The Stochastic Disturbance Specification and its Implications for Log-Linear Regression

1979 ◽  
Vol 11 (7) ◽  
pp. 781-790 ◽  
Author(s):  
J M Haworth ◽  
P J Vincent
Keyword(s):  
Spatial Analysis ◽  
Linear Regression ◽  
Conditional Expectation ◽  
Linear Models ◽  
Model Specification ◽  
Stochastic Disturbance ◽  
Log Linear

Model specification is a crucial factor in regression. We show that in log-linear models, although the estimated relationship represents the conditional expectation of ln Y, the antilogarithm does not give the conditional expectation of Y. This has important implications in spatial analysis.

Log-Linear Modelling and Spatial Analysis

1985 ◽  
Vol 17 (7) ◽  
pp. 931-951 ◽  
Author(s):  
E Aufhauser ◽  
M M Fischer
Keyword(s):  
Spatial Analysis ◽  
Linear Models ◽  
Generalised Linear Models ◽  
Migration Patterns ◽  
Poisson Sampling ◽  
The Past ◽  
The Social ◽  
The Family ◽  
Conventional Models ◽  
Log Linear

In the past decade the social sciences have seen an upsurge of interest in analysing multidimensional contingency tables using log-linear models. Two broad families of log-linear models may be distinguished: the family of conventional models and the family of unconventional models (that is, quasi-log-linear and hybrid models). In this paper a brief review of such models is presented and some linkage to the class of generalised linear models suggested by Nelder and Wedderburn is provided. The great potential of log-linear models for spatial analysis is illustrated in applying conventional and unconventional models in a migration context to identify intertemporal stability of migration patterns. The problem that the effective units migrating are households rather than individuals is coped with by postulating a compound Poisson sampling scheme.

scholarly journals Scaling, normalizing, and per ratio standards: an allometric modeling approach

1995 ◽  
Vol 79 (3) ◽  
pp. 1027-1031 ◽  
Author(s):  
A. M. Nevill ◽  
R. L. Holder
Keyword(s):  
Linear Regression ◽  
Multiple Regression ◽  
Linear Models ◽  
Predictor Variable ◽  
Mean Power ◽  
Physiological Variables ◽  
Model Form ◽  
Ratio Standards ◽  
Log Linear ◽  
Ratio Variables

The practice of scaling or normalizing physiological variables (Y) by dividing the variable by an appropriate body size variable (X) to produce what is known as a “per ratio standard” (Y/ X), has come under strong criticism from various authors. These authors propose an alternative regression standard based on the linear regression of (Y) on (X) as the predictor variable. However, if linear regression is to be used to adjust such physiological measurements (Y), the residual errors should have a constant variance and, in order to carry out parametric tests of significance, be normally distributed. Unfortunately, since neither of these assumptions appear to be satisfied for many physiological variables, e.g., maximum oxygen uptake, peak and mean power, an alternative approach is proposed of using allometric modeling where the concept of a ratio is an integral part of the model form. These allometric models naturally help to overcome the heteroscedasticity and skewness observed with per ratio variables. Furthermore, if per ratio standards are to be incorporated in regression models to predict other dependent variables, the allometric or log-linear model form is shown to be more appropriate than linear models. By using multiple regression, simply by taking logarithms of the dependent variable and entering the logarithmic transformed per ratio variables as separate independent variables, the resulting estimated log-linear multiple-regression model will automatically provide the most appropriate per ratio standard to reflect the dependent variable, based on the proposed allometric model.

When and why are log-linear models self-normalizing?

2015 ◽  
Author(s):  
Jacob Andreas ◽  
Dan Klein
Keyword(s):  
Linear Models ◽  
Log Linear

Log-Linear Models with Dependent Spatial Data

1983 ◽  
Vol 15 (6) ◽  
pp. 801-813 ◽  
Author(s):  
B Fingleton
Keyword(s):  
Spatial Data ◽  
Statistical Models ◽  
Linear Models ◽  
Square Lattice ◽  
Categorical Variables ◽  
Systematic Sampling ◽  
Pairwise Correlations ◽  
Independent Observations ◽  
Intersection Points ◽  
Log Linear

Log-linear models are an appropriate means of determining the magnitude and direction of interactions between categorical variables that in common with other statistical models assume independent observations. Spatial data are often dependent rather than independent and thus the analysis of spatial data by log-linear models may erroneously detect interactions between variables that are spurious and are the consequence of pairwise correlations between observations. A procedure is described in this paper to accommodate these effects that requires only very minimal assumptions about the nature of the autocorrelation process given systematic sampling at intersection points on a square lattice.

scholarly journals Log-Linear Models for Frequency Data: Sufficient Statistics and Likelihood Equations

1973 ◽  
Vol 1 (4) ◽  
pp. 617-632 ◽  
Author(s):  
Shelby J. Haberman
Keyword(s):  
Linear Models ◽  
Frequency Data ◽  
Sufficient Statistics ◽  
Log Linear

Educational Homogamy Among Married and Unmarried Couples in Europe

2008 ◽  
Vol 30 (1) ◽  
pp. 28-52 ◽  
Author(s):  
Dana Hamplova
Keyword(s):  
Linear Models ◽  
Married Couples ◽  
European Social Survey ◽  
Social Survey ◽  
Educational Homogamy ◽  
Educational Barriers ◽  
Educational Groups ◽  
Institutional Contexts ◽  
Using Data ◽  
Log Linear

In this article, educational homogamy among married and cohabiting couples in selected European countries is examined. Using data from two waves (2002 and 2004) of the European Social Survey, this article compares three cultural and institutional contexts that differ in terms of institutionalization of cohabitation. Evidence from log-linear models yields two main conclusions. First, as cohabitation becomes more common in society, marriage and cohabitation become more similar with respect to partner selection. Second, where married and unmarried unions differ in terms of educational homogamy, married couples have higher odds of overcoming educational barriers (i.e., intermarrying with other educational groups).

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

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