Analysis Of Multidimensional Contingency Tables Research Articles

Differentiation of two Kampo formulae, yokukansankachimpihange and chotosan, for treatment of headache using a predictive model derived from a patient‐based questionnaire database

ABSTRACTAimThe aim of this study was to identify specific indications for treatment with either yokukansankachimpihange or chotosan, Kampo agents commonly used to treat headache refractory to conventional treatments.MethodsOn multidimensional contingency table analysis using the Kampo database, specific symptoms associated with positive outcome for each agent were identified according to Akaike information criterion, and logit regression was used to predict outcome for both agents in individual patients. This predictive model was validated in another 157 patients (M/F, 12/145; age, 20–84 years). The Kampo treatment with the higher probability of positive outcome in each patient was then used for that patient for 1 month.ResultsSpecific symptoms identified as indications for yokukansankachimpihange were stiffness in the back (partial regression coefficient, 2.25), painful sensation in the eyes (3.28), and irritability (0.25). Those for chotosan were morning headache (partial regression coefficient 3.68), vasodilatation of sublingual veins (1.62), and stiff shoulder (1.28). Yokukansankachimpihange may mainly relieve triggering factors of headache. In the validation study, the model predicted greater efficacy for yokukansankachimpihange in 79 patients (M/F, 4/75; age, 20–84 years) and for chotosan in 78 patients (M/F, 8/70; age, 22–78 years). After treatment for 1 month, the predictive accuracy was 76%.ConclusionsSix symptoms serving as practical indications for selection of either yokukansankachimpihange or chotosan to treat patients with headache, were identified.

Multiple taxicab correspondence analysis

We compare the statistical analysis of multidimensional contingency tables by multiple correspondence analysis (MCA) and multiple taxicab correspondence analysis (MTCA). We will show in this paper: First, MTCA and MCA can produce different results. Second, taxicab correspondence analysis of a Burt table is equivalent to centroid correspondence analysis of the indicator matrix. Third, along the first principal axis, the projected response patterns in MTCA will be clustered and the number of cluster points is less than or equal to 1+ the number of variables. Fourth, visual maps produced by MTCA seem to be clearer and more readable in the presence of rarely occurring categories of the variables than the graphical displays produced by MCA. Two well known data sets are analyzed.

Malignant Liver Tumors Treated with MR Imaging–guided Laser-induced Thermotherapy: Experience with Complications in 899 Patients (2,520 lesions)

To evaluate the complications from laser-induced thermotherapy (LITT) of malignant liver tumors and demonstrate that LITT is safe as an outpatient procedure. During 8 years, 899 patients with malignant liver tumors were treated with magnetic resonance (MR) imaging-guided LITT. A total of 2,132 LITT procedures were performed to treat 2,520 lesions. To account for the technical evolution of LITT during this time and the change from performing the procedure on an inpatient basis to performing it on an outpatient basis, patients were assigned to four groups. Overall complication rates and major and minor complications in the inpatient versus outpatient groups were evaluated. Multidimensional contingency table analysis with the chi(2) test was performed. On the basis of a total of 2,132 LITT procedures performed, complications were divided into major and minor categories and detected at clinical or imaging studies. Major complications included three deaths (0.1%) within 30 days after LITT, pleural effusion requiring thoracentesis in 16 (0.8%) cases, hepatic abscess requiring drainage in 15 (0.7%) cases, bile duct injury in four (0.2%) cases, segmental infarction in three (0.1%) cases, and hemorrhage requiring transfusion in one (0.05%) case. Minor complications included postprocedural fever in 710 (33.3%), pleural effusion not requiring thoracentesis in 155 (7.3%), subcapsular hematoma in 69 (3.2%), subcutaneous hematoma in 24 (1.1%), pneumothorax in seven (0.3%), and hemorrhage in two (0.1%) cases. Outpatient management did not significantly affect pleural effusion (P =.96) or subcapsular hematoma (P =.33) rate. MR imaging-guided LITT with local anesthesia is safe and yields an acceptably low rate of major complications.

Modelling in new housing choice—An application

This paper develops a model, using multidimensional contingency table analysis, to begin to unravel some of the complexities of house buying. The model has important practical implications in helping builders, developers and planners educate house buyers and influence the choices which they make. Academic and practitioner research suggests that the ‘hierarchy of effects’ principle can be used to explain the way customers buy houses. The assumption is that ‘primary’ choice issues, like size, price and locality must be satisfied before ‘secondary’ ones, such as whether the property has double glazing, a fitted kitchen or a security system. This paper develops a model of housing choice based on a number of secondary choice issues, such as preferences for different property features, preferences for alternative property designs and how knowledgeable customers were about energy efficiency issues. The modelling techniques applied include cluster analysis and multidimensional contingency table analysis. The work is the result of a UK research project investigating how energy efficient new housing can be marketed.

Discussion of the Papers by Edwards, and Wermuth and Lauritzen

Discussion of the Papers by Edwards, and Wermuth and Lauritzen

Semantics of an Avian Alarm Call System: the Male Domestic Fowl, Gallus Domesticus

AbstractVocal alarm signals of male domestic fowl given in the presence of predators and other ground and aerial objects were recorded and analyzed. Studies were conducted under semi-naturalistic conditions and a telemetric technique was used to facilitate high quality sound recording. Cockerels gave ground alarm calls specifically to objects moving on the substrate and aerial alarm calls to objects moving above in free space. Vocalizations were associated with both dangerous and harmless objects. We therefore investigated variation in sound structure of aerial alarm calls with reference to flying predators and non-predators. A multidimensional contingency table analysis revealed a significant tendency for qualitatively different aerial alarm calls to be associated with flying predators and non-predators. Differences in call structure were restricted to the two first units of the alarm call. We tested the hypotheses that variation in aerial alarm call structure might be affected by either the distance separating the bird from the object or the angular size of the object projected onto the retina of the cockerel. Statistical analysis showed that the angular size was a good predictor of variation of the second unit of alarm call. The distance it self was less predictive. The first unit of the alarm call was not affected by either the distance or the angular size of the object. We propose that this part of the call has a more general function of alerting the conspecific companions. We conclude that alarm vocalizations of male domestic fowl refer specifically to a certain type of stimulus object, either moving on the ground or flying. For alarm calls correlated with aerial stimuli the specific angular size of a stimulus object moving in the air is a good predictor of call structure. We suggest that this way of dealing with flying objects as stimuli for alarm calls is the result of a predator detection strategy in which the benefits of an expanded field of vision, an important adaptation for ground-dwelling birds, exceed the costs of alarming to harmless birds and other aerial objects.

Elementary Analysis of Multidimensional Contingency Tables. Application to a Medical Example1/2

AbstractBy the aid of analysing a medical example a three—step procedure for analysing multi—dimensional contingency tables is introduced. This procedure has some good properties.Step one is due to catch the relationship structure between the variables connected by the contingency table. Hereby only so—called graphical models, a subclass of hierarchical models in regard of the parameters of the log—linear model, are admitted. The models can be generated by combination of hypotheses of pairwise conditional independence. Hereby a so‐called Extended Combination Procedure is proposed using the position of the Chain of (hierarchical) Hypotheses. A useful symbolic notation for ‘Dependence Models’ in addition to that in form of ‘Independence Models’ and ‘Minimal Sets’ is proposed. Step two analyses the significant conditional pairs in regard to the question for what attribute level combinations of the condition complexes the relations remain significant.Step three investigates those tables recognised as significant in step two more closely to get ideas about the ‘sources’ of dependencies and possibilities of collapsing parts of the table.The procedure is mostly used in explorative data analysis although the simple steps can be used to test hypotheses, too.

Statistical Analysis of Multiple Sociometric Relations

Abstract Loglinear models are adapted for the analysis of multivariate social networks, a set of sociometric relations among a group of actors. Models that focus on the similarities and differences between the relations and models that concentrate on individual actors are discussed. This approach allows for the partitioning of the actors into blocks or subgroups. Some ideas for combining these models are described, and the various models and computational methods are applied to the analysis of data for a corporate interlock network of the 25 largest organizations in Minneapolis/St. Paul and for a classic network of 18 monks in a cloister. The computational techniques all involve variations on the standard iterative proportional-fitting algorithm used extensively in the analysis of multidimensional contingency tables.

Statistical Analysis of Multiple Sociometric Relations

Abstract Loglinear models are adapted for the analysis of multivariate social networks, a set of sociometric relations among a group of actors. Models that focus on the similarities and differences between the relations and models that concentrate on individual actors are discussed. This approach allows for the partitioning of the actors into blocks or subgroups. Some ideas for combining these models are described, and the various models and computational methods are applied to the analysis of data for a corporate interlock network of the 25 largest organizations in Minneapolis/St. Paul and for a classic network of 18 monks in a cloister. The computational techniques all involve variations on the standard iterative proportional-fitting algorithm used extensively in the analysis of multidimensional contingency tables.

Courtship Sequences and Ethological Isolation in Two Species of Sunfish (Lepomis Spp) and Their Hybrids

AbstractThe role of courtship behaviour in ethological isolation was studied by analysing courtship sequences between different crosses of pumpkinseed (Lepomis gibbosus), bluegill (L. macrochirus), and their hybrid sunfish. Crosses were established in large laboratory tanks, under an artificially advanced photoperiod and temperature regime, and in outside pools. Male-female interactions were filmed and videotaped. In the field, underwater films of naturally occurring courtship and spawning were taken. A behavioural repertoire was described and the data converted to pairs of male and female acts (dyads). Two contexts were distinguished (spawn and nonspawn) depending on whether courtship led to spawning or not. Several methods of analysis were used. Multidimensional contingency table analysis with factors of preceding act, following act, and cross, enabled examination of the dependence of the response of any individual (sex or species) upon the species of partner. Multidimensional Scaling of the crosses, based on a chi-square measure of overall dissimilarity for each context, revealed the relative proximities among the different interspecific and hybrid crosses and the parentals. The results generally agreed well with those produced by a clustering technique. The conclusions are: (1) The differences between the courtship and spawning behaviour of the parentals are evidence for a behavioural isolating mechanism. (2) Interspecific and hybrid crosses tend to be intermediate to parentals. (3) Courting and spawning behaviour is different in the laboratory and field environments. (4) Hybrids likely originate from crosses of male bluegills and female pumpkinseeds.

The Eastern Ontario survey: a study of drug-treated psychiatric problems in the mentally handicapped.

This study surveyed psychiatric problems treated with psychotropic medication among mentally handicapped at five regional centres in Eastern Ontario. Of the 2,158 residents studied, 920 (43%) were identified as problem cases, ranging from 36% to 83% in different institutions. Aggressivity, hyperactivity, and self-injury are the most prevalent conditions among more than thirty problem categories. Analysis of multidimensional contingency tables revealed that each of these three problems is involved with a distinct pattern of interactions with the set of demographic and clinical variables. The diversity of these interaction patterns points out the inadequacy of any unitary hypothesis of the pathogenesis and the inadvisability of adopting over-generalized treatment modalities. It is proposed that rational planning of service should rely on a realistic estimation of individuals' needs and a better understanding of the scope and nature of the problem.

Evidence of Sex Discrimination: In Similar Populations, Men Are Paid Better Than Women

Abstract. Nationally women earn only 60 percent of the salary income earned by men. Numerous uncontrolled factors, however, might cause such sex‐related differences in salary. In this study, certain factors usually uncontrolled are controlled with the choice of sample populations and by using multidimensional contingency table analysis. The samples consisted of male graduates of University of Hawaii College of Business (n = 311) and female graduates of that college (n = 94). In this comparison, women earned 81 percent of the salary earned by men, although, by the usual measures their backgrounds were similar. Factors of ethnicity, type of job taken, participation rate, and college major did not explain the salary differences between men and women. From this it is inferred that the difference arises from sex discrimination.

The analysis of contingency tables by graphical models

Some aspects of the analysis of multidimensional contingency tables in practice are considered. The class of graphical models defined by Darroch, Lauritzen & Speed (1980) is described, strategies for model selection based on this class are considered and an example is given.

Erratum: Space utilization in a community of temperate reef fishes inhabiting small experimental artificial reefs

Using multidimensional contingency table analysis, we investigated the pattern of space use in an assemblage of nearshore reef fishes inhabiting small artificial reefs in Barkley Sound, British Columbia. Two variables, (1) shelter type and size, and (2) elevation above substrate, were specifically studied. All species had precise microhabitat requirements, and they all showed segregation in the spatial dimension, with the exception of the pair Sebastes caurinus – S. maliger. Only Sebastes melanops showed consistent shifts in its space use in response to increases in the density of the other members of the community, indicating that, with this exception, interspecific competition was probably a weak force in this system.

Space utilization in a community of temperate reef fishes inhabiting small experimental artificial reefs

Using multidimensional contingency table analysis, we investigated the pattern of space use in an assemblage of nearshore reef fishes inhabiting small artificial reefs in Barkley Sound, British Columbia. Two variables, (1) shelter type and size, and (2) elevation above substrate, were specifically studied. All species had precise microhabitat requirements, and they all showed segregation in the spatial dimension, with the exception of the pair Sebastes caurinus – S. maliger. Only Sebastes melanops showed consistent shifts in its space use in response to increases in the density of the other members of the community, indicating that, with this exception, interspecific competition was probably a weak force in this system.

The Interregional Linkages between National and Regional Input-Output Models

Elements of information theory are applied to the problem of estimating interregional flow coefficients in a national system of regions. The inclusion of constraints relating to the capacity of the transportation system justifies the adoption of Jaynes' principle of maximum uncertainty, in place of iterative proportional fitting procedures developed for multidimensional contingency table analysis. The inclusion of a priori information is also discussed.

On tests of homogeneity of factorially-structured populations: An additive approach

SUMMARY Lancaster's additive approach to absence of interaction in contingency tables has been used quite frequently in agriculture in recent years, sometimes incorrectly. In this paper, we wish to compare the frequency distributions of response for a number of treatment groups which are factorially structured. An additive model is proposed which enables us to examine the role of the individual factors in explaining any differences among responses. Test statistics are developed, and the theory is illustrated with a number of agricultural experiments. The analysis of multidimensional contingency tables has received a good deal of attention in recent years. The most commonly used analyses are based on log linear models and the multiplicative definition of zero higher-order interactions. However, there has also been some interest in the additive model developed by Lancaster (1949, 1951, 1971). The two approaches have been compared by Darroch (1974), Murphy (1978) and O'Neill (1982). Although they often lead to the same conclusions there may be instances when large differences arise. This paper considers the partition of x2 in three-way factorial experiments involving frequency data, in which one of the factors is a response variable and the other two factors have bivariate marginal totals fixed by the experimental design. Such experiments are common in agriculture, where for example a number of animals are allocated randomly to treatment groups factorially structured and then classified according to their response. Lancaster's method is based on an expansion of the theoretical probabilities using orthonormal functions which are simply related to the columns of an orthogonal matrix. The partitioning produces main effects and interactions in a similar way to the traditional analysis of variance, with a further decomposition into single degrees of freedom corresponding to linear and nonlinear trends, or to comparisons within and between treatment groups. However the method has a few complications. First, even under the null hypothesis of no second-order interaction, the test statistic is not asymptotically x2 if first-order interactions are present. This problem was pointed out by many authors including Plackett (1962), Darroch (1962), Goodman (1964), Lancaster

Proposals for a descriptive analysis of multidimensional contingency tables of unarrayed numerical distributions

Proposals for a descriptive analysis of multidimensional contingency tables of unarrayed numerical distributions

Cancer and drinking water in Louisiana: colon and rectum.

A case-control mortality study conducted in 20 parishes (countries) of South Louisiana to determine what relationship drinking Mississippi River water might have on mortality from colon or rectal cancer, found a significant risk for rectal cancer associated with surface water. Rectal and colon cancer deaths (692 and 1167) from 1969 to 1975 were matched to non-cancer deaths by age at death (+/- 5 years), year of death, sex and race, and within groups of parishes with similar industrial and urban-rural characteristics, each group being defined so as to ensure that it included as nearly as possible equal populations using water from ground and surface sources, based on the 1970 census. Colon cancer did not relate significantly to any water variable, but rectal cancer associated strongly with surface, or Mississippi River, water. The odds ratio for rectal cancer between those who were born and died on ground water was 2.07 with 95% C.I.: (1.49-2.88). A multi-dimensional contingency table analysis found the association between rectal cancer and surface water significant at the .0001 level and not dependent on age, race, sex or year of death. The risk for men was slightly higher than for women, but both sexes showed an increased risk. Chlorination also associated significantly with rectal cancer. Among those who used river water, the risk increased inversely as the distance from the mouth, with greater risk downstream from the many industries which line the river.

Factors that affect Type I and Type II error rates in the analysis of multidimensional contingency tables.

Factors that affect Type I and Type II error rates in the analysis of multidimensional contingency tables.