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Bounty Ended with 100 reputation awarded by T.J. Gaffney
Looked at Fisher paper and determined it was irrelevant
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jvbraun
jvbraun
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This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching prediction example: You want to best predict the occurrence of a categorical variable by a combination of other categorical variables. You do this by finding the split with the maximal $\chi^2$ value.

A description of the algorithm and the issues around adjusting for statistical significance are given in (Kass, 1980). Some In that paper the Bonferroni correction is used to adjust for the selection of the maximal $\chi^2$ value.

Some actual theory is available for the case of reduction to a $2\times2$ table (Kass, 1975). (Fisher may have addressed similar issues based on the references in that last paper.)

There is an R package called CHAID which implements the algorithm and is available on R-Forge.

Although it is a little different from your question, there is a similar situation that arises when dichotomizing a continuous variable to predict another dichotomous variable. Namely, where should you put the cut-point? This is discussed in (Miller and Siegmund, 1980) and (Halpern, 1982), among others.

Yet another setting where this type of question comes up is in change-point estimation or segmentation, though it has been too long since I looked at those papers to recall authors.

References:

Halpern, J. (1982). Maximally selected chi square statistics for small samples. Biometrics, 1017-1023.

Kass, G. V. (1975). Significance testing in automatic interaction detection (AID). Applied Statistics, 178-189.

Kass, G.V. (1980). An Exploratory Technique for Investigating Large Quantities of Categorical Data. Applied Statistics, 29(2), 119-127.

Miller, R. and Siegmund, D. (1980). Maximally Selected Chi-Squares. Technical Report 64. Stanford, Calif, Division of Biostatistics, Stanford University.

This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching prediction example: You want to best predict the occurrence of a categorical variable by a combination of other categorical variables.

A description of the algorithm and the issues around adjusting for statistical significance are given in (Kass, 1980). Some theory is available for the case of reduction to a $2\times2$ table (Kass, 1975). (Fisher may have addressed similar issues based on the references in that last paper.)

There is an R package called CHAID which implements the algorithm and is available on R-Forge.

Although it is a little different from your question, there is a similar situation that arises when dichotomizing a continuous variable to predict another dichotomous variable. Namely, where should you put the cut-point? This is discussed in (Miller and Siegmund, 1980) and (Halpern, 1982), among others.

Yet another setting where this type of question comes up is in change-point estimation or segmentation, though it has been too long since I looked at those papers to recall authors.

References:

Halpern, J. (1982). Maximally selected chi square statistics for small samples. Biometrics, 1017-1023.

Kass, G. V. (1975). Significance testing in automatic interaction detection (AID). Applied Statistics, 178-189.

Kass, G.V. (1980). An Exploratory Technique for Investigating Large Quantities of Categorical Data. Applied Statistics, 29(2), 119-127.

Miller, R. and Siegmund, D. (1980). Maximally Selected Chi-Squares. Technical Report 64. Stanford, Calif, Division of Biostatistics, Stanford University.

This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching prediction example: You want to best predict the occurrence of a categorical variable by a combination of other categorical variables. You do this by finding the split with the maximal $\chi^2$ value.

A description of the algorithm and the issues around adjusting for statistical significance are given in (Kass, 1980). In that paper the Bonferroni correction is used to adjust for the selection of the maximal $\chi^2$ value.

Some actual theory is available for the case of reduction to a $2\times2$ table (Kass, 1975).

There is an R package called CHAID which implements the algorithm and is available on R-Forge.

Although it is a little different from your question, there is a similar situation that arises when dichotomizing a continuous variable to predict another dichotomous variable. Namely, where should you put the cut-point? This is discussed in (Miller and Siegmund, 1980) and (Halpern, 1982), among others.

Yet another setting where this type of question comes up is in change-point estimation or segmentation, though it has been too long since I looked at those papers to recall authors.

References:

Halpern, J. (1982). Maximally selected chi square statistics for small samples. Biometrics, 1017-1023.

Kass, G. V. (1975). Significance testing in automatic interaction detection (AID). Applied Statistics, 178-189.

Kass, G.V. (1980). An Exploratory Technique for Investigating Large Quantities of Categorical Data. Applied Statistics, 29(2), 119-127.

Miller, R. and Siegmund, D. (1980). Maximally Selected Chi-Squares. Technical Report 64. Stanford, Calif, Division of Biostatistics, Stanford University.

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jvbraun
jvbraun
  • 2.4k
  • 15
  • 20

This procedure is basically the idea behind "CHi-squared Automated Interaction Detection", or "CHAID" described by G.V. Kass in 1980. The general setting is very similar to your television watching prediction example: You want to best predict the occurrence of a categorical variable by a combination of other categorical variables.

A description of the algorithm and the issues around adjusting for statistical significance are given in (Kass, 1980). Some theory is available for the case of reduction to a $2\times2$ table (Kass, 1975). (Fisher may have addressed similar issues based on the references in that last paper.)

There is an R package called CHAID which implements the algorithm and is available on R-Forge.

Although it is a little different from your question, there is a similar situation that arises when dichotomizing a continuous variable to predict another dichotomous variable. Namely, where should you put the cut-point? This is discussed in (Miller and Siegmund, 1980) and (Halpern, 1982), among others.

Yet another setting where this type of question comes up is in change-point estimation or segmentation, though it has been too long since I looked at those papers to recall authors.

References:

Halpern, J. (1982). Maximally selected chi square statistics for small samples. Biometrics, 1017-1023.

Kass, G. V. (1975). Significance testing in automatic interaction detection (AID). Applied Statistics, 178-189.

Kass, G.V. (1980). An Exploratory Technique for Investigating Large Quantities of Categorical Data. Applied Statistics, 29(2), 119-127.

Miller, R. and Siegmund, D. (1980). Maximally Selected Chi-Squares. Technical Report 64. Stanford, Calif, Division of Biostatistics, Stanford University.