Copyright Sociological Research Online, 1996
Analyzing tables where the response variable has ordered categories through model building has been problematic in software packages such as GLIM (Aitken et al., 1989). Recent developments in statistical modelling have offered new possibilities and this paper explores one option, namely the continuation ratio model which was initially reported by Fienberg and Mason (1979). The fitting of this model to data in tabular form is possible in GLIM although not especially trivial and by and large this approach has not been employed in sociological research. In this paper I outline the continuation ratio model and comment upon how it can be fitted to data by sociologists using the GLIM software. In addition I present a short description of the relative merits of such an approach.
Presenting this paper in an electronic format facilitates the possibility of replicating the analysis. The data is appended to the paper in the appropriate format along with a copy of the GLIM transcript. A dumped GLIM4 file is also attached.
No. of Higher Passes* | White | Asian | Afro Caribbean | |||
---|---|---|---|---|---|---|
Males | Female | Males | Females | Males | Females | |
Zero | 50 | 44 | 50 | 49 | 62 | 58 |
One - Three | 25 | 28 | 25 | 29 | 27 | 30 |
Four + | 25 | 28 | 25 | 22 | 11 | 12 |
* O' level and C.S.E. results.
No. of Higher Grade Passes | ||
---|---|---|
Zero (%) | Some Passes (%) | |
White | ||
Males | 50 | 50 |
Females | 44 | 56 |
Asian | ||
Males | 50 | 50 |
Females | 49 | 51 |
Afro Caribbean | ||
Males | 62 | 38 |
Females | 58 | 42 |
No. of Higher Grade Passes | ||
---|---|---|
One - Three (%) | Four + (%) | |
White | ||
Males | 50 | 50 |
Females | 50 | 50 |
Asian | ||
Males | 50 | 50 |
Females | 58 | 42 |
Afro Caribbean | ||
Males | 71 | 29 |
Females | 71 | 29 |
No. of Higher Passes | White | Asian | Afro Caribbean | |||
---|---|---|---|---|---|---|
Males | Females | Males | Females | Females | ||
Zero | 6566 | 5697 | 262 | 188 | 141 | 148 |
One - Three | 3283 | 3626 | 132 | 111 | 61 | 77 |
Four + | 3283 | 3626 | 132 | 85 | 25 | 31 |
r is the number of successes
n is the number of trials
cutpt is the two partitions or cut-points
the ethnicity variables are coded 1=no and 2=yes
Gender is coded as Male=1 and Female=2.
r | n | cutpt | Asian | Afro Caribbean | gender |
---|---|---|---|---|---|
6566 | 13132 | 1 | 1 | 1 | 1 |
3283 | 6566 | 2 | 1 | 1 | 1 |
5697 | 12949 | 1 | 1 | 1 | 2 |
3626 | 7257 | 2 | 1 | 1 | 2 |
262 | 526 | 1 | 2 | 1 | 1 |
132 | 264 | 2 | 2 | 1 | 1 |
188 | 384 | 1 | 2 | 1 | 2 |
111 | 196 | 2 | 2 | 1 | 2 |
141 | 227 | 1 | 1 | 2 | 1 |
61 | 86 | 2 | 1 | 2 | 1 |
148 | 256 | 1 | 1 | 2 | 2 |
77 | 108 | 2 | 1 | 2 | 2 |
Table 6 - GLIM4 Input File
[o] GLIM 4, update 8 for Sun SPARCstation / Solaris on 10 Jul 1996 at 17:58:16 [o] (copyright) 1992 Royal Statistical Society, London [o] [i] ? $units 12$ [i] ? $data r n cutpt asian afro gender$ [i] ? $dinput 12$ [i] File name? data [i] ? $factor cutpt 2 asian 2 afro 2 gender 2$ [i] ? $yvar r$ [i] ? $err b n$ [i] ? $fit cutpt-1$ The term 'afro caribbean' is reduced to 'afro' in the GLIM syntax. |
Model | Variables | in deviance | df. |
---|---|---|---|
A | Cutpt | - | - |
B | Cutpt + asian | 2.850 | 1 |
C | Cutpt + afro caribbean | 61.550 | 1* |
D | Cutpt + afro caribbean + gender | 59.760 | 1* |
E | Cutpt + afro caribbean + gender + afro caribbean.gender | 0.038 | 1 |
F | Cutpt + afro caribbean + gender + cutpt.afro caribbean | 4.436 | 1* |
G | Cutpt + afro caribbean + gender + cutpt.afro caribbean + cutpt.gender | 33.960 | 1* |
* Significant at 5% level.
By restoring the dumped GLIM4 file 'newycs.dum' that is provided the modelling process can be replicated. Download newycs.zip or newycs.dum.sit
estimate | s.e. | parameter |
---|---|---|
-0.0007558 | 0.01704 | CUTPT(1) |
-6.942e^{-5} | 0.02413 | CUTPT(2) |
0.5249 | 0.09377 | AFRO CARIBBEAN(2) |
-0.2343 | 0.02423 | GENDER(2) |
0.3739 | 0.1849 | CUTPT(2). AFRO CARIBBEAN(2) |
0.2401 | 0.04120 | CUTPT(2).GENDER(2) |
Whites and Asians | |
---|---|
Males | 1 |
Females | 0.79 |
Afro Caribbean | |
Males | 1.69 |
Females | 1.34 |
Whites and Asians | |
---|---|
Males | 1 |
Females | 1 |
Afro Caribbean | |
Males | 2.46 |
Females | 2.47 |
SummaryEthnicity is importantOverall ethnicity is important but Asian young people are not systematically different to white young people in terms of their educational achievement. Afro Caribbeans are doing worse than their white and Asian colleagues, both in terms of having qualifications and in terms of their level of qualifications. Gender is importantFemales do better than males in terms of having some rather than no qualifications. However, when we consider those young people that have qualifications, females no longer have an advantage. |
and are fitted conditional probabilities for the two partitions (cut-points _{1 }and _{2}) for white and Asian (_{1}) males (_{1}).
and are the fitted conditional probabilities for the partitions (cut-points _{1 }and _{2}) for white and Asian (_{1}) females _{2}. The fitted conditional probabilities for the two cut-points for the various factors combinations can be readily computed in a similar fashion.
P_{1} = H_{1} , P_{2} = (1-H_{1} ) H_{2} , and P_{3} = 1- P_{1} - P_{2}.
The calculations can be viewed and the unconditional fitted probabilities are reported in Table 11.
Number of Higher Grade Passes | |||
---|---|---|---|
Zero | One - Three | Four + | |
White and Asian | |||
Males | 0.50 | 0.25 | 0.25 |
Females | 0.44 | 0.28 | 0.28 |
Afro Caribbean | |||
Males | 0.62 | 0.26 | 0.12 |
Females | 0.57 | 0.28 | 0.15 |
Table 12: Estimates of Regression Diagnostic for Particular Estimates of e.p.m.f. and Each Value of j*
Estimate of r when: | ||||||
e.p.m.f. | _{1} | _{2} | _{3} | j*=1 | j*=2 | j*=3 |
White and Asian | ||||||
Males | 0.50 | 0.25 | 0. 25 | -0.75 | 0.25 | 1.25 |
Females | 0.44 | 0.28 | 0.28 | -0.84 | 0.16 | 1.16 |
Afro Caribbean | ||||||
Males | 0.62 | 0.26 | 0. 12 | -0.5 | 0.5 | 1.50 |
Females | 0.57 | 0.28 | 0.15 | -0.58 | 0.42 | 1.42 |
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