The restriction on the right of existence

The right to work and the right of property are two bases of the right of existence. The impact of ALLR on the right of existence is similar to on the right to work, its impact on labor group is much more than on enterpriser group. The reason is that usually the ability of a labor using property to earn profit is much less than that of an enterpriser. Labors usually use their manpower to earn a living. Similarly, in the case of using transportation vehicles to make a living e.g. the ALLR offenders who applied for constitutional interpretation were small truck drivers who used their truck to make a living. Therefore, ALLR may represent a serious impact on the right or existence.

2.1.4 The constitution interpretations No. 284 and 531

The Constitutional Court in Taiwan to interpret the Constitution can be in many ways such as to judge whether constitution fits in with the aim, to distribute the power of the State, to confirm the Constitution and to implement the Constitution. Hence, the outcome of the constitutional interpretation cannot be simply determined whether it corresponds to or violates the Constitution. It also cannot to check only on the interpretation or the document of explanation, but on all the points of view (Hwang, 2000). The interpretation of the Constitutional Court usually cannot derive an objective and firmly believed result, but a trend or tendency. For the basic rights and legal profits that protected by the Constitution, the Constitution Court except to judge whether it corresponds to the Constitution, the more important thing is to interpret the relevant rights, the essence and content of legal profits.

Meanwhile, according to the relations among the basic rights to set up principles and system,

to harmonize and balance personal rights and group rights, to protect human rights, and glorify a constitutional government.

Although both the interpretations of the opinion of the Road Traffic Safety Act 62 are on the aim of enhancing the road safety, protecting the others profit and maintaining the society order. And it doesn’t violate the Constitution. However, the interpretation on may, 2001 mentioned that: “in the cases of the drivers having improved their behaviors and having the ability to re-fit the society, the authority has to study whether it is needed to provide a chance for those drivers to rehabilitate their driver licenses.”

To compare the two interpretations, the latter obviously more conform to the spirit of protecting human’s right than the former. From the second paragraph of the latter interpretation, it seems that to revoke a person’s driver license forever and without rehabilitation during the rest of life is unreasonable.

2.2 Literature of license suspension/revocation

Many drivers, given a sentence of license S/R continue to drive, but at reduced levels (Hagen et al., 1980; Ross and Gonzales, 1988; Smith and Maisey, 1990). Ingraham and Waller (1971) found at least 30% of drivers given license S/R for drunk driving continued to operate a vehicle despite the licensing action. Williams et al. (1984) indicated that 65% of drivers confessed to operating a vehicle while under license S/R. Ross and Gonzales (1988) reported that 66% of suspended drivers were still driving on the road. DeYoung (1999) estimated that three-quarters of S/R drivers continued to drive, but they apparently drove less, and with more care. Malenfant et al. (2002) showed 57% of motorists were still driving while their licenses were suspended.

Although many S/R drivers continue to drive, many studies have explored the effectiveness of administrative license revocation (ALR) and support the view that it is a positive step in reducing subsequent alcohol-involved driving by offenders (Zador et al., 1989;

Henderson and Kedjidjian, 1992; Lund, 1993; Sweedler and Stewart, 1993; NHTSA, 1993).

Most of these studies have demonstrated that this sanction is effective over a short term (Homel, 1981; McKnight and Voas, 1991; Mann et al., 1991; Peck, 1991; Siskind, 1996).

However, ALR is usually no longer than a few years, and prior research has commonly focused on a relatively short-term license S/R. Very few studies have explored the effectiveness of ALR over the long term.

In addition, driving while under S/R is difficult to enforce. It can only be detected when the driver of a vehicle has been stopped by the police for committing another traffic offence (Voas and Deyoung, 2002); thus, offenders are likely to be encouraged by the belief that there is little danger of being caught (Knoebel and Ross, 1997).

2.3 Literature of methodology 2.3.1 Logistic regression model

Regression methods have become an integral component of any data analysis concerned with the relationship between an outcome variable and one or more explanatory variables.

The most common regression method is conventional regression analysis, either linear or nonlinear, when the outcome variable is continuous (iid). However, when the outcome variable is discrete, conventional regression analysis is not appropriate. Moreover, there are primary assumptions are not satisfied when the outcome variable is categorical. One is the outcome variable in conventional regression analysis must be continuous, another is the outcome variable can take nonnegative values (Al-Ghamdi, 2002).

Statistical analyses are often based on general linear models that were developed to handle continuous independent data. A common example of the general linear model is ANOVA. The generalized linear model is an extension of the general linear model to handle both discrete and continuous data (McCullagh and Nelder, 1989). One of the most common types of the generalized linear model is logistic regression. The generalized linear model

transforms the data via a link function. In logistic regression the link function is the logit link function. An iterative process is used to solve for the parameter estimates. The coefficients represent the log-odds of an outcome being present when all other variables are held constant.

The logistic regression model is widely used analytical tool in traffic safety research.

From a methodological viewpoint, a wide variety of approaches have been employed to study fatality risk. For example, Kim et al. (1995) use data on accidents in Hawaii to illustrate the use of a categorical log linear model to examine personal and behavioral predictors of crash and injury severity, while Shankar et al. (1996) describe the development of a nested procedure for the analysis of accident severity on rural freeways. In the UK, Jones and Bentham (1995) calculated Odds ratios to determine probabilities of fatality amongst traffic accident causalities according to a complex matrix of explanatory variables. However, despite this apparent diversity of methodologies, common to most investigations is the requirement for a statistical model, which will predict fatality risk for an individual based upon a range of explanatory variables. In line with this, the most frequently used technique is the generalized linear modeling (GLM) methodology of logistic regression (Menard, 1995).

The logistic regression model applies maximum likelihood estimation after transforming the categorical dependent variable into a logit variable. A logit is the log of the odds ratio. It does not assume equal distribution of the dependent variable for each level of the independent variable, nor necessarily a linear relationship between the independent and dependent variables. Moreover, the logistic regression model does not assume a normal distribution of the variables. As such, it is a particularly robust model for various traffic safety analyses (Kima, 2003). It is one form of statistical model called ‘generalized linear model’ with a logit (also called ‘log odds’, i.e. ln p/(1-p)) link function. This model has many advantages over ordinary least square regression models where the dependent variable is not continuous or normal in its distribution, and has constant variances. Logistic regression allows one to

predict a binary outcome from a set of explanatory variables that may be continuous, categorical, or a mixture of the two. The basic model form and statistical test method for logistic regression is introduced as followed.

The dependent variable in logistic regression is dichotomous; that is, it is assumed to follow a Bernoulli distribution. Therefore, it takes the value 1 with a probability p of an event occurred, and the value 0 with probability 1-p of an event not occurred.

The form of the logistic regression equation is:

( )

( )

where p (x) is the probability of an event occurred, which is a function of a set of factor vectors, x; α is the constant of the equation, and β_i is the coefficient of the i^th factor.

The coefficients of the logistic model can be obtained by using the maximum likelihood estimation (MLE) method. To test the statistical significance in the model of each coefficient, βi, a Wald test is usually used. The Wald test calculates a squared Z statistic, yielding a Wald statistic of asymptotic chi-square distribution with one degree of freedom, which is:

2

As for the overall test of the model, the likelihood-ratio test is widely used. This test employs the ratio of the maximized value of the likelihood function for the model with constant term only ( ) over the model, with a constant and estimated coefficient ( ).

Using negative two times of log transformation of the likelihood-ratio yields an asymptotic p degree of freedom of the chi-squared statistic. The likelihood-ratio test statistic equals:

)

L(c L(βˆ)

[

]

where log( ) and log( ) are respectively the values of the log likelihood function at its maximum, and p is the number of estimated coefficients.

)

L(c L(βˆ)

The goodness-of-fit measure, ρ², was defined as followed:

))

To interpret the model conveniently, logit (i.e. ln p/(1-p)) can be converted easily into a statement about odds ratio (O.R.) of the dependent variable simply by using the exponential function. For example, if the xi variable increases one unit while holding the remainder variables constant, the O.R. of these two levels for x_i will be exp ( ) and the 95% confidence interval (C.I.) for O.R. will be exp ( ± Z

β^ˆi

β^ˆi 0.95*SE (β^ˆ_i)).

Logistic regression is often used for analyzing motor vehicle crash data. In predicting accident frequency, Milton and Mannering (1997) state: “The use of linear regression models is inappropriate for making probabilistic statements about the occurrences of vehicle accidents on the road.” They showed that the negative binomial regression is a powerful predictive tool and one that should be increasingly applied in future accident frequency studies. Kim et al.

(1996) developed a logistic model and used it to explain the likelihood of motorists being at fault in collisions with cyclists. Covariates that increase the likelihood of motorist fault include motorist age, cyclist age, cyclist alcohol use, cyclists making turning actions, and rural locations. Kim et al. (1994) attempted to explain the relationship between types of crashes and injuries sustained in motor vehicle accidents. By using techniques of categorical data analysis and comprehensive data on crashes in Hawaii during 1990, a model was built to relate the type of crash (e.g. rollover, head-on, sideswipe, rear-end, etc.). They also developed an “odds multiplier” that enabled comparison according to crash type of the odds of particular

levels of injury relative to non-injury. The effects of seatbelt use on injury level were also examined, and interactions among belt use, crash type, and injury level were considered. They discussed how log linear analysis, logit modeling, and estimation of ‘odds multipliers’ might contribute to traffic safety research.

Kim et al. (1995) built a structural model relating driver characteristics and behavior to type of crash and injury severity. They explained that the structural model helps to clarify the role of driver characteristics and behavior in the causal sequence leading to more severe injuries. They estimated the effects of various factors in terms of odds ultipliers, which is how much does each factor increase or decrease the odds of more severe crash types and injuries.

Nassar et al. (1997) developed an integrated accident risk model (ARM) for policy decisions using risk factors affecting both accident occurrences on road sections and severity of injury to occupants involved in the accidents. Using negative binomial regression and a sequential binary logit formulation, they developed models that are practical and easy to use. Mercier et al. (1997) used logistic regression to determine whether either age or gender (or both) was a factor influencing severity of injuries suffered in head-on automobile collisions on rural highways. Hilakivi et al. (1989) also used logistic regression in predicting automobile accidents of young drivers. They examined the predictive values of the Cattel 16-factor personality test on the occurrence of automobile accidents among conscripts during 11-month military service in a transportation section of the Finnish Defense Forces. James and Kim (1996) developed a logistic regression model to describe the use of child safety seats for children involved in crashes in Hawaii from 1986 through 1991. The model reveals that children riding in automobiles are less likely to be restrained, drivers who use seat belts are far more likely to restrain their children, and 1- and 2-year-olds are less likely to be restrained.

2.3.2 Generalized estimating equations (GEEs) 2.3.2.1 The form of GEEs

McCullagh and Nelder (1989) introduced the Generalized Linear Model (GLM) for exponential family data with the form

fy (y, θ, φ) = exp｛f(yθ - b(θ))/a(φ) + c(y, φ)｝,

where a( ), b( ), and c( ) are given, θ is the canonical parameter, and φ is the dispersion parameter. The GLM is then given by

g(μ_i) = g(E[Y_i]) =x_i^'β,

where x_i is a p x 1 vector of covariates for the i^th subject, and β is a p x 1 vector of regression parameters. One of the attractive properties of the GLM is that it allows for linear as well as non-linear models under a single framework. It is possible to fit models where the underlying data are normal, inverse Gaussian, gamma, Poisson, binomial, geometric, and negative binomial by suitable choice of the link function g( ) (Hilbe, 1994).

Liang and Zeger (1986) and Zeger and Liang (1986) introduced generalized estimating equations (GEEs) to account for the correlation between observations in generalized linear regression models. One aspect of the approach builds upon previous methods of variance estimation developed to protect against inappropriate assumptions about the variance (Huber 1967; White 1980, 1982). The GEEs method is an extension of the generalized linear model, and is applicable in the analysis of correlated discrete outcome data (Liang and Zeger, 1986).

The appeal of GEEs is the interpretation of the data is the same as when a model that assumes independence is used, yet it is a valid method for correlated data (Zeger and Liang, 1992).

GEEs are often used when analyzing longitudinal or nested data. Several previous studies have examined the use of GEEs in the analysis of longitudinal injury-related and illness-related data. For example, Williamson et al. (1996) found when modeling longitudinal injury data under certain circumstances the use of GEEs resulted in different conclusions compared to logistic regression. While Williamson’s study addressed correlation of

in time. Diggle, Liang, and Zeger (1994) provided a detailed review of marginal models as well as other approaches, which including random effects models and transition models.

Let , i = 1,….., n; j = 1,……, t be the jth outcome for the ith subject, where we assume that observations on different subjects are independent, though we allow for association between outcomes observed on the same subject. In the GEEs setting, we are not assuming that is a member of the exponential family, but we are assuming that the mean and variance are characterized as in the GLM. We assume the marginal regression model

Yij

Yij

g(E[Y_ij]) = x_i^'β,

where x_ij is a p x 1 vector of study variables (covariates) for the i^th subject at the j^th outcome, β consists of the p regression parameters of interest and g( ) is the link function. Common choices for the link function might be g(a) = a for measured data (the identity link) g(a) = log(a) for count data (log link), or g(a) = log(a/(1-a)) for binary data (logit link). GEEs have been a popular approach to regression model fitting for this type of data. In the case of a binary data with the logit link, it will be that

log(E[Y_ij]/(1 - E[Y_ij])) = x_i^'β,

which implies that

E[Y_ij] = μ_ij= exp(x_ij^'β)/(1 + exp(x_ij^'β) ,

and if the outcomes are binary, it will be that var(Y_ij) =V_ij= exp(x_ij^' )/(1 + exp(x_ij^' )) ²,

In addition to this marginal mean model, it is needed to model the covariance structure of the correlated observations on a given subject. Assuming no missing data, the t x t covariance matrix of Y_i is modeled as

V = i φA_i^1/2R(α)A_i^1/2,

where A_i is a diagonal matrix of variance functions v(μ_ij), and R(α) is the working correlation matrix of Y _i indexed by a vector of parametersα.

2.3.2.2 Specification of working correlation matrix

There are a variety of common structures that may be appropriate to use to model the working correlation matrix. In general if the number of observations per cluster is small in a balanced and complete design, then an unstructured matrix is recommended. For datasets with mistimed measurements, it may be reasonable to consider a model where the correlation is a function of the time between observations. For datasets with clustered observations, there may be no logical ordering for observations within a cluster and an exchangeable structure may be most appropriate. Comparisons of estimates and standard errors from several different correlation structures may indicate sensitivity to misspecification of the variance structure.

For both the independence working structure and the fixed working structure, no estimation of α is performed. It is noted that use of the exchangeable working correlation matrix with measured data and identity link function is equivalent to a random effects model with a random intercept per cluster.

2.3.2.3 Empirical and model based variance estimators

Zeger and Liang (1986) referred to Vi as a working matrix because it is not required to be correctly specified for the parameter estimates and the estimated variance of the parameter estimates to be consistent (as long as the mean model itself is correct and there is no missing data). However, Liang and Zeger (1986) showed that there could be important gains in efficiency realized by correctly specifying the working correlation matrix. Sets of estimating equations are solved, through an iterative process, to find the value of the estimatorβ. An empirical variance estimator can be used to estimate var(β). This variance estimator is also referred to as a robust estimator. Another variance estimate available from GEE models is the

model are correctly specified. Since in general the analyst will not know the correct covariance structure, the empirical variance estimate will be preferred when the number of clusters is large. When the number of clusters is small, say < 20; the model based variance estimator may have better properties (Prentice 1988) even if the working variance is wrong.

This is because the robust variance estimator is asymptotically unbiased, but could be highly biased when the number of clusters is small.

2.3.2.4 Missing data issues

Longitudinal or clustered studies often have missing data, either by design or happenstance. If a litter in a teratology study is the level of clustering, litter size may vary between litters. If the missingness can be thought of as being missing completely at random in the sense of Little and Rubin (1987), then the consistency results established by Liang and Zeger (1986) hold. However, the notation and calculations for arbitrary missing data patterns are more complicated than in the balanced and complete case. Robins, Rotnitzky, and Zhao (1995) proposed methods to allow for data that is missing at random. Their inverse probability censoring weight approach requires that the missingness law be modeled, and that weights corresponding to the inverse probability of missingness be included in the GEEs. This will yield consistent parameter estimates, but the variance will tend to be incorrect.

Unfortunately, the method of Robins et al. (1995) only works well when there is dropout.

That is, once a subject misses a time, that subject is not seen again. Often subjects miss a single observation, and then are seen at the next time. In summary, when fitting GEEs, the analyst must consider not only the model for the mean, but also the model for the variance and the underlying missingness process.

Chapter 3 The ALLR policy

A driver who holding a driver’s license in Taiwan is required to obey the Regulation of Road Safety as well as the Regulation of Freeway Traffic Management while driving his/her vehicle on the road. Once the driver breaks these regulations, the driver and/or his vehicle will

A driver who holding a driver’s license in Taiwan is required to obey the Regulation of Road Safety as well as the Regulation of Freeway Traffic Management while driving his/her vehicle on the road. Once the driver breaks these regulations, the driver and/or his vehicle will