A study of Coleman's linear model for attributes
Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Feldman, Jacqueline [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1970 |
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| Schlagwörter: |
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| Anmerkung: |
© Kluwer Academic Publishers 1970 |
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| Übergeordnetes Werk: |
Enthalten in: Quality & quantity - Kluwer Academic Publishers, 1967, 4(1970), 2 vom: Dez., Seite 255-297 |
|---|---|
| Übergeordnetes Werk: |
volume:4 ; year:1970 ; number:2 ; month:12 ; pages:255-297 |
| Links: |
|---|
| DOI / URN: |
10.1007/BF00199566 |
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| Katalog-ID: |
OLC2063476063 |
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| 520 | |a Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. | ||
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10.1007/BF00199566 doi (DE-627)OLC2063476063 (DE-He213)BF00199566-p DE-627 ger DE-627 rakwb eng 050 VZ 3,4 ssgn Feldman, Jacqueline verfasserin aut A study of Coleman's linear model for attributes 1970 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1970 Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. Linear Model Regression Model Linear Function Statistic Theory General Treatment Enthalten in Quality & quantity Kluwer Academic Publishers, 1967 4(1970), 2 vom: Dez., Seite 255-297 (DE-627)129084328 (DE-600)4140-3 (DE-576)014417715 0033-5177 nnns volume:4 year:1970 number:2 month:12 pages:255-297 https://doi.org/10.1007/BF00199566 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-SOW GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4325 GBV_ILN_4700 AR 4 1970 2 12 255-297 |
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10.1007/BF00199566 doi (DE-627)OLC2063476063 (DE-He213)BF00199566-p DE-627 ger DE-627 rakwb eng 050 VZ 3,4 ssgn Feldman, Jacqueline verfasserin aut A study of Coleman's linear model for attributes 1970 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1970 Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. Linear Model Regression Model Linear Function Statistic Theory General Treatment Enthalten in Quality & quantity Kluwer Academic Publishers, 1967 4(1970), 2 vom: Dez., Seite 255-297 (DE-627)129084328 (DE-600)4140-3 (DE-576)014417715 0033-5177 nnns volume:4 year:1970 number:2 month:12 pages:255-297 https://doi.org/10.1007/BF00199566 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-SOW GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4325 GBV_ILN_4700 AR 4 1970 2 12 255-297 |
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10.1007/BF00199566 doi (DE-627)OLC2063476063 (DE-He213)BF00199566-p DE-627 ger DE-627 rakwb eng 050 VZ 3,4 ssgn Feldman, Jacqueline verfasserin aut A study of Coleman's linear model for attributes 1970 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1970 Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. Linear Model Regression Model Linear Function Statistic Theory General Treatment Enthalten in Quality & quantity Kluwer Academic Publishers, 1967 4(1970), 2 vom: Dez., Seite 255-297 (DE-627)129084328 (DE-600)4140-3 (DE-576)014417715 0033-5177 nnns volume:4 year:1970 number:2 month:12 pages:255-297 https://doi.org/10.1007/BF00199566 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-SOW GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4325 GBV_ILN_4700 AR 4 1970 2 12 255-297 |
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10.1007/BF00199566 doi (DE-627)OLC2063476063 (DE-He213)BF00199566-p DE-627 ger DE-627 rakwb eng 050 VZ 3,4 ssgn Feldman, Jacqueline verfasserin aut A study of Coleman's linear model for attributes 1970 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1970 Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. Linear Model Regression Model Linear Function Statistic Theory General Treatment Enthalten in Quality & quantity Kluwer Academic Publishers, 1967 4(1970), 2 vom: Dez., Seite 255-297 (DE-627)129084328 (DE-600)4140-3 (DE-576)014417715 0033-5177 nnns volume:4 year:1970 number:2 month:12 pages:255-297 https://doi.org/10.1007/BF00199566 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-SOW GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4325 GBV_ILN_4700 AR 4 1970 2 12 255-297 |
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10.1007/BF00199566 doi (DE-627)OLC2063476063 (DE-He213)BF00199566-p DE-627 ger DE-627 rakwb eng 050 VZ 3,4 ssgn Feldman, Jacqueline verfasserin aut A study of Coleman's linear model for attributes 1970 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic Publishers 1970 Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. Linear Model Regression Model Linear Function Statistic Theory General Treatment Enthalten in Quality & quantity Kluwer Academic Publishers, 1967 4(1970), 2 vom: Dez., Seite 255-297 (DE-627)129084328 (DE-600)4140-3 (DE-576)014417715 0033-5177 nnns volume:4 year:1970 number:2 month:12 pages:255-297 https://doi.org/10.1007/BF00199566 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-SOW GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4103 GBV_ILN_4125 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4325 GBV_ILN_4700 AR 4 1970 2 12 255-297 |
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A study of Coleman's linear model for attributes |
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A study of Coleman's linear model for attributes |
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Feldman, Jacqueline |
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Quality & quantity |
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1970 |
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Feldman, Jacqueline |
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a study of coleman's linear model for attributes |
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A study of Coleman's linear model for attributes |
| abstract |
Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. © Kluwer Academic Publishers 1970 |
| abstractGer |
Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. © Kluwer Academic Publishers 1970 |
| abstract_unstemmed |
Conclusion Coleman's linear model for attributes parallels the classical regression model for real variables. The aim is to obtain, from the data, a set of numbers which serve as measures of the effect of a set of characteristics on an attitude. The probability of the attitude is assumed to be a linear function of the parameters. We have distinguished the case where the distribution of the population into the different classes defined by the characteristics is random (model A) from the case where this distribution is given (model B). We have shown that, for large samples, these two models have very similar properties. Coleman's method of estimation, a least-squares method, leads to very simple solutions, and this even in the general case. It has, however, certain shortcomings: it uses only proportions, and not the magnitude of the classes, and does not lead to a test of goodness-of-fit. We know, however, the asymptotic distribution of the estimates from which we get confidence regions and tests for definite values of the parameters. We propose two other methods, the maximum likelihood and the minimum X12, which both lead to unbiased estimates with asymptotic minimum variances, and to tests of hypotheses of the X2 type. The min. X12 is particularly well suited in a linear context. Section II is devoted to the case where all variables are dichotomies, and contains a numerical example. Section III is devoted to the general treatment of the model and demonstrates its properties from basic results in probability and statistic theory, which are recalled in the Appendix. © Kluwer Academic Publishers 1970 |
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