The effect of non-normality on estimating the variance of the combined ratio estimate in complex surveys

The performance of the balanced half-sample, jackknife and linearization methods for estimating the variance of the combined ratio estimate is studied by means of a computer simulation using artificially generated non-normally distributed populations.

The results of this investigation demonstrate that the variance estimates for the combined ratio estimate may be highly biased and unstable when the underlying distributions are non-normal. This is particularly true when the number of observations available from each stratum is small. The jack-     

The politic,philosophy and practice of OR—A personal view of the issues

It is almost 50 years since Sir Henry Tizzard created the group of scientists in RAF Fighter Command who were to coin the term ‘Operational Research’. The group still exists, though its work, and the work of other defence OR groups, has changed from solving acute operational problems by the extrapolation of observed data, to an attempt at predicting the outcome of policy choices that are beyond experience. Inevitably this has forced OR further into a political arena. Yet most OR practitioners are scientists used to investigating apolitical and benign nature. In this paper the author gives a personal view of what he believes OR is trying to achieve, what practical problems and pressures have to be faced and attempts to give guidance on how to proceed.     

A comparison of three methods of estimating the logistic regression coefficients

A Sampling experiment performed using data collected for a large clinical trial shows that the discriminant function estimates of the logistic regression coefficients for discrete variables may be severely biased. The simulations show that the mixed variable location model coefficient estimates have bias which is of the same magnitude as the bias in the coefficient estimates obtained using conditional maximum likelihood estimates but require about one-tenth of the computer time.     

Imaging: A Tool for Data Reduction

This article illustrates the use of high-resolution color graphic images obtained from raster terminals to reduce an immense amount of data into a few meaningful time series. The steps that were taken to achieve this data reduction and their appropriate images are given. The time series were analyzed using Box and Jenkins time series methods (see also McCleary and Hay 1980), and the results are discussed.     

A Simplified Method of Calculating an Overall Goodness-of-Fit Test for the Cox Proportional Hazards Model

Gronnesby and Borgan (1996) propose an overall goodness-of-fit test for the Cox proportional hazards model. The basis of their test is a grouping of subjects by their estimated risk score. We show that the Gronnesby and Borgan test is algebraically identical to one obtained from adding group indicator variables to the model and testing the hypothesis the coefficients of the group indicator variables are zero via the score test. Thus showing that the test can be calculated using existing software. We demonstrate that the table of observed and estimated expected number of events within each group of the risk score is a useful adjunct to the test to help identify potential problems in fit.     

A Cautionary Note on the Use of the Grønnesby and Borgan Goodness-of-Fit Test for the Cox Proportional Hazards Model

Grønnesby and Borgan (1996, Lifetime Data Analysis 2, 315–328) propose an omnibus goodness-of-fit test for the Cox proportional hazards model. The test is based on grouping the subjects by their estimated risk score and comparing the number of observed and a model based estimated number of expected events within each group. We show, using extensive simulations, that even for moderate sample sizes the choice of number of groups is critical for the test to attain the specified size. In light of these results we suggest a grouping strategy under which the test attains the correct size even for small samples. The power of the test statistic seems to be acceptable when compared to other goodness-of-fit tests.     

Goodness of fit tests for the multiple logistic regression model

Several test statistics are proposed for the purpose of assessing the goodness of fit of the multiple logistic regression model. The test statistics are obtained by applying a chi-square test for a contingency table in which the expected frequencies are determined using two different grouping strategies and two different sets of distributional assumptions. The null distributions of these statistics are examined by applying the theory for chi-square tests of Moore Spruill (1975) and through computer simulations. All statistics are shown to have a chi-square distribution or a distribution which can be well approximated by a chi-square. The degrees of freedom are shown to depend on the particular statistic and the distributional assumptions.

The power of each of the proposed statistics is examined for the normal, linear, and exponential alternative models using computer simulations.     

A comparison of the Hosmer–Lemeshow,Pigeon–Heyse,and Tsiatis goodness-of-fit tests for binary logistic regression under two grouping methods

Algebraic relationships between Hosmer–Lemeshow (HL), Pigeon–Heyse (J²), and Tsiatis (T) goodness-of-fit statistics for binary logistic regression models with continuous covariates were investigated, and their distributional properties and performances studied using simulations. Groups were formed under deciles-of-risk (DOR) and partition-covariate-space (PCS) methods. Under DOR, HL and T followed reported null distributions, while J² did not. Under PCS, only T followed its reported null distribution, with HL and J² dependent on model covariate number and partitioning. Generally, all had similar power. Of the three, T performed best, maintaining Type-I error rates and having a distribution invariant to covariate characteristics, number, and partitioning.     

System dynamics: Portraying bounded rationality

This paper examines the linkages between system dynamics and the Carnegie School in their treatment of human decision making. It is argued that the structure of system dynamics models implicitly assumes bounded rationality in decision making and that recognition of this assumption would aid system dynamicists in model construction and in communication with other social science disciplines. The paper begins by examining Simon's ‘principle of bounded rationality’ which draws attention to the cognitive limitations on the information gathering and processing powers of human decision makers. Forrester's ‘Market Growth Model’ is used to illustrate the central theme that system dynamics models are portrayals of bounded rationality. Close examination of the model formulation reveals decision functions involving simple rules of thumb and limited information content. Finally, there is a discussion of the implications of Carnegie philosophy for system dynamics as it affects communication, model structuring, model analysis and future research.