WEBVTT
Kind: captions
Language: en
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Maximum likelihood estimates of two different
models that are nested
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can be compared using the likelihood ratio
test.
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The idea is the same as in regression analysis
and the F test.
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So in an F test, in regression analysis, we
have two models.
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One is the constraint model and another one
is the unconstrained model.
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Here, Model 2 is the more general, unconstraint
model.
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And Model 1 is a special case of Model 2,
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because we get Model 1 from Model 2 by saying
that
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these regression coefficients that are estimated
here
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are actually zeros in Model 1,
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because we don't include these variables.
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Then we do some math,
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we calculate the sum of squares or R-squared
of these models,
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we compare that to degrees of freedom,
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we get the statistic that follows the F distribution.
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In maximum likelihood estimates,
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we don't have the R-squared, we don't have
the sum of squares,
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instead, we use the deviance statistic.
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So here in Kraimer's paper, we have two models.
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So Model 1 is the constraint model,
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Model 2 is the unconstrained model,
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because we have this coefficient here that's
estimated,
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here it is constrained to be zero.
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So, we have one degree of freedom difference
between these two models.
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Then we can calculate the likelihood ratio
test of
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whether adding this one more parameter increases
the model fit more
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than what can be expected by chance only,
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by comparing these deviances or -2 times log-likelihood.
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So, Model 2 is the unrestricted model,
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Model 1 is the restricted model.
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We calculate the difference between the deviances,
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which is 3.79.
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And that difference follows the chi-square
distribution
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with one degree of freedom,
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because there is only one parameter difference
here.
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And the p-value for that would be 0.05,
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which says that there is no statistically
significant difference between the models
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that's on the border of 0.05 level.
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And it's also shown here
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that this is not very, very significant here.
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In contrast to the F test,
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which always, if you have one parameter,
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gives you the same exact p-value as t test,
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the significance test statistic here from
z test,
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and the likelihood ratio, p-value,
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they don't necessarily have the exact same
value,
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because these are based on large sample approximations
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that may not work as exactly as intended in
a small samples.
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So there can be some scenarios like here,
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we have a significant coefficient, p is less
than 0.05.
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But here we don't, we have p that is more
than 0.05.
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But it's on the boundary.
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So we could just say that there is weak evidence
for the existence of this relationship.