Lesson plan
NM-method
The NM-method or Naszodi–Mendonca method is the operation that can be applied in statistics, econometrics, economics, sociology, and demography to construct counterfactual contingency tables. The method finds the matrix X ( X \in \mathbb{R}^{n \times m } ) which is "closest" to matrix Z ( Z \in \mathbb{N}^{n \times m } called the seed table) in the sense of being ranked the same but with the row and column totals of a target matrix Y ( Y \in \mathbb{N}^{n \times m }) . While the row totals and column totals of Y are known, matrix Y itself may not be known. Since the solution for matrix X is unique, the NM-method is a function: X=\text{NM}(Z, Y e^T_m, e_nY): \mathbb{N}^{n \times m} \times \mathbb{N}^{n} \times \mathbb{N}^{m} \mapsto \mathbb{R}^{n \times m} , where e_n is a row vector of ones of size 1\times n , while e^T_m is a column vector of ones of size m\times 1 . The NM-method was developed by Naszodi and Mendonca (2023) (and first applied by Naszodi and Mendonca (2019) to solve for matrix X in problems, where matrix \boldsymbol{Z} is not a sample from the population characterized by the row totals and column totals of matrix Y , but represents another population.…
Article summary
The NM-method or Naszodi–Mendonca method is the operation that can be applied in statistics, econometrics, economics, sociology, and demography to construct counterfactual contingency tables. The method finds the matrix X ( X \in \mathbb{R}^{n \times m } ) which is "closest" to matrix Z ( Z \in \mathbb{N}^{n \times m } called the seed table) in the sense of being ranked the same but with the row and column totals of a target matrix Y ( Y \in \mathbb{N}^{n \times m }) . While the row totals and column totals of Y are known, matrix Y itself may not be known. Since the solution for matrix X is unique, the NM-method is a function: X=\text{NM}(Z, Y e^T_m, e_nY): \mathbb{N}^{n \times m} \times \mathbb{N}^{n} \times \mathbb{N}^{m} \mapsto \mathbb{R}^{n \times m} , where e_n is a row vector of ones of size 1\times n , while e^T_m is a column vector of ones of size m\times 1 . The NM-method was developed by Naszodi and Mendonca (2023) (and first applied by Naszodi and Mendonca (2019) to solve for matrix X in problems, where matrix \boldsymbol{Z} is not a sample from the population characterized by the row totals and column totals of matrix Y , but represents another population.…
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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