Table 2 |
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Summary of significance tests for combining different estimates from m imputed datasets after MI |
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Estimate |
F |
Test statistic |
Degrees of freedom (df) |
Relative increase in variance (r) |
|
|
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A) Scalar |
F1, v |
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v = (m - 1)(1 + r-1)2 |
|
|
|
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B) Multivariate |
|
H0:Q = Q0, k = number of parameters |
where a = k(m - 1) |
|
|
|
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C) χ2 statistics w1,..., wm |
|
k = df associated with χ2 tests |
|
|
|
|
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D) Likelihood Ratio χ2 statistics wL1,..., wLm |
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k = number of parameters in fitted model |
|
|
|
|
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KEY: F = value from the F-distribution, which the test statistic is compared to.
B = between imputation variance. T = total variance for the combined MI estimate. wj, j = 1,..., m = χ2 statistics associated with testing the null hypothesis Ho : Q = Qo on each imputed dataset, such that the significance level for the jth imputed dataset is P{
|
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Marshall et al. BMC Medical Research Methodology 2009 9:57 doi:10.1186/1471-2288-9-57 |
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, H0: Q = Q0
where a = k(m - 1)
= average of the m imputed data estimates.
= within imputation variance.
> wj}, where 
= average of the repeated χ2 statistics.
= average of the m likelihood ratio statistics, wL1,..., wLm, evaluated using the average MI parameter estimates and the average of the estimates
from a model fitted subject to the null hypothesis.
