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Response to M.B. Brown
Computational Statistics & Data Analysis 3 (1985) 145-146 North-Holland
145
Response to M.B. Brown S. K U L L B A C K and J.C. K E E G E L Received April 1985
The following outlines our response to the M. Brown rejoinder. 1. Last sentence first paragraph. "One method...other." One can get to the top of the Washington Monument by climbing the stairs or riding the elevator. We prefer to ride the elevator. 2. Last sentence second paragraph. " K & K forced.., both algorithms." K & K used the same model as defined by the linear independent constraints. 3. Last sentence third paragraph. "Therefore, the two.., their zero frequencies." K & K do not understand the same generic model differing in the zero frequencies. In the MDI approach a model is defined by the linearly independent constraints imposed on the estimated cell frequencies. 4. Fourth paragraph. The model (DE, DN, DM, DB, ENMB) is clearly one with the dependent two level variable D. K & K omit pairs with two zeros because those correspond to binomials with no observations. As B & F state in the first sentence of Section 2.2 of their original paper." When there is a zero in a marginal configuration defined by a log-linear model the cells comprising that marginal zero have expected values that are zero." This situation exists with the configuration ENMB. In the computer output of the programs used by K & K the observed values are listed along with their logarithms. Zero observed values are automatically replaced by 0.000001 because the computer gets upset when asked to give the logarithm of zero. If K & K had included all zeros the computer would have produced no output since it would have had to invert a singular matrix. The selection of the set of observed cells by K & K was not arbitrary but consistent with the principles of MDI. With respect to the specific comments: (1) The choice of linearly independent constraints by K & K is to insure that the matrix inversion involved in the Newton-Raphson type algorithm deals with a non-singular matrix. K & K do not choose to eliminate certain cells a priori. That depends on the observations and the model design. (2) K & K prefer a parameterization in which the parameters in the logit representation are the same as the corresponding parameters in the loglinear representation. (3) Noted. K & K ' s original comments were prepared prior to a previous rejoinder by B&F. 0167-9473/85/$3.30 © 1985, Elsevier Science Publishers B.V. (North-Holland)
146
S. Kuilback, J.C. Keegel / Response to M.B. Brown
(4), (5), (6) repeat previous assertions. As mentioned above K & K do not see the reasoning. For the analysis of count data and contingency tables in particular the MDI approach includes the maximum liltelihood approach as a special case. Experience with the MDI approach on many practical problems including some with large data sets have convinced K& K and others of its utility. This discussion hopefully will expose it to more practitioners.
145
Response to M.B. Brown S. K U L L B A C K and J.C. K E E G E L Received April 1985
The following outlines our response to the M. Brown rejoinder. 1. Last sentence first paragraph. "One method...other." One can get to the top of the Washington Monument by climbing the stairs or riding the elevator. We prefer to ride the elevator. 2. Last sentence second paragraph. " K & K forced.., both algorithms." K & K used the same model as defined by the linear independent constraints. 3. Last sentence third paragraph. "Therefore, the two.., their zero frequencies." K & K do not understand the same generic model differing in the zero frequencies. In the MDI approach a model is defined by the linearly independent constraints imposed on the estimated cell frequencies. 4. Fourth paragraph. The model (DE, DN, DM, DB, ENMB) is clearly one with the dependent two level variable D. K & K omit pairs with two zeros because those correspond to binomials with no observations. As B & F state in the first sentence of Section 2.2 of their original paper." When there is a zero in a marginal configuration defined by a log-linear model the cells comprising that marginal zero have expected values that are zero." This situation exists with the configuration ENMB. In the computer output of the programs used by K & K the observed values are listed along with their logarithms. Zero observed values are automatically replaced by 0.000001 because the computer gets upset when asked to give the logarithm of zero. If K & K had included all zeros the computer would have produced no output since it would have had to invert a singular matrix. The selection of the set of observed cells by K & K was not arbitrary but consistent with the principles of MDI. With respect to the specific comments: (1) The choice of linearly independent constraints by K & K is to insure that the matrix inversion involved in the Newton-Raphson type algorithm deals with a non-singular matrix. K & K do not choose to eliminate certain cells a priori. That depends on the observations and the model design. (2) K & K prefer a parameterization in which the parameters in the logit representation are the same as the corresponding parameters in the loglinear representation. (3) Noted. K & K ' s original comments were prepared prior to a previous rejoinder by B&F. 0167-9473/85/$3.30 © 1985, Elsevier Science Publishers B.V. (North-Holland)
146
S. Kuilback, J.C. Keegel / Response to M.B. Brown
(4), (5), (6) repeat previous assertions. As mentioned above K & K do not see the reasoning. For the analysis of count data and contingency tables in particular the MDI approach includes the maximum liltelihood approach as a special case. Experience with the MDI approach on many practical problems including some with large data sets have convinced K& K and others of its utility. This discussion hopefully will expose it to more practitioners.