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.