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Background: Inactivity levels in the USA are considered a critical public-health issue. Promoting physical activity through active transportation may prove effective to increase activity levels. The purpose of this study was to understand perceptions and likelihood of using various bicycle infrastructures for transportation by Las Vegas residents. Methods: A survey was developed and administered (n = 457). Multinomial regression was used to create predictions to determine which infrastructures were perceived as safe and most likely to be used for transportation; frequencies were analyzed. Results: The infrastructure chosen least often (2.2%) had the least amount of distance separating bikers from vehicles, and the least amount of protection. The type most likely to be used (27.6%) contained the most signage and significant separation from vehicles. The infrastructure least likely perceived to be adequate for biker safety was a shared bus/bike lane with 19.4% agreeing this was safe. Probabilities revealed differences in infrastructure preferences based on demographic characteristics. Conclusions: In order to increase active transportation rates effectively, residents' perceptions of safety and infrastructure preferences should be considered. Results from this study showed that respondents had many safety concerns with the current bicycling infrastructure in Las Vegas and provided ideas for future infrastructure investments and related policies.
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Multinomial logistic regression to estimate and predict
perceptions of bicycle and transportation infrastructure
in a sprawling metropolitan area
Courtney Coughenour1, Alexander Paz2, Hanns de la Fuente-Mella3, Ashok Singh4
1
School of Community Health Sciences, University of Nevada Las Vegas, 4505 S. Maryland Pkwy, Box 3050, Las Vegas, NV 89154-4015, USA
2
Department of Civil and Environmental Engineering and Construction, University of Nevada Las Vegas, 4505 Maryland Parkway, Box 454015, Las Vegas, NV 89154-4015, USA
3
Facultad de Ciencias Econo´micas y Administrativas, Pontificia Universidad Cato´lica de Valparaı
´so, Avenida Brasil, 2830, Valpar
´so, Chile
4
William F. Harrah College of Hotel Administration, University of Nevada Las Vegas, 4505 Maryland Parkway, Box 6021, Las Vegas, NV 89154-4015, USA
Address correspondence to Courtney Coughenour, E-mail: courtney.coughenour@unlv.edu
ABSTRACT
Background Inactivity levels in the USA are considered a critical public-health issue. Promoting physical activity through active transportation
may prove effective to increase activity levels. The purpose of this study wasto understand perceptions and likelihood of using various bicycle
infrastructures for transportation by Las Vegas residents.
Methods A survey was developed and administered (n¼457). Multinomial regression was used to create predictions to determine which
infrastructures were perceived as safe and most likely to be used for transportation; frequencies were analyzed.
Results The infrastructure chosen least often (2.2%) had the least amount of distance separating bikers from vehicles, and the least amount of
protection. The type most likely to be used (27.6%) containedthe most signage and significant separation from vehicles. The infrastructure least
likely perceived to be adequate for biker safety was a shared bus/bike lane with 19.4% agreeing this was safe. Probabilities revealed differences in
infrastructure preferences based on demographic characteristics.
Conclusions In order to increase active transportation rates effectively, residents’ perceptions of safety and infrastructure preferences should be
considered. Results from this study showed that respondents had many safety concerns with the current bicycling infrastructure in Las Vegas and
provided ideas for future infrastructure investments and related policies.
Keywords communities, environment, physical activity
Introduction
Physical inactivity in the USA is one of the leading causes of
death, contributing to multiple chronic diseases and shor-
tened life expectancy. Nationwide, 50% of the population
self-reports that they participate in enough aerobic physical
activity, which is 150 min of moderate physical activity per
week.
1
This is insufficient to meet the 2008 Physical Activity
Guidelines for Americans. However, a sample that represented
national norms, using physical activity levels that were mea-
sured objectively, found that only 9.6% actually met the guide-
lines.
2
At this point, the level of inactivity of Americans has
reached an alarming level, and has become a critical public
health issue.
For decades, attempts to increase levels of physical activity
focussed on changing behaviours at the individual level, target-
ing one person at a time. While these efforts may be effective
in the short term, studies have shown that such interventions
have low rates of maintenance after the interventions have
ceased.
3,4
For this reason, the promotion of physical activity by
means of active transportation may prove effective as a means
Courtney Coughenour, Assistant Professor
Alexander Paz, Associate Professor
Hanns de la Fuente-Mella, Associate Professor
Ashok Singh, Professor
#The Author 2015. Published by Oxford University Press on behalf of Faculty of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com. 1
Journal of Public Health | pp. 1 8 | doi:10.1093/pubmed/fdv179
Journal of Public Health Advance Access published December 13, 2015
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to increase activity levels. Active transportation incorporates
physical activity into daily routines, such as walking to and from
work or errands, enabling the attainment of minutes of physical
activity without the conscious decision, and a high level of
commitment required for recreational physical activity.
In an attempt to increase physical activity levels, more
recent efforts have involved approaches at a population level.
The Community Preventive Services Task Force—a group of
independent, unpaid, public health and prevention experts that
provide evidence-based findings and recommendations on a
number of topics—recommended the use of environmental
and policy approaches to increase physical activity, specifically,
policies on street-scale urban-design land use.
5
Evidence shows
that street-scale elements—such as the availability of sidewalks,
bicycling facilities, proximity to transit stops
6
as well as adequate
lighting
7
are associated with increased minutes of physical activ-
ity. As such, understanding street-scale factors that may result
in an increase in active transportation rates may be one way to
increase rates of physical activity effectively.
The metropolitan area around Las Vegas, NV is sprawling,
similar to many metropolitan areas developed in the post-
automobile era. Although this region consists of over 2
million residents, it lacks a central urban core that most trad-
itional—that is, older—cities have; this results in housing and
other land uses (retail, office and commercial) being spread
over long distances. Given the amount of urban sprawl in Las
Vegas, active transportation that incorporates the use of bicyc-
ling would enable residents to travel longer distances in more
convenient amounts of time by means of either active trans-
port alone or in combination with public transportation.
The purpose of this study was to understand perceptions
and likelihood of using various types of bicycle infrastructures
for transportation purposes by Las Vegas residents.
Methodology
A survey questionnaire was developed to capture preferences
about seven alternative configurations for bike-lanes. Figure 1
shows each of the seven configurations. The survey included
socioeconomic characteristics as well as other questions
related to infrastructure, biking habits and the use of transit.
The survey was administered in person and online; it targeted
bus riders, bike riders and drivers of personal vehicles.
Trained surveyors approached residents at bus stops, on bus
routes, and at local businesses and common areas surround-
ing major transit corridors. An identical survey was distribu-
ted online through local biking and non-biking member lists.
In addition, a snowball methodology for sampling was used,
by which respondents were asked to share the survey link
with local friends and relatives. The survey included Likert
scale, multiple choice, open-ended and demographic ques-
tions; it took 10 min to complete, and the respondents
were not compensated. This study design was given exempt
status from the Internal Review Board (IRB) of the University
of Nevada, Las Vegas (UNLV).
A discrete choice model was estimated to determine signifi-
cant attributes and socioeconomic characteristics that are likely
to influence preferences about the various infrastructure con-
figurations in the survey. Probit and multinomial Logit models
were estimated to determine the best model specification. A
multinomial rather than a binary model is required because
the number of available choices, infrastructure configurations,
were seven. A multinomial Logit model is an extension of mul-
tiple regression modelling, where the dependent variable is dis-
crete instead of continuous, enabling the modeling of discrete
outcomes. In particular, we were interested in characterizing
the probability of individual choices conditioned to the values
of the attributes and socioeconomic characteristics. The estima-
tion requires defining the reference category with which the
results will be compared. Thus, the infrastructure choice which
most resembled the dominant infrastructure type in the Las
Vegas metropolitan area was used as the reference category
(non-painted 5-ft bike lane). The model can be used to estimate
choice probabilities. In addition, the model provides informa-
tion about the relative importance of the explanatory variables
(significant attributes and socioeconomic characteristics).
Results
Descriptive analysis
Overall, 457 surveys were completed in their entirety. Of the
respondents, 67.8% reported using a personal vehicle as their
primary mode of transportation, 26.2% reported using public
transit (bus) and 6.0% reported using a bicycle. Four respon-
dents reported that walking was their primary mode of trans-
portation; however, they were removed from analysis due to
the small sample size.
The respondents were asked a series of questions regarding
safety as well as the likelihood they would use one or more of
seven different options for bicycling infrastructures. In add-
ition, they were asked to choose one option that they would
most likely use if they used bicycling for transportation. The
most frequently chosen infrastructure the respondents were
most likely to use was option B (27.8%), a non-painted 8-ft
bicycle lane with a 3-ft buffer and reflective posts on a non-
major roadway. The least chosen infrastructure was Option A
(2.0%), a non-painted 5-ft bicycle lane with no buffer on a
non-major roadway. Respondents perceived Option C as the
safest and having the most adequate signage. Figure 1shows
each of the seven configurations along with the respondents’
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perceptions of safety and likelihood of use, and the frequency
in which each configuration was chosen as the most preferred
alternative.
Multinomial logistic regression
First, a linear model was run on the response as a function of
the predictors to ensure that there were no multicollinearity
issues; only predictors with variance inflation factors (VIF)
,2 were included in this model (VIF age: 1.342; VIF gender:
1.069; VIF how_often_ public transport: 1.354; VIF auto-
mobiles_household: 1.208; VIF bike_daily: 1.116; VIF
income: 1.517).
Table 1provides the list of categorical socioeconomic char-
acteristics as well as the list of choices available to the partici-
pants in the survey. In addition, age information was collected
with a minimum, maximum, average and standard deviation
AB
CD
Fig. 1 Each infrastructure option, perceptions of safety and likelihood of use foreach, and frequencies which that option was chosen as the infrastructure type
most likely to be utilized.
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of 16, 77, 37.78, 13.13, respectively. The dependent variable
had one value observed in 422 subpopulations, and the most
frequently chosen infrastructure was B (27.8%). Of the
respondents, 69.8% reported they did not bike daily; 59.5%
were male, 34.4% reported a yearly income less than $30 000,
and 37.4% reported that they never used public transporta-
tion. Regarding the model fitting information, the
x
2
ratio
tests had a value of 296.689 (P-value ,0.000) (AIC criterion
1396; Hannan-Quinn criterion: 1463), indicating good model
fit. In addition, acceptable values were obtained from pseudo
r
2
(Cox and Snell: 0.478; Nagelkerke: 0.495).
Logit models provided better goodness of fit compared with
the general Probit models. This is likely because the unob-
served factors are not normally distributed; the goodness-of-fit
indicators and power of classification of the best Probit model
are lower than those obtained by the best Logit model.
E
G
F
Fig. 1 Continued
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The best Probit model resulted in the following:
x
2
ratio tests:
9.40822 (P-value ,0.00905798) and the goodness-of-fit
indicators and power of classification with a AIC criterion:
1547, Hannan-Quinn criterion: 1566,
x
2
ratio tests: 14.1785
(P-value ,0.0277), and power of classification: 34.1%.
Table 2indicates that the power of the logistic multinomial
model was suitable, as it correctly classified 45.7% of the
known observations and could be expected to project future
estimates. Table 3shows the multinomial logistic regression
model for all coefficients. The reference category for the
model was Infrastructure A, as it best represented the most
common infrastructure in the Las Vegas metropolitan area.
When examining the odds ratio, people who reported
biking daily compared with those who do not bike daily were
most likely to choose Infrastructure D over A. People who
reported an income of $70000$89 999 were most likely to
choose Infrastructure B, and people who reported using public
transit very often were most likely to choose Infrastructure
D. Those who reported using public transit rarely, compared
with those who reported never using it, had increased odds of
0.17 of choosing Infrastructure B over A.
Regarding the predictions, the above-mentioned parameters
were used to estimate the future value of the possibilities of oc-
currence. The probabilities were examined of both males and
females of the oldest and youngest age categories reported by
respondents, the mean age and those who reported biking daily
and not biking daily. The oldest age group was most likely to
fall in the highest income category, and had at least two vehicles
in the household. The youngest age category was most likely
to fall into the lowest income category, and had no vehicles in
the household. The mean age was 38 years, and the median
income was $50 000 –$69 999. Thus, these categories were
used to estimate probabilities.
Table 1 Categorical variables
Category NMarginal
percentage (%)
Infrastructure
choice
A 9 2.0
B 127 27.8
C 124 27.1
D 20 4.4
E 28 6.1
F 87 19.0
G 62 13.6
Bike daily Yes bike trips daily 138 30.2
No bike trips daily 319 69.8
Gender Male 272 59.5
Female 185 40.5
Income Less than $30 000 157 34.4
$30 000 –49 999 59 12.9
$50 000 –69 999 77 16.8
$70 000 –89 999 43 9.4
$90 000 –150 000 79 17.3
Greater than 150 000 42 9.2
How often do
you use public
transportation?
Very often 62 13.6
Often 50 10.9
Rarely 74 16.2
Very rarely 100 21.9
Never 171 37.4
Ethnicity American Indian or Alaska Native 2 0.4
Asian 37 8.1
Black or African American 40 8.8
Hispanic, Latino or Spanish origin 57 12.5
Native Hawaiian or other Pacific
Islander
11 2.4
White 290 63.7
Some other race 18 4.0
Table 2 Power of classification
Observed Predicted
A B C D E F G Percent correct
A 0 4 5 0 0 0 0 0.0%
B 0 95 14 0 1 5 12 74.8%
C 0 25 90 0 0 8 1 72.6%
D 0 8 11 0 0 1 0 0.0%
E 0 21 2 0 0 3 2 0.0%
F 0 22 50 0 1 12 2 13.8%
G 0 42 4 0 0 4 12 19.4%
Overall percentage 0.0% 47.5% 38.5% 0.0% 0.4% 7.2% 6.3% 45.7%
MULTINOMIAL LOGISTIC REGRESSION TO ESTIMATE AND PREDICT PERCEPTIONS OF BICYCLE 5
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Table 3 Results of a multinomial logistic regression model reflecting the choice of infrastructure
Infrastructure choice
B
Exp (B)
C
Exp (B)
D
Exp (B)
E
Exp (B)
F
Exp (B)
G
Exp (B)B SE B SE B SE B SE B SE B SE
Intercept 4.730* 2.276 4.433* 2.328 3.206 2.572 3.165 2.466 3.586 2.354 4.136* 2.352
Age 0.033 0.032 1.034 20.009 0.032 0.991 0.012 0.037 1.012 0.042 0.035 1.043 0.011 0.032 1.011 0.037 0.033 1.038
Number vehicles
in household
20.407 0.323 0.666 20.313 0.313 0.731 20.346 0.364 0.707 20.726 0.400 0.484 20.384 0.320 0.681 20.476 0.342 0.621
Bike daily
a
20.988 0.822 0.372 22.413* 0.823 0.090 21.824* 0.950 0.161 20.963 0.903 0.382 22.576* 0.843 0.076 21.894* 0.857 0.150
Gender
b
21.167 0.888 0.311 20.607 0.878 0.545 20.609 0.982 0.544 20.590 0.984 0.554 20.704 0.888 0.495 21.150 0.912 0.317
Less than $30 000
c
20.883 1.358 0.413 0.623 1.427 1.864 0.155 1.554 1.168 21.124 1.513 0.325 0.697 1.461 2.008 21.186 1.437 0.306
$30 000 –$49 999
c
20.403 1.548 0.668 1.153 1.605 3.168 0.410 1.758 1.507 20.120 1.650 0.887 1.442 1.634 4.229 20.106 1.603 0.899
$50 000 –$69 999
c
20.289 1.320 0.749 20.004 1.408 0.996 21.589 1.780 0.204 20.830 1.456 0.436 0.044 1.448 1.045 20.310 1.371 0.734
$70 000 –$89 999
c
17.383* 0.571 3.541E7 17.251* 0.887 3.105E7 16.671* 1.347 1.739E7 17.278* 0.825 3.189E7 16.888* 1.058 2.159E7 18.323 0.000 9.072E7
$90 000 –150 000
c
0.536 1.503 1.709 0.342 1.629 1.408 0.121 1.787 1.129 0.371 1.578 1.450 1.962 1.606 7.113 0.482 1.547 1.619
Public transit—very
often
d
24.878* 1.572 0.008 20.396 1.205 0.673 22.421* 1.467 0.089 219.575 3040.751 3.153E-9 21.269 1.240 0.281 24.180* 1.601 0.015
Public transit—often
d
21.883 1.416 0.152 0.659 1.380 1.933 0.144 1.482 1.155 218.076 2869.592 1.411E-8 0.531 1.396 1.700 22.755 1.709 0.064
Public transit—rarely
d
21.796* 1.017 0.166 21.053 1.055 0.349 21.044 1.164 0.352 21.028 1.087 0.358 20.684 1.043 0.504 21.166 1.046 0.312
Public transit—very
rarely
d
0.044 1.282 1.045 0.535 1.301 1.707 216.970 2423.646 4.268E-8 20.034 1.358 0.966 0.394 1.309 1.483 20.103 1.312 0.902
Model fitting information. AIC criterion: 1396; Hannan-Quinn criterion: 1463; 22 Log Likelihood: 1312.
a
Reference category: no bike trips daily.
b
Reference category: females.
c
Reference category: greater than $150 000.
d
Reference category: public transit—never.
*P-value 0.05, SE ¼standard error.
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A female 18 years of age who did not bike daily, had an
income less than $30 000, used public transit often, and did
not have a vehicle in her household was more likely to choose
Infrastructure A than the other infrastructure types. A female
with the same characteristics who does bike daily was more
likely to choose C, D and F over Infrastructure A. In contrast,
a male 18 years of age who did not bike daily, had an income
less than $30 000, used public transit often, and did not have
a vehicle in the household was more likely to choose C over A
in 52% of the cases. A male with the same characteristics
who did bike daily was more likely to choose B, C, D and F
over A.
A male 38 years of age who reported biking daily and had
an income between $50 000 and $69 999, used public transit
rarely, and had one vehicle in his household was more likely to
choose B, E and G over Infrastructure A; a male with the
same characteristics who did not bike daily was more likely to
choose B over A in 58% of the cases. A female 38 years of
age who reported biking daily and had an income between
$50 000 and $69 999, used public transit rarely, and had one
vehicle in the household was more likely to choose B and E
over Infrastructure A. Females with the above characteristics
who did not bike daily were more likely to choose A over all
other infrastructures.
A male or female 77 years of age who reported biking daily,
had an income between $90 000 and $150 000, used public
transit very rarely, and had two vehicles in the household were
more likely to choose B, C, E, F and G over infrastructure
A. A female with the same characteristics who did not bike
daily was more likely to choose B, E and G over A; males of
the same characteristics who did not bike daily were more
likely to choose B, E, F and G over A.
Discussion
Main finding of this study
Results of this study reveal that respondents were more likely
to use biking infrastructures that provide adequate signage
and space separation from vehicles. These findings provide
guidance and design concepts for retrofitting as well as future
infrastructure investments and related policies in the Las
Vegas metropolitan area.
What is already known on this topic
Land-use policies for street-scale urban design have been
shown to be effective at increasing the rates of physical activ-
ity. Specific street-scale factors also have been associated with
increased rates of active transportation. Given the sprawling
design of the metropolitan area of Las Vegas, Nevada, the use
of a bicycle by itself or a bicycle in combination with public
transportation would best enable a convenient commute time.
If policy-makers and public health professionals are to be
successful at increasing active transportation through bicycle
travel, it is imperative to understand what types of infrastruc-
tures that the residents perceive as safe and report being likely
to use.
What this study adds
This study sampled various transit users to estimate safety
and likelihood of use of seven different bicycle infrastructures
in the Las Vegas metropolitan area. The infrastructure type
that was chosen the least by respondents as the most likely to
be used (2.0%) contained the least amount of space and pro-
tection from vehicles. Correspondingly, only 51.9% agreed
that the bike lane was adequate enough to provide safety, and
42.5% thought there was adequate signage. Unfortunately,
this simple, striped 5-ft bike lane resembles most bicycling
infrastructures currently in the Las Vegas metropolitan area.
The infrastructure type least likely perceived as adequate for
biker safety was the shared bus/bike lane, with 19.4% of
respondents in agreement. This infrastructure type is rela-
tivelyrareintheUSA,andismorecommonintheUK.
8
The safety and satisfaction of such lanes are understudied,
and it should be examined in more detail before any
large-scale implementation, specifically since the results in
this study indicate that they were not preferred by many nor
perceived as safe.
The infrastructure option that was rated the highest on all
measures was a painted 8-ft bike lane with a 3-ft buffer and
reflective posts. Of the seven options, this infrastructure con-
tained the most signage by means of green paint on the lane
in the roadway as well as reflector posts to remind drivers not
to enter the lane. It provided a significant amount of space
for the bicyclist to travel. This finding seems to indicate that
survey respondents would be most likely to travel by bicycle
for active transportation if they perceive safe separation from
vehicles.
Probabilities revealed differences in infrastructure prefer-
ences based on (i) gender and (ii) whether or not individuals
reported biking daily. All respondents who reported biking
daily, regardless of age category or gender, chose at least one
other infrastructure that offered more protection from vehicles
than Infrastructure A. It is possible that prior biking experience
may have shaped preferences towards the infrastructures that
offered more space or protection from vehicles.
There was a small gender difference in the youngest and
median age categories with females who did not bike daily;
they were more likely to choose Infrastructure A than was any
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other. This is surprising, as Infrastructure A offered less pro-
tection from vehicles. Furthermore, past research found that
females were more likely to prefer separate paths.
9,10
Limitations of this study
This study is not without limitations. About 60% of respon-
dents were male compared with 50% of the residents in the
Las Vegas metropolitan area. In addition, most of the respon-
dents reported using a personal vehicle for their primary
mode of transportation. The surveyors made numerous
attempts to target and collect survey data from residents who
used a bicycle as their primary mode of transportation, but
they found this population difficult to locate. This is not sur-
prising, given that the US Census Bureau
11
estimated that only
0.4% of Las Vegas residents use a bicycle when commuting to
work. The power of the model classification is low, and a large
part of this is provided by categories B and C. However, it is
important to point out that understanding perceptions of those
who are not current bicycle commuters likely is most useful in
attracting new users and increasing the overall number of active
commuters.
Estimates of the parameters for some categories are very
large as a consequence of the data. However, all estimates and
odds ratios are consistent with each other, and have appropriate
standard error values.
12,13
That is, we have bias in the estimation.
With the nationwide epidemic of inactivity and associated
health effects, increasing activity levels through active trans-
portation is one potential resolution. To do so, it is imperative
that policy-makers, public health professionals and urban
planners work together to create infrastructure changes, and
adequately design new infrastructures that are most likely to
be utilized and attract new active transportation users.
Funding
This study was funded by the Regional Transportation
Commission of Southern Nevada and Mineta Transportation
Institute. Agreement no: SUB2111004903UNLV.
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... Cross-sectional data can be used in cross-sectional regression, which is a regression analysis of cross-sectional data, which was conducted in this research. Analysis of cross-sectional data usually consists of comparing the differences among selected subjects, through which the assumptions associated with the problem of spherical disturbances are reviewed and evaluated and the other tests are proposed for its validation [56], performing the necessary transformations for its validation without affecting the economic nature of the model [57]. ...
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... The dimension that we have applied for this study is that of media content, due to the importance that political communication acquires in social processes, through an econometric analysis (Coughenour et al., 2016;De la Fuente-Mella et al., 2020;Elórtegui et al., 2020;Umaña et al., 2020). The media are fundamental actors in the creation of the agenda and in the identification of topics of interest in public opinion. ...
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In this research, the bankruptcy situation of companies listed on the Santiago de Chile Stock Exchange and the São Paulo Stock Exchange are tested, through models: Z-Score, Logit and Probit, comparing the forecast of the companies classified as likely to fail, in order to assess whether the models could anticipate a possible crisis situation. The results indicate that, for the year 2016, the bankruptcy of 13 Chilean companies and 59 Brazilian companies, mostly belonging to the construction and manufacturing sector in both countries, was forecast. It is concluded that the Z-Score and Z1 Models would be more applicable to the economies under study, as they were correct in the forecast of all Chilean companies and 49 Brazilian companies, and it is always necessary to complement the tools oriented to financial analysis.
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The objective of this research is to examine bankruptcy prediction models and their application in companies in Chile. For this, bankruptcy regulations in Chile and internationally, specifically the United States and Colombia, are analyzed. In turn, the procedures that companies can use today are examined. In addition, the existing prediction models are compared. The model chosen for the development of the research is the Altman Z-score, with which it is sought to confirm its validity, applying it to Chilean companies. For this research, companies were classified into two groups: healthy companies and companies with financial problems. According to the results, the Altman Z-score model on companies, five companies could be found which may need to take advantage of bankruptcy regulations.
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Conditional logistic regression was developed to avoid "sparse-data" biases that can arise in ordinary logistic regression analysis. Nonetheless, it is a large-sample method that can exhibit considerable bias when certain types of matched sets are infrequent or when the model contains too many parameters. Sparse-data bias can cause misleading inferences about confounding, effect modification, dose response, and induction periods, and can interact with other biases. In this paper, the authors describe these problems in the context of matched case-control analysis and provide examples from a study of electrical wiring and childhood leukemia and a study of diet and glioma. The same problems can arise in any likelihood-based analysis, including ordinary logistic regression. The problems can be detected by careful inspection of data and by examining the sensitivity of estimates to category boundaries, variables in the model, and transformations of those variables. One can also apply various bias corrections or turn to methods less sensitive to sparse data than conditional likelihood, such as Bayesian and empirical-Bayes (hierarchical regression) methods.
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We evaluated perceived social and environmental supports for physical activity and walking using multivariable modeling. Perceptions were obtained on a sample of households in a southeastern county. Respondents were classified according to physical activity levels and walking behaviors. Respondents who had good street lighting; trusted their neighbors; and used private recreational facilities, parks, playgrounds, and sports fields were more likely to be regularly active. Perceiving neighbors as being active, having access to sidewalks, and using malls were associated with regular walking.
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Breslow (1981, Biometrika 68, 73-84) has shown that the Mantel-Haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications. For cohort studies, however, estimation of a common risk ratio or risk difference can be of greater interest. Under a binomial sparse-data model, the Mantel-Haenszel risk ratio and risk difference estimators are consistent in sparse stratifications, while the maximum likelihood and weighted least squares estimators are biased. Under Poisson sparse-data models, the Mantel-Haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent, while the weighted least squares estimators are again biased; similarly, of the common rate difference estimators the weighted least squares estimators are biased, while the estimator employing "Mantel-Haenszel" weights is consistent in sparse data. Variance estimators that are consistent in both sparse data and large strata can be derived for all the Mantel-Haenszel estimators.
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Although telephone and mail are often used to promote physical activity adoption, their ability to produce long-term maintenance is unclear. In this study, 140 men and women aged 50-65 years received 1 year of telephone counseling to adopt higher (i.e., more vigorous) versus lower intensity (i.e., moderate) exercise. After 1 year, participants were rerandomized to a 2nd year of contact via (a) telephone and mail or (b) predominantly mail. Participants who were prescribed higher intensity exercise and received predominantly mail had better exercise adherence during the maintenance year than those who received telephone and mail. Both strategies were similarly effective in promoting maintenance in the lower intensity condition. Results suggest that after successful adoption of physical activity with the help of telephone counseling, less intensive interventions are successful for physical activity maintenance in older adults.
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Females are substantially less likely than males to cycle for transport in countries with low bicycle transport mode share. We investigated whether female commuter cyclists were more likely to use bicycle routes that provide separation from motor vehicle traffic. Census of cyclists observed at 15 locations (including off-road bicycle paths, on-road lanes and roads with no bicycle facilities) within a 7.4 km radius of the central business district (CBD) of Melbourne, Australia, during peak commuting times in February 2004. 6589 cyclists were observed, comprising 5229 males (79.4%) and 1360 females (20.6%). After adjustment for distance of the bicycle facility from the CBD, females showed a preference for using off-road paths rather than roads with no bicycle facilities (odds ratio [OR]=1.43, 95% confidence interval [CI]: 1.12, 1.83), or roads with on-road bicycle lanes (OR=1.34, 95% CI: 1.03, 1.75). Consistent with gender differences in risk aversion, female commuter cyclists preferred to use routes with maximum separation from motorized traffic. Improved cycling infrastructure in the form of bicycle paths and lanes that provide a high degree of separation from motor traffic is likely to be important for increasing transportation cycling amongst under-represented population groups such as women.