turns negative.
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So that's a way of making U-shaped effects using interactions.
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A typical way of drawing
these models is to draw boxes
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and then you have an arrow,
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which presents a causal relationship,
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or a regression relationship,
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and then you have these arrows from the third box,
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that go to the middle of this arrow.
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And this particular paper studies
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the effect of service provider
performance on rating,
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and then there is a customer gender/racial bias,
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that acts as a moderator for this relationship.
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So the strength of these relationships depends on
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the customers' possible bias
against the service provider.
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How we estimate these kinds of models
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can be understood by writing
the model in this kind of form.
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So we're saying here that the effect
of X has some base value beta1,
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and then it depends also on the value of M,
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so it's beta1 + beta2m.
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If beta 2 is a large number,
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then it means that the M has
a strong moderating effect,
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if it's a value that is close to zero,
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then there is no moderation effect.
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We can't estimate that kind of model
directly in the regression analysis,
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but if you write it differently then we can.
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So we can rewrite it without the parentheses,
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and it becomes beta0 + beta1x + beta2mx + beta3m.
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So the idea of, how we estimate these
kinds of moderation models is that,
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we multiply the moderator and the
interesting variable together,
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and then we add all two
variables and their product
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as independent variables
to the regression analysis.
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Here this equation shows that the
effect of X on Y is no longer constant.
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So it's not a constant effect,
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like we had in a regression analysis,
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because it depends on the value of M.
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And to understand, how we interpret these effects
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that is not constant but
depend on another variable,
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we need to introduce the
concept of marginal effect.
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So the marginal effect is the idea that
the effect of one variable on another
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depends on other variables,
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and it's constant at a certain point
but it can vary between points.
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So let's take a look at
regression analysis example.
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So normal regression analysis gives you a line,
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and the marginal effect is,
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how much Y changes, when X changes a little.
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So it's a derivative or a tangent for this line.
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And because this is a line,
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the derivative or the direction
of the line is always constant.
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And the marginal effect is a line.
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So marginal effect is,
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how much Y changes when X changes a little,
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or a very small amount at a particular point.
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When we have nonlinear effects,
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for example a log-transformed dependent variable,
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then the marginal effect is no longer constant.
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We can see here that the direction
of the line is different,
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it goes up but less strongly as it goes here.
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So the regression line here, if we draw it here,
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then it's much steeper than here.
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So the marginal effect for
nonlinear effects depends on,
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which part of the curve we are looking at.
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And typically when we do interactions,
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we are interested in interpreting
the marginal effects.