Frank M.T.A. Busing

Delete-m Jackknife for Unequal m

In this paper, the delete-mj jackknife estimator is proposed. This estimator is based on samples obtained from the original sample by successively removing mutually exclusive groups of unequal size. In a Monte Carlo simulation study, a hierarchical linear model was used to evaluate the role of nonnormal residuals and sample size on bias and efficiency of this estimator. It is shown that bias is reduced in exchange for a minor reduction in efficiency. The accompanying jackknife variance estimator even improves on both bias and efficiency, and, moreover, this estimator is mean-squared-error consistent, whereas the maximum likelihood equivalents are not.

Avoiding degeneracy in metric unfolding by penalizing the intercept

It has long been thought that degeneracy in unfolding only concerned non-metric unfolding. Recently, Busing, Groenen, and Heiser have established that degeneracy occurs for all transformations that include estimation of an intercept and a slope. Consequently, degeneracy also plagues metric unfolding, since one member of the metric transformation family, the interval transformation, includes estimation of both an intercept and a slope. In this paper, a simple solution is proposed to the degeneracy problem for metric unfolding by penalizing for an undesirable intercept. An application of this approach will illustrate its potential.

Assessing the asymmetric effects on branch rivalry of Spanish financial sector restructuring

Spanish financial institutions have been heavily affected by the banking crisis that began in 2008. Many of them, especially Spanish savings banks (or Cajas), had to merge with other institutions or had to be rescued. We address the question of up to what point the nature of competition in this sector has changed as a result of the crisis. Although institutions compete in many ways, we concentrate on their presence in the main street through bank branches open to the public (i.e., retail banking competition). Our measure of inter-firm rivalry is based on a geographical proximity measure that we calculate for the years 2008 (before the crisis) and 2012 (the last available data set). The technical approach is based on multidimensional unfolding, a methodology which allows us to graphically represent the asymmetric nature of such rivalry. These maps visualise the salient aspects of the system during the two dates analysed, and can be understood without a detailed technical knowledge.

Unfolding Incomplete Data: Guidelines for Unfolding Row-Conditional Rank Order Data with Random Missings

Unfolding creates configurations from preference information. In this paper, it is argued that not all preference information needs to be collected and that good solutions are still obtained, even when more than half of the data is missing. Simulation studies are conducted to compare missing data treatments, sources of missing data, and designs for the specification of missing data. Guidelines are provided and used in actual practice.

104 Parents’ risk perception about childrens’ injuries and burns: a multidimensional unfolding technique

Background Unintentional injuries are a significant issue of public health, accounting 60% of infant mortality around the globe. In Mexico, burns are the most frequent injury at home. This research explores parents risk perceptions about children’s injuries and burns. Methods Multidimensional unfolding is a technique that maps ranking data into a low-multidimensional space that allows for a visual comprehension of the data. 28 parents of Guadalajara, Mexico (15 mothers, 13 fathers), were asked to sort three series of cards (adverse events, agents that could cause a burn, and people who take care of a child) by two different criteria: probability and severity. The last series was sorted only by probability. Results The five perceptual maps have two dimensions, which show two sets of objects each: the subjects (the sample of 28 parents) as numbers, and the objects (either adverse events, agents that could cause a burn or people who take care of a child) as labels. The closer a number is to a label, the more probable or severe the label is considered by that number. Unfolding also permits for sub-dimensions or clusters in the configuration. Parents perceived as more probable to happen: fall, choking, and cut. They did not considered cut and fall as severe. Sun, hot liquids, and hot objects were the most probable agents. None perceived sun, ice, hot objects, smoke, and steam as severe agents. Mother and father were considered the least probable to experience a children’s injury. Conclusions Multidimensional unfolding is an exploratory technique; ideal for research for the first time in Mexico, parents perceived risks or not. For example, smoke was perceived as not probable to cause a burn and ignore as severe. According to the World Health Organisation, burns include the respiratory damage resulting from smoke, being the most frequent cause of death. Parents were omitting important information. This is only the first step, is essential further investigation in this area.

1025 Technologies’ use, perceived risks, benefits and laws: a multidimensional unfolding tecnique

Background The use of the technologies in the everyday life brings benefits and risks, being a lot of them in home. According to the World Health Organisation, 90% of injuries to young children occur in or around home. Burns being in this place, the most frequent injury in Mexico. Methods Multidimensional unfolding is a technique that maps ranking data into a low-multidimensional space that allows for a visual comprehension of the data. 28 parents of Guadalajara, Mexico (15 mothers, 13 fathers), were asked about frequency of use of technologies; involving cooking equipment, light, and heat sources. Then they sorted them in a series of cards, by three different criteria: perceived risk, benefits and the necessity for law implementation in their use. Results The most used technologies were gas stove, lighter, water heater, iron, matches and microwave. The least used technologies were oil lamp, fireworks, wood stove, gas grill and electric grill. The three perceptual maps obtained have two dimensions, which show two sets of objects each: the subjects (the sample of 28 parents) as numbers, and the objects (each technology) as labels. Parents perceived: more risks from fireworks and wood stove; most benefits from gas stove, water heater, and microwave; and the need of laws for fireworks. Conclusions Laws are one of the most efficient ways to get people to adopt safe behaviours. Although it is important to consider that, people are more willing to accept laws for those things that they do not use or perceive as beneficial. In this case, parents did not use fireworks and also perceived them as risky without benefit and with the necessity of laws. Unlike the gas stove, being the most used, perceived with more benefits; without risks, and no need for laws. This is the first exploration in Mexico about the theme. An overwhelming majority of burns occur in house and kitchen; it requires further research about overconfidence and optimism bias around technologies.