Matrix Programming Language Research Articles

Synthesizing Population for Microsimulation-based Integrated Transport Models Using Atlantic Canada Micro-data

Due to the lack of availability of micro-data of population characteristics, the synthesis of individual and household attributes is a necessary step for developing a disaggregate, dynamic travel demand forecasting model. Agent-based micro-simulation models attempt to forecast travel behaviour of individuals and households by simulating the behaviour of the singular actors in the system. The framework for generating synthesis population presented in this paper is a fundamental contribution to the development of an Integrated Transport, Land Use and Environment Modelling System in Nova Scotia, Canada. In this paper, a population is synthesized for individuals and households in Atlantic Canada using the Fitness Based Synthesis (FBS) approach. A synthetic algorithm is designed that allows both individual and household attribute levels to synthesize simultaneously. Unequal probabilities based on the sampling weight are used in the household selection step of the algorithm. In this way, the performance and accuracy of the synthetic population produced has been improved. The synthetic algorithm is tested for two functions: first, using the one level (household) control tables; and second, using two levels (individual and household) control tables. The data used in this study is collected from the 2006 Canadian Census and the 2006 Public Use Micro-data File (PUMF). The algorithm is implemented using a high-level matrix programming language for numerical computation in MATLAB. The results show that the synthetic population with both individual and household level attributes has the best fitness value.

The marginal willingness-to-pay for attributes of a hypothetical HIV vaccine

This paper estimates the marginal willingness-to-pay for attributes of a hypothetical HIV vaccine using discrete choice modeling. We use primary data from 326 respondents from Bangkok and Chiang Mai, Thailand, in 2008–2009, selected using purposive, venue-based sampling across two strata. Participants completed a structured questionnaire and full rank discrete choice modeling task administered using computer-assisted personal interviewing. The choice experiment was used to rank eight hypothetical HIV vaccine scenarios, with each scenario comprising seven attributes (including cost) each of which had two levels. The data were analyzed in two alternative specifications: (1) best-worst; and (2) full-rank, using logit likelihood functions estimated with custom routines in Gauss matrix programming language. In the full-rank specification, all vaccine attributes are significant predictors of probability of vaccine choice. The biomedical attributes of the hypothetical HIV vaccine (efficacy, absence of VISP, absence of side effects, and duration of effect) are the most important attributes for HIV vaccine choice. On average respondents are more than twice as likely to accept a vaccine with 99% efficacy, than a vaccine with 50% efficacy. This translates to a willingness to pay US$383 more for a high efficacy vaccine compared with the low efficacy vaccine. Knowledge of the relative importance of determinants of HIV vaccine acceptability is important to ensure the success of future vaccination programs. Future acceptability studies of hypothetical HIV vaccines should use more finely grained biomedical attributes, and could also improve the external validity of results by including more levels of the cost attribute.

Analyzing Longitudinal Data in the Presence of Informative Dropout: The Jmre1 Command

Many studies in various research areas have designs that involve repeated measurements over time of a continuous variable across a group of subjects. A frequent and serious problem in such studies is the occurrence of missing data. In many cases, missing data are caused by an event that leads to a premature termination of the series of repeated measurements on some subjects. When the probability of the occurrence of this event is related to the subject-specific underlying trend of the variable of interest, this missingness process is called informative censoring or informative dropout. Standard likelihood-based methods (for example, linear mixed models) fail to give consistent estimates. In such cases, one needs to apply methods that simultaneously model the observed data and the missingness process. In this article, we review a method proposed by Touloumi et al. (1999, Statistics in Medicine 18: 1215–1233) to adjust for informative dropout in longitudinal data analysis. We also present the jmre1 command, which can be used to fit the proposed model. The estimation method combines the restricted iterative generalized least-squares method with a nested expectation-maximization algorithm. The method is implemented mainly using Stata's matrix programming language, Mata. Our example is derived from the epidemiology of the HIV infection.

Computing the Moore–Penrose inverse of a matrix with a Computer Algebra System

In this paper Derive functions are provided for the computation of the Moore–Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore–Penrose inverse. Making it possible to compute the Moore–Penrose inverse easily with one of the most commonly used Computer Algebra Systems–and to have the blueprint to write such a function in other Computer Algebra Systems or in a matrix programming language such as Gauss–may promote the use of generalized inverses in the teaching of linear algebra.

Efficient Calculation of Jackknife Confidence Intervals for Rank Statistics

An algorithm is presented for calculating concordance-discordance totals in a time of order N log N , where N is the number of observations, using a balanced binary search tree. These totals can be used to calculate jackknife estimates and confidence limits in the same time order for a very wide range of rank statistics, including Kendall's tau, Somers' D, Harrell's c, the area under the receiver operating characteristic (ROC) curve, the Gini coefficient, and the parameters underlying the sign and rank-sum tests. A Stata package is introduced for calculating confidence intervals for these rank statistics using this algorithm, which has been implemented in the Mata compilable matrix programming language supplied with Stata.

User-Friendly Parallel Computations with Econometric Examples

This paper shows how a high-level matrix programming language may be used to perform Monte Carlo simulation, bootstrapping, estimation by maximum likelihood and GMM, and kernel regression in parallel on symmetric multiprocessor computers or clusters of workstations. The implementation of parallelization is done in a way such that an investigator may use the programs without any knowledge of parallel programming. A bootable CD that allows rapid creation of a cluster for parallel computing is introduced. Examples show that parallelization can lead to important reductions in computational time. Detailed discussion of how the Monte Carlo problem was parallelized is included as an example for learning to write parallel programs for Octave.

A Recursive Algorithm For Fractionally Differencing Long Data Series

We propose a recursive algorithm to fractionally difference time series data. The algorithm eliminates the need to evaluate the gamma function directly, and hence avoids the overflow problem that arises when fractionally differencing a long data series. The proposed algorithm can be implemented using any general matrix programming language. An implementation using SAS is presented. The algorithm and the code provide a practical approach to including fractional differencing as part of a time series data analysis.

Econometric and Statistical Computing Using Ox

This paper reviews the matrix programming language Ox from the viewpoint of an econometrician/statistician. We focus on scientific programming using Ox and discuss examples of possible interest to ...

Review of SsfPack 2.2: statistical algorithms for models in state space

Summary SsfPack is a set of procedures with a strong link to the object-oriented matrix programming language Ox. In this review I Þrst discuss installation issues and prerequisites for a productive use of SsfPack, namely statistical and econometric knowledge, programming skillsandadditionalsoftware. NextIdiscussthedocumentationandsampleprograms. Before concluding I discuss extensions in the direction of user-friendly programs.

R: yet another econometric programming environment

SUMMARY This article reviews R, an open-source S-like high-level matrix programming language that can be used for econometric simulations and data analysis. Copyright # 1999 John Wiley & Sons, Ltd.

A genetic algorithm (GA) approach to the calculation of canonical variates (CVs)

Genetic algorithms (GAs) are numerical search routines that mimic the evolutionary processes in nature. The GA's equivalents of chromosomes and genes are the unknown parameters in a mathematical model, and just as in biological evolution, these breed and mutate to produce improved solutions with each successive generation. In this paper, GAs are disclosed for tackling multivariate classification problems, using an approach derived from the dimension-reduction method of canonical variates analysis. These algorithms can be applied directly to high-dimensional data (where the number of variates exceeds the number of observations). The incorporation of cross-validation guards against model overfitting. The algorithms are presented in the Matlab matrix programming language.

Discriminant analysis with singular covariance matrices. A method incorporating cross-validation and efficient randomized permutation tests

A computationally efficient approach has been developed to perform two-group linear discriminant analysis using high-dimensional data. The analysis is based on Fisher's method and incorporates two important validation stages: 1, full leave-one-observation-out cross-validation; 2, randomized permutation distribution testing. The resulting algorithm and software are known as CREDIT (cross-validated random-permutation-tested efficient discrimination based on an adjusted generalized inverse for the sample total covariance matrix). The algorithm has been implemented in the SAS/IML matrix programming language and provides dramatic improvements in computational efficiency compared with existing software for discriminant analysis incorporating validation stages 1 and 2 above. Application of CREDIT to nine multivariate data sets indicates that the predictive performance of the approach, assessed using cross-validation, is comparable with that of other methods for discriminant analysis. Comparisons with two specific methods are included. Randomized permutation tests show that success rates using the true response classes are almost always better than success rates using random permutations of the classes. This gives confidence that there is a useful linear discriminant relationship present in the data being analysed. For a randomly selected training set (used to construct the discriminant rule) the success rates for CREDIT are unbiased predictive success rates for allocating other observations to groups. Predicting group memberships for future observations using any discriminant model based on singular estimates of covariance matrices must be performed with great care. A discussion of methods to test the concordance of future observations with the training set is given.

Data Analysis Using GAUSS and Markov

GAUSS can be used in a variety of ways for statistical computing. Most simply, it is an interactive matrix calculator. It is also a standard statistical package in which you specify the data, variables, and type of analysis and let the program do the computations. And, finally, GAUSS is a powerful matrix programming language that is ideal for statistical computations. GAUSS's strength lies in its ability to move among these levels of use. This article begins with a review of GAUSS's main features, followed by a didactic example of the different ways that a multiple regression can be computed. This leads to a demonstration of GAUSS's programming capabilities for a series of nonstandard statistical problems.

A PC program for performing multigroup longitudinal comparisons using the Potthoff-Roy analysis and orthogonal polynomials

A PC-program performing the Potthoff-Roy (PR) multigroup ( G-sample) analysis of longitudinal data is described and illustrated. This program and the underlying statistical model are useful in the comparison of several longitudinal samples. Applications include the study of growth, development, adaptation, aging, and treatment effects (in short, any phenomenon in which the passage of time is important) for which serial data are available. Specifically, this method fits polynomials to the average growth curves in the samples, and tests hypotheses concerning the curves themselves and the individual coefficients of the polynomials. The program features the utilization of orthogonal polynomial regression coefficients (OPRCs) and is written in GAUSS, a relatively inexpensive yet comprehensive matrix programming language. It is documented that using OPRCs to comprise the within-individual or time design matrix has several advantages over the more usual choice of the successive-powers-of- t form of this matrix and an example of one important such advantage is provided. GAUSS was employed to make the program readily-accessible (i.e., executable code) to biomedical investigators. The GAUSS compiler is not required to run this program. Information regarding the availability of the program is provided in the Appendix.

FAN: a program for the analysis of concentration fluctuation data

FAN is a software program designed to be an efficient and flexible tool for data analysis and signal processing of turbulent fluctuations in time series of various atmospheric boundary-layer variables (e.g., scalar concentration, wind speed and direction, etc.) measured in full-scale atmospheric field experiments. It is intended to ease data management and analysis of high-volume data sets obtained from modern high-resolution boundary layer field programs and laboratory experiments. A number of characteristics features of FAN such as the command-line interpreter, the structure of the command-mode statements and matrix programming language, the graphical capabilities for data representation and visualization, and the built-in functions for data analysis (e.g., probabilistic and statistical analysis, time series and spectral analysis, etc.) are described. The application of FAN to a case example is provided to illustrate and demonstrate its utility and efficacy for analysis of a high-volume concentration fluctuation data set.

Implementation of Hills' growth curve analysis for unequal-time intervals using GAUSS.

Longitudinal data are widely regarded as the most efficient and informative type of data with which to investigate growth. Paradoxically, appropriate statistical methods for analyzing longitudinal data have been unavailable; with the exception of a computer program for executing Rao's (Biometrika 46:49-58, 1959) one-sample polynomial growth curve analysis (Schneiderman and Kowalski, Am. J. Phys. Anthropol. 67:323-333, 1985) and another applying the Preece-Baines function (Brown and Townsend, Ann. Hum. Biol. 9:495-505, 1982), no programs for analyzing longitudinal data are generally available to the scientific community. Whereas much of the pediatrically oriented work has involved fitting growth curves for individual children, the concern here is the estimation of growth trends for populations. An Adequate understanding of average tendencies is a prerequisite to understanding the growth of individuals. The present paper implements Hills' (Biometrics 24:189-196, 1968) analysis, which is formally equivalent to Rao's but uses finite differences instead of orthogonal polynomials. This method is suitable for data collected at unequal time points and generates explicit measures of velocity and acceleration. The polynomial specification of the curve that best fits the data is also determined with this method. An additional advantage of this approach is that it is conceptually simpler than the classic model of Rao. An application of this method is given using the same craniofacial growth data as in our earlier (1985) paper for comparability. We provide an easy to use program written in GAU's (Edlefson and Jones, Kent, WA; Applied Technical Systems, 1985), a matrix programming language that runs on PC-compatible microcomputers. This implementation for PCs extends the accessibility to investigators who may not have access to mainframe computers.