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The iterative proportional fitting algortihm adjust a matrix to given margins. It is known that the estimates converge to the maximum likelihood estimate. My question is as follows.

I have a matrix with cells representing a sample and further, I have the population margins. If I start the algorithm instead of using the sample with a Identitiy matrix, does this affect the interpretation of the results?

As, I read the literature IPF converges to the maximum likelihood estimates for any positive matrix. Yet, I also read that the initial values have some effect on the results, which are vanishing after each iteration of IPF. My initial thought would be that the resulting values if I start with an identity matrix represent the unbiased MLE values.

S.K.
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1 Answers1

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It makes a huge difference. The IPF algorithm basically maintains the odds ratios in the starting values and changes the counts such that they match the desired margins. So if you take the data as starting values, you maintain the odds ratios you found in the data. If you start with all 1s you find the counts that would occur if the two variables are independent.

Maarten Buis
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