submitted in partial fulfillment for the degree of master of science
Hester Verdenius
11198184
master information studies
data science
faculty of science
university of amsterdam
24-06-2021
Internal Supervisor External Supervisor Title, Name Dr. Frank Nack Dr. Rudi Turksema
Affiliation UvA, FNWI, IvI The Netherlands Court of Audit Email F.M.Nack@uva.nl r.turksema@rekenkamer.nl
Abstract
For the Dutch government to be more effective in the fight against environmental crime, the timing of envi-ronmental violations of companies that work with haz-ardous substances (the so called BRZO companies in the Netherlands) should be known to make more tar-geted inspections. In order to know when to inspect, the timing of a violation should be predicted. This study investigates if time-to-event analysis is an effec-tive method for predicting the timing of such a viola-tion, as well as which factors predict whether a com-pany violates, or not, and if there is a pattern. A Cox Proportional Hazard and a Weibull method are used to predict and are tested against a linear regression model that serves as the baseline model.
The results show that all proposed time-to-event models perform better than linear regression and that Cox PH had the highest performance. The type of industry the company is in and the company size are relevant factors for predicting violations; and there is a decreasing probability on violations over time. It is concluded that time-to-event is an appropriate method for predicting the timing of an environmental offence.
1
Introduction
In the Netherlands, there are companies that work with large quantities of substances that are potentially haz-ardous to the environment and the citizens, i.e. Shell, and it is extra important that these companies follow the rules, that are stricter than for normal compa-nies, to prevent serious accidents. These companies are covered by the BRZO1 regulations (henceforth BRZO
companies) in the Netherlands.
BRZO companies are inspected regularly by a super-visor who records whether violations have been com-mitted. Whenever a violation is signalled, the govern-ment must take legal or administrative action. How-ever, currently there is no insight in how effective the sanctions taken by the government are. A recent re-port concluded that the current system is not working properly, due to reluctance of local and provincial gov-ernment to create the conditions for the environmental services to do their work optimally ([2], p.50). They
1In Dutch: “Besluit Risico’s Zware Ongevallen”. In English:
“Major Accident Risks Decree”
recommended to invest more in quality and robustness of the supervision on BRZO companies.
The Netherlands Court of Audit is a High Council of State and an independent institute that monitors if Dutch central governmental expenditures are econom-ical, effective, and efficient. At the time of writing, research on the effectiveness of fighting environmental crimes is taking place. The first report of this ongo-ing investigation covered the poor data quality regard-ing the registration of BRZO companies [5]. This data quality was improved afterwards by completing miss-ing data and straightenmiss-ing out mixed data. This im-provement was a precondition for a second report on the effectiveness of sanctions on BRZO companies that violated environment rules, where this thesis is a part of.
One way to be more effective in fighting environmen-tal crime, is to spot the violation earlier. To achieve this, one could either inspect more frequently, or should know when to inspect. The latter would be more ef-ficient, therefore the timing of the violations is impor-tant and should be predictable. This will improve in-spections by enabling them to have a more targeted timing. However, these predictions need to be close to the actual timing of a violation. It is preferable to pre-dict the timing too early or a little late, as then the unhealthy situation can still be fixed; predictions over a month too late are considered not acceptable.
The research question of this thesis is: Is time-to-event analysis a good method to predict the timing of a new violation of a BRZO company? The subques-tions are: What is the pattern of violasubques-tions of BRZO companies; and which factors predict timing of viola-tions? There is no existing literature yet that investi-gates these timings of violations from companies using time-to-event analysis.
This paper continues with a related literature re-view in Section 2 on which the formulated hypothesis is based. Section 3 describes the approach that was fol-lowed in order to answer the research questions. Section 4 presents the results of the experiments, in Section 5 these results are discussed. A conclusion is drawn and some future work is suggested in Section 6.
2
Related Work
The literature related to this subject can be divided into two parts: domain and method. The domain liter-ature and the method literliter-ature are summarised first. Secondly, based on the gathered literature, the hypoth-esis is formulated on which the approach is based.
2.1
Domain Literature
The domain in this research is “effectively fighting cor-porate environmental crime”. This domain can be sub-divided in to two parts as well, based on two ques-tions: What are the reasons companies comply or do not comply to the environment rules; and what law enforcement methods are effective when fighting envi-ronmental crime and crime in general?
2.1.1 Environmental Crime Motivations
Reasons for companies to violate environmental law have been researched mostly by sociological studies.
Although company characteristics seem unrelated to violation rate [14][9] or patterns of incompliance [21], big companies do seem to make fewer violations than small companies [39][14]. This is a consequence of a negative relation between violation rate and inspec-tions, together with the fact that bigger businesses get inspected more often [14]. Additionally, some indus-try types have more difficulties complying than others [9][30]. These industries are petrochemicals, pharma-cists, electrical products, automobile factories [30] and pulp factories [9].
The trend has been observed that in the beginning of a supervision trajectory, a BRZO company makes more violations than at the end of the supervision trajectory. However, there exists a small group of companies in the wholesale and retail storage and distribution that continue to commit high-frequency and stable numbers of violations over the years [21].
Some studies did not take the severity of violations into account, which make small violations seem equal to gross disregards [21]. On the other hand, one small violation could also have bigger environmental impact than severe violations [14].
2.1.2 Effects of Enforcement
Overall, law enforcement reduces crime rates [18][31][16]. Different types and severity of pun-ishments have different degrees of effect [10][15][31]. However, enforcement is not a guarantee for effective crime reduction [32][11], because the behaviour of violation patterns is not only explained by enforce-ment and deterrence, but also by deployenforce-ment strategy, social pressure, financial status or spatial distribution of criminal activity [18][3][11].
In contradiction to what Erasmus once said: “It is better to prevent than to cure”, in fighting crime it is more effective to repress than to prevent [4][29].
In The Netherlands, BRZO companies are inspected regularly, and this is probably also the case outside The Netherlands. Inspections have little deterrent fect [3][33], although they do not have a significant ef-fect on long-term compliance [13].
Administrative action in The Netherlands has the purpose of stopping and restoring. This causes crimi-nal motives to remain unnoticed, which in turn causes unachievable prevention [10]. These administrative ac-tions are mostly fines, which work significantly less ef-fectively than physical measures (ordinances) [32].
2.2
Method Literature
Studies that use time-to-event methods are, among others, mostly done in the medical domain. Papers that describe the time-to-event analysis techniques, set out different methods and their objectives [20][28]. A Kaplan-Meier model [19] is useful for estimating the probability of surviving after a certain point in time. A Cox Proportional Hazard model [8], or Cox PH for short, has the advantage of obtaining the effect of co-variates. Frailty models [36] are useful for incorporat-ing heterogeneity between individuals and can be used for modelling data with repeating events. Methods that are used for recurrent events data are Andersen–Gill, Poisson and negative binomial methods [26]. An Aalen model [1] assumes the effects of covariates to be addi-tive. Parametric models make assumptions about the patterns of time series data. Two examples of a para-metric model are a Weibull model and an exponential model.
Time-to-event is not only used in the medical do-main. A random survival tree model was used to
pre-dict eBook demand in a library. Their most complex model achieved an AUC of 0.81 [17]. A Cox PH and a Kaplan-Meier model were used to predict the timing of onset of childbearing women in Nigeria [22]. Two types of Cox models were used to predict the timing of young adults joining gangs [25]. A Cox model with a Bayesian approach was used to predict the timing of insurance claims showing their marginal model had the highest performance [6]. A basic Cox model was used to predict the failure time of drug criminals [7] and to predict the recidivism of young first-time offenders based on assigned judicial dispositions [27].
Comparative papers suggest that survival Support Vector Machines, with regression constraints, per-formed better than regression based survival methods in the medical domain [38]. In a comparative study in the criminal recidivism domain, all methods seem to perform well (including Cox PH, neural nets, Aalen, random survival forest and Weibull) except the survival forest tree model and the exponential model [37]. Fur-thermore, no other papers where found that researched time-to-event analysis on corporations that recidivate in environmental crimes, let alone for Dutch BRZO companies.
2.3
Hypothesis
After evaluating all aspects of the literature review the following hypotheses can be made:
A: Time-to-event methods can be used to predict the timing of a new violation of a BRZO company. The Cox PH model, a recurrent model or a Weibull model are the most appropriate methods.
B: Relevant factors that influence the time to a new violation include the administrative punishment severity on the previous violation, the severity of the previous violation, the number of inspections on a company, the size of the company, the type of industry and the length of the trajectory. C: There is a decreasing trend in company violations
between the start and end of a supervision trajec-tory.
3
Approach
Previous work shows that time-to-event analysis meth-ods can be used to predict the time to an event of
in-terest. The Netherlands Court of Audit provided the improved data to research the ability to predict the timing of violations. The previous studies did not use baseline models, which is considered a methodological problem in those works; so a simple baseline model is made in order to test the proposed models.
In this section the dataset will be described first, af-ter which the processing of the time series to a col-lection of time-to-event data is set out. Then, a de-scription of the models used is given and an evaluation method is proposed.
3.1
Dataset Description
For this research two databases were combined to make the final dataset. The first dataset is the improved dataset from Section 1, which is an administrative time series of inspections on all the inspected BRZO compa-nies from 2015 until 2020. BRZO company supervisors record their inspections in this database, including the date, the amount of violations seen, which the type of violations observed and what the type of administra-tive punishment the government acts with. The other dataset is from the Dutch Chamber of Commerce and consists of details and characteristics of BRZO compa-nies. When a company is created, the owners need to register it at the Chamber of Commerce 2. The
loca-tions, amount of workers, the names of officials, autho-rised signatories and curators are registered as well as the type of industry the company is in and a description of business activities. The industry type is subdivided into three levels of detail (an overview is provided in Appendix B).
The severity of violation is indicated as unknown, low, middle or high (see Figure 6 in Appendix A for the frequencies of the violation types). It is possible that in one inspection multiple violations are covered. The type of administrative punishments is more textu-ally descriptive, see Figure 4 in Appendix A for their frequencies. The following order of severity is used, from very severe to mildly severe [12], in five groups:
1. Very severe: Criminal law / Official report of find-ings
2. Severe: Temporary stop of operations / Adminis-trative penalty / AdminisAdminis-trative punishment
Industry type (low, middle, high) Company size Violation type Enforcem-ent type Inspection date Time be-tween in-spections Trajectory length at t Number of in-spections at t Censored event
cat. int. cat. cat. date int. int. int. bool.
Table 1: The green boxes are the variables that are copied from the original datasets, the orange boxes are the variables that were computed.
3. Medium: Administrative warning / Order to a penalty / Administrative enforcement order 4. Mild: Informing / A new inspection
5. No sanction / Unknown sanction
The none/unknown group is not treated as the light-est punishment, but is seen as a gap in the data and a limitation. If the unknown enforcement category comes out as a significant factor, it indicates that this lack of registration needs to be improved in the future to be able to get more insight in behaviour of compliance of BRZO companies.
Appendix C contains more explanatory statistical plots that describe the dataset more thoroughly.
3.2
Dataset Preprocessing
To perform the proposed research approach, the two datasets described in Section 3.1 were merged into one. Some features were selected from the original sets and some variables needed to be calculated to obtain the necessary covariates, see Table 1. The type of industry of a company was retrieved together with an indicator of company size (which will be measured by amount of workers because this was the only available measure for company size), type of violation (if applicable) what administrative punishment was placed on a violation, and the date of inspection. The data was processed to a series of time intervals between inspections where a violation has been signalled.
The target value, i.e. the duration to the next envi-ronmental violation, was calculated by subtracting the inspection date where a violation was detected from the inspection date of the previous violation. The variables from the literature are assumed to have effect on this time interval, they may increase or decrease the length significantly. Ergo, the timing of the new violation was computed by adding the target value to the previous violation date. Due to the unavailability of the exact
time of the event of interest, an assumption needed to be made that the date at which the inspection took place and the violation was detected, is equal to the date where the rules were breached. However, this as-sumption makes the results less reliable because the predictions do not represent exactly when the violation happened. The start of the trajectory has been set to the first inspection of a company. The length of the trajectory was dynamically added to take the pattern of more violations in the beginning and less in the end into account.
After the last violation of a company, the amount of remaining days in the dataset is the censored interval, which means further violations did not occur for the registered period. The end of the trajectory was set to the date of the last recorded inspection of a company.
Since the amount of violations will be left out in this research (see Section 2.3), the class of the most serious offence will represent the severity of the violation. The punishment belonging to these violations was assumed to be the severest of those registered as well. Since there is no clearer order between the punishments other than the clustered ordering given in the previous section, the punishments were divided into those five groups instead of their individuals, using a mapper.
The categorical variables used (industry types, type of violation and type of enforcement) had different datetypes in the dataset. Industry type is in a sin-gle column with a short description, whereas type of violation and enforcement are occurrence-hot encoded. These three were all transformed into one-hot encoded factors. Even though the function for the models in R does this automatically, the process of feature selection, given in Section 3.4.2, required having the categories in separate columns.
Every violation in the dataset is linked to the lation type and enforcement type of the previous vio-lation of the company. If the viovio-lation is the first the
company has made, previous violation values will be both equal to the unknown class since there was no previous violation type and no type of enforcement.
The dynamic total number of inspections at time t for a company was counted and added as a factor as well, in order to take the amount of inspections and belonging pattern into account.
Before processing, the dataset contained 19,685 in-spections of which 4,210 (21%) inin-spections were on companies with incomplete information. Those were discarded from the data, which means that 96 (20%) companies were left out. After preprocessing, the re-sulting dataset that was used, contains 3,088 time-to-event data points of 386 companies with 386 censored events.
3.3
Models
Time-to-event analysis describes the time interval be-tween a start time and the time of an event of interest. It can happen that in the recorded length of time the event did not occur; this is called censoring. It is pos-sible to assume that there are no censored events by dropping them from the data. This research though investigates the usefulness of censored events as well, in order to produce the best model possible, by us-ing two datasets; the dataset with censorus-ing and the dataset without censoring, but with an equal test set (this is explained further in Section 3.4.1). If the best performing model is one of the models without cen-sored events, the step of including these events during the preprocessing can be left out.
Several previous works that predict time to an event successfully used a Cox PH model. From the guide lit-erature in Section 2.2, a recurrent model or a Weibull model seemed suitable to use as well. With the limited scope of this short study in mind, only one of these last two is chosen to predict with. Since the pattern is a meaningful covariate and the recurrent events can be modelled via integrating variables from previous viola-tions from a company and dynamic time variables, the recurrent model is left out of this research.
In addition to applying the findings in the literature, a few tests were done to see a potential applicability of the model type to this domain. Firstly, a recurrent model with frailty was tried. Secondly, the data was first cleared of outliers and used on the proposed Cox PH, Weibull and linear regression models. However,
Figure 1: Predicting diagram.
these methods yielded equivalent, if not worse, results, to the extent that they were on average 15% from the best performance, which are given in Section 4.
A brief description of the methods is given in the next three subsections.
3.3.1 Cox PH
Cox Proportional Hazard is a regression model for time-to-event data. This method is advantageous for taking covariates into account and analysing their effects. A property of Cox PH is that it assumes a constant haz-ard ratio over time. This method is implemented with the survival package for R [34][35], using the coxph function.
The output of a Cox PH prediction method is a prob-ability at time t for the event not to occur, also called the survival probability. The predictions for this model are made, as presented in Figure 1, by going through every test datapoint and looping over an interval of time steps from 0 to 2,000, because the dataset con-tains 5 years of inspections, this is 1,826.25 days which is capped to 2,000. Steps of 100 days are used for faster search. If the probability is below the defined thresh-old in the next step, the 100 days between the 100 days interval is looped over to find the final prediction.
The threshold is set at 50% survival probability after a small-scaled hyperparameter search, since then the survival rate seems low enough and it is more beneficial to predict a violation too early than too late.
3.3.2 Weibull
Weibull is a parametric method that makes assump-tions about patterns in the time intervals. This means that in contradiction to Cox PH, the hazard ratio con-tinuously increases or decreases over time in a shape that is decided by estimated parameters. This is an advantage over Cox PH if it is indeed the case that
the amount of violations a company makes decreases over the trajectory time. With this method, the ef-fects of covariates are analysed as well with the log likelihood function. This method is implemented with the survival package for R [34][35], using the survreg function with ‘Weibull’ as the distribution parame-ter. Predicting with this method is simpler, the func-tion directly predicts the time to the event. The survreg.predict function in R has a parameter option for the type of prediction where ‘response’ predicts the time to event.
3.3.3 Linear Regression
The linear regression model predicts the days between violations linearly, which potentially establishes a neg-ative amount of days as result. Due to this effect this model may predict a violation to happen in the past, which is wrong, and is therefore a baseline to com-pare the time-to-event models to. This model is im-plemented with the lm function in R.
Linear regression would perform poorly on censored data because it can not handle censored events, for the reason that it will try to predict events that did not occur. Training it on censored data would lead to a poor model. It was chosen not to include this model, as it would make for an easily surpassed baseline.
3.4
Experimental Set Up
Since this is a supervised approach, it is necessary to divide the data into a training set and test set, in order to measure the performance of the models. The rele-vant features are selected based on the training set. To address the performance and to be able to compare the models, metrics are computed and compared to each other.
3.4.1 Test and Training Split
Because the dataset looks small at this point and there needs to be enough data to train the models on, the train-test proportion is 90%-10%, which is a common practice for small datasets. As mentioned before, there are two datasets used, one with censored events and one without. The set without censoring is a simple division according to the proportion. On the other hand, the experiment with censoring was not meant to be tested
on events that did not happen. Therefore, the censored events will occur in the training set only. The test set is equal for both the models with censoring and without censoring, to be able to fairly compare their performances.
3.4.2 Feature Selection
Before selecting by hand, an automated feature se-lection method is performed, using the automated Stepwise method and the Boruta [24] method in R, because manual selection would take significant effort for the 143 features present, due to the amount of in-dustry categories in the dataset.
Stepwise method selects the optimal features based on the Akaike information criterion (AIC) score. Since doing this on 143 columns at once is too complicated for the method, the features are split up first into groups of around 10 and the Stepwise method is executed once for every group. From the summary of the output mod-els, the relevant features are selected using a 99.9% sig-nificance level to keep the number of selected features as low as possible. Lastly, the automatic Stepwise method is run again on this last selection, giving the resulting features. Table 4 in Appendix D presents the accepted features using the Stepwise method.
The Boruta function is a form of a random forest tree classifier [23]. It repeatedly shuffles the features and compares their Z-score to capture the important covariates. Based on these Z-scores and a threshold defined by the feature with the maximum Z-score, the method ‘rejects’ or ‘accepts’ features or it can be inde-cisive. To select as few features as possible, only the accepted features are selected. Figures 13 and 14 in Appendix D show the correlations of all the features with the red colour indicating that the variable is re-jected, orange that it is indecisive, and green that it is an accepted feature.
Every model type will have different effects from dif-ferent covariates, that is why there is a final selection step done per model, illustrated in Figure 2. The se-lected features from the two selection methods are used as covariates in the model, after which the insignificant features are dropped using the step-down procedure and a significance level of 90%, as to not remove too many. These two models are compared by an appro-priate metric, which is R2 for linear regression, con-cordance score for Cox PH, and AIC for Weibull. The
Figure 2: The flow of feature selection per model.
best model is selected as the final model. The features that are significant for the best performing model are the features that have the most important effects on the length of the time intervals between violations for the respective method.
3.4.3 Procedure
The experiments test which model is better at predict-ing the timpredict-ing of a violation made by a BRZO company. To determine which model performs better, the mod-els are compared against each other using the number of predictions that have a difference between the pre-dicted date and actual date that is greater than the one month threshold. The assumption is made, based on the judgement of a domain expert, that 30 days too late is the maximum error to remain effective, which make the predictions that are within these 30 days correct. Having a very early prediction is considered fine. A model with a lower percentage of predictions that fall outside the one month threshold is better than a model with a higher percentage.
If all the time-to-event models perform better than the baseline model, it can be concluded that time-to-event analysis is a good method for predicting the tim-ing of a violation.
4
Results
The first experiment, in Section 4.1, consists of select-ing the features that are important with their correla-tion that indicates what the effect is of the covariates. The next experiment tests the models on the test set and computes the performance metrics, in Section 4.2.
4.1
Feature Selection
Table 2 shows the features that were selected per model. For linear regression, a negative coefficient means that if the value of this factor increases, or is 1 instead of 0, the time between violations decreases. A positive coef-ficient means that if the value of this factor increases, or is 1 instead of 0, the time between violations increases. The coefficients of time-to-event analysis do not repre-sent the time between violations, but the probability of the event occurring over time. This means that a neg-ative coefficient means a lower risk of the event taking place at time t for companies with a higher value of that variable.
The features that are significant for the best model and interpretation are:
• As the length of trajectory gets 1 unit longer, the chance of new violations shrinks;
Feature Linear Regres-sion Cox PH without censoring Cox PH with censoring Weibull without censoring Weibull with censoring Length of trajectory at time t 0.18 -0.0009 -0.0014 0.0016 0.002 Number of inspections at time t -6.2 0.037 0.041 -0.05 0.06 Unknown previous violation type 68.3 ∈/ -0.33 0.33 0.59 Light enforcement on previous violation -42.9 ∈/ -0.23 -0.31 -0.48 Low industry type: Manufacturing of basic
iron and steel and/of ferroalloys
275.11 -2.7 -1.33 3.42 2.84
Low industry type: Manufacturing of petro-chemical products
/
∈ ∈/ ∈/ -0.73 -0.82 Middle industry type: Manufacturing of
pri-mary metals
-91.7 0.97 ∈/ -2.66 -1.78 Middle industry type: Manufacturing of coke
oven products and petroleum processing
/
∈ ∈/ ∈/ ∈/ -0.49
Low industry type: Manufacturing of alu-minium
600.4 -2.02 ∈/ 4.06 ∈/ Low industry type: Manufacturing of plastic
plates, films, tubes and profiles
/
∈ ∈/ -0.46 ∈/ ∈/ Low industry type: Management and
opera-tion of electricity, natural gas and hot water transmission networks
314.9 -0.81 -0.44 ∈/ ∈/
Number of workers ∈/ -0.000057 ∈/ ∈/ ∈/ Low industry type: Manufacturing of metal
structures and parts thereof
/
∈ -1.69 ∈/ ∈/ ∈/ Low industry type: Manufacturing of
fertiliz-ers and nitrogen compounds
85.3 ∈/ ∈/ ∈/ ∈/
Table 2: Coefficient values of the significant selected features. /∈ means that the feature was not in the selected features collection for the corresponding model.
Metric linear regres-sion Cox PH without censoring Cox PH with censoring Weibull without censoring Weibull with censoring Proportion of too late
predic-tions above threshold of all pre-dictions
0.55 0.26 0.32 0.39 0.40
Average difference in days be-tween predicted and actual tim-ing
130.4 117.8 121.7 118.3 137.5
Amount of days too late predic-tions above threshold
148 70 98 108 111
the chance of a new violations grows;
• Companies in the manufacturing of basic iron and steel and/or ferroalloys have a lower risk of making new violations than other industry types;
• Companies in Manufacturing of primary metals have a higher risk of making new violations than other industry types;
• Companies in manufacturing of aluminium have a lower risk of making new violations than other industry types;
• Companies in management and operation of elec-tricity, natural gas and hot water transmission net-works have a lower risk of making new violations than other industry types;
• A company with a higher number of workers has a slightly lower risk of making new violations; • Companies in manufacturing of metal structures
and parts thereof have a lower risk of making new violations than other industry types.
4.2
Performance
Table 3 shows the performance of all models. In short, it shows the average amount of days the models pre-dicted the timing too early and too late, the amount of predictions that were a month too late and the corre-sponding percentages.
A domain expert was consulted to interpret the re-sults, whether the difference between the predicted tim-ing and actual timtim-ing is too long or not. The base-line model has the lowest performance and the Cox PH without censoring model has the highest perfor-mance with an average difference of 117.8 days, which is almost four months, which is considered as too long. 74% of predictions made with this model were predicted within 30 days from the actual timing.
4.3
Validation
The hypotheses in Section 2.3 stated that the timing of violations made by BRZO companies can be pre-dicted with a time-to-event method, with type of indus-try, type of previous violation, type of enforcement on the previous violation, number of inspections, length of trajectory and the size of the company as covari-ates. The performances in Table 3 support hypothesis A, because all the time-to-event models outperform the baseline model. Given that type of previous violation
and type of enforcement on the previous violation ap-pear insignificant in Table 2, hypothesis B cannot be accepted. On the other hand, Table 2 shows that there is a decreasing trend of violations over time, thus hy-pothesis C can be accepted.
5
Discussion
The results show that the baseline model has the lowest performance, which makes sense since linear regression is not meant to be suitable for time to event predictions. Cox PH without censoring is the best performing method, indicating that the time to compute the cen-sored events can be left out of the methodology to save time. 74% of predictions were below the threshold and thus considered correct, this is above chance but still not a high percentage. It is questionable, when used in a real life context, if this model performs good enough. This means that a domain expert might need to look after the results when used in practice. Cox PH came out as a good model for this type of data, regardless of the related literature having a different type of data and features for their Cox PH models [22][25][6][7][27]. The results confirm the previously found result of Kluin et. al. [21] that there is a decreasing pattern in violations as the supervision trajectory gets longer. They found this result for a certain group of companies where the results presented here finds it for all com-panies. They used the same inspections dataset and a group-based trajectory modelling method. It may be the case, though, that there is still an average de-creasing pattern in violations when taking all types of companies into account and that this study was more focused on splitting the groups and finding their indi-vidual pattern.
This research found that the severity of the enforce-ment on the previous violation does not have a signifi-cant effect on the probability of a new violation event, which is interesting because previous studies found that different degrees of punishment do have effect [10][15]. However, the research of JBT EAU [10] is a crimino-logical qualitative exploration of the experiences of en-forcers and thus it is a remarkably different method. It is likely that the experiences of supervisors is dif-ferent from what the data says is a significant effect, which may indicate that there is something special in the data, or that the observations of the inspectors are
misplaced. The research of Grasmick et al. [15] has been done on crime data of American individuals. Laws and rules are different in other countries and different for persons than for companies, being another situation with different effects.
There seems to be some inconclusiveness on the ef-fect of company characteristics. The results show that company size and some certain industry types have a significant effect. However, some related studies state that company characteristics do not relate to making violations [14][9], while they also found that there are some types of industries that violate more than oth-ers [9][30] as well as that bigger companies make less violations [39][14]. It seems that the statement that characteristics are unrelated, is wrong. The industry types that have problems complying in those studies are different from the results of this thesis. The only industry with a higher probability of violations is the manufacturing of primary metals industry, while in the previous studies petrochemicals, pharmaceuticals, pulp mills and automobile factories have problems with com-plying [30][9]. This difference probably arises because these studies might have had a different collection of industry types differs in size from the one used in this study. Moreover, they were not performed on Dutch companies, which may cause different results. Besides, all levels of industry types were used in this research, though it might be that the results would be more in agreement with each other if only one level was used in the experiments. This is, however, not certain since it has not been tested.
Some related studies state that the severity of vi-olations was not taken into account and that this is something for future studies [21][14]. In contrast, the results of this thesis show that for this type of dataset, the weight of the violation does not need to be included. There are some limitations in this study. It was already stated that the inspection dataset has errors, mainly missing data [5], but the exact error needs to be known to make an error calculation. So, even though it is known that there is something wrong, the data is still granted and can be worked with.
Due to the fact that the exact date of a violation is unknown (also called the “dark number” in crimi-nology), an assumption had to be made that the date of the violation was close enough to the date of the belonging inspection, that the dates are equal.
Conse-quently, the models predict the timing of an inspection where a violation is detected instead of the timing of that underlying violation. Methodologically, this is a problem. However, from the punishment point of view, it tells when the inspection is supposed to be where the company can be punished for a committed environmen-tal crime. Hence, if the intention of the prediction is to find a date so that a company is punished, the predic-tion should be a bit later than the violapredic-tion event and the company will be sanctioned, which is good as long as the prediction is not too late.
There were different types of enforcement in the data. In this approach it has been chosen to categorise these enforcements from light to heavy punishment, accord-ing to [12]. However, this resulted in these categories being not significantly relevant for the best performing model. It has not been examined if other categorisa-tions would work better in this situation; for example, the categorisation could have been left out, or it could have been grouped by physical measure and imposing of a fine [32].
It has not been verified if there is a selection bias in the data where certain companies get inspected more or less than others.
There is only one dataset for inspections of BRZO companies in the Netherlands, thus the method could only be applied to this specific dataset. Additionally, rules and laws are different in other countries. There-fore it is not likely that the resulting model will gener-alise to other existing datasets.
6
Conclusion and Future Work
The research question of this thesis was whether time-to-event analysis is a good method for predicting the timing of violations made by BRZO companies in the Netherlands. In addition, it was investigated which factors explain why companies do or do not comply with the environmental rules.
It can be concluded, based on the findings, that time-to-event is a good method and preferable over a simple linear regression model. The important variables that explain the duration are the length of the trajectory, the number of inspections, the type of industry and the company size measured in amount of workers. It has been found that as the supervision trajectory of a company persists, the probability that a company
makes violations decreases linearly.
This work contributes to a gap in the research in time-to-event predicting of rule breaking by Dutch BRZO companies. The benefit of this thesis for the government is the knowledge on which factors prolong the time between violations and which factors do not have a significant effect. The resulting model suggests a moment in time to perform an inspection where, in 74% of the cases, a violation will either be prevented or an offence was made at most one month ago.
Nevertheless, improvements can be made in future studies. Firstly, potential flaws in the dataset, like missing data, skewed data, and selection bias, can be measured to make error calculations and improve the results. Secondly, a different categorisation technique for type of enforcement can be tested, as mentioned in the discussion in Section 5. For example, categorising it in tactic (ordinances, fines, etc.) or just as its individ-ual punishment could be more effective. Thirdly, the levels of industry types can be deducted to one level. It should be experimented with which level to use, but the middle level or the most detailed look appropriate according to the results. Lastly, there are more time-to-event methods than used in this research. Other models can be used in as an approach that might perform even better than the method proposed in this thesis.
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Appendices
A
Dataset Description
B
Hierarchy of Type of Industries
Consulting, research and other specialist business services Advertising and market research
Market and Opinion Research Offices
Architects, engineers and technical design and advice; inspection and control Technical design and advice for earth, water and road construction
Technical design and advice for process engineering
Holdings (not financial), intra-group intra-group services and management consultancy Holdings (not financial)
Industrial design and design, photography, translation and other consultancy Other specialist business services
Research and development work
Other scientific research and development work (not biotechnological)
Extraction and distribution of water; waste and wastewater management and remediation Remediation and other waste management
Remediation and other waste management
Waste collection and treatment; preparation for recycling Collection of harmless waste
Preparation for recycling of metal waste (except scrapping ships, cars, white goods, computers, etc.)
Preparation for recycling of waste (not metal waste) Treatment of harmless waste
Treatment of hazardous waste (not nuclear waste) Financial Institutions
Financial institutions (not insurance and pension funds) Financial holding companies
Industry
Manufacture of beverages Manufacture of beer
Manufacture of chemical products Manufacture of dyes and dyes Manufacture of essential oils
Manufacture of fertilisers and nitrogen compounds Manufacture of industrial gases
Manufacture of other basic organic chemicals n.e.c. Manufacture of other chemical products n.e.c.
Manufacture of other inorganic basic chemicals n.e.c.
Manufacture of perfumes and cosmetics
Manufacture of pesticides and other agrochemicals Manufacture of petrochemical products
Manufacture of photochemical products Manufacture of plastics in primary form Manufacture of powder and explosives
Manufacture of soaps, detergents, polishes and cleaning products Manufacture of synthetic and artificial fibers
Manufacture of synthetic rubber in primary form
Manufacture of coke oven products and petroleum processing Petroleum Refining
Manufacture of electrical equipment
Manufacture of other electrical equipment Manufacture of foodstuffs
Breaking, purifying and refining of salt
Manufacture of crude vegetable and animal oils and fats Manufacture of feedingstuffs
Manufacture of potato products
Manufacture of starches and starch products Manufacture of sugar
Refining of vegetable and animal oils and fats Slaughterhouses (not poultry)
Manufacture of metal products (not machines and equipment) General metalworking
Manufacture of chains and springs
Manufacture of metal structures and parts thereof Surface treatment and coating of metal
Manufacture of other goods
Manufacture of other goods n.e.c.
Manufacture of other machinery and equipment
Manufacture of hoisting, lifting and transport equipment
Manufacture of machinery for textile, apparel and leather production Manufacture of other means of transport
Manufacture of aircraft and components therefor (other than aircraft seats) Manufacture of other non-metallic mineral products
Manufacture. Of other non-metallic content. Mineral products (not abrasive, grinding and polishing agents.)
Manufacture of pharmaceutical raw materials and products Manufacture of pharmaceutical products, not raw materials
Manufacture of primary metals Manufacture of aluminium
Manufacture of basic iron and steel and of ferroalloys Manufacture of lead, zinc and tin
Manufacture of rubber and plastic products
Manufacture of linoleum and other hard floor coverings not made of plastics Manufacture of other plastic products
Manufacture of plastic plates, films, tubes and profiles Repair and installation of machines and equipment
Repair and maintenance of ships (not recreational ships) Mining of minerals
Extraction of minerals (not oil and gas) Extraction of other minerals n.e.c.
Production, distribution and trade in electricity, natural gas, steam and cooled air Production, distribution and trade in electricity, natural gas, steam and cooled air
Management and operation of electricity, natural gas and hot water transmission networks Production of electricity by thermal, nuclear and combined heat and power plants
Trade in electricity and gas through mains Rental of and trade in real estate
Rental of and trade in real estate Property management
Rental of immovable property (not of living space) Rental of movable property and other business services
Job placement, employment agencies and personnel management Lending agencies
Other business services
Other business services n.e.c. Transportation and storage
Land transport
Road freight transport (no removals) Storage and transport services
Freight forwarders, ship brokers, charterers and other intermediaries in the transport of goods
Loading, unloading and transhipment activities for seagoing shipping Loading, unloading and transhipment activities not for seagoing shipping
Storage in distribution centers and other storage (not in tanks, cold stores, etc.) Storage in tanks
Wholesale and retail trade; repair of motor vehicles Retail (not in cars)
Gas stations
Shops selling flowers and plants, seeds and garden supplies Trade in and repair of motor vehicles, motorcycles and trailers
Wholesale and brokerage of car parts and accessories (not tires) Wholesale trade and intermediation (not in cars and motorcycles)
Brokerage of fuels, ores, metals and chemical products Wholesale of arable products and animal feed general range
Wholesale of chemical raw materials and chemicals for industrial application Wholesale of ferrous metals and semi-finished products
Wholesale of liquid and gaseous fuels Wholesale of other consumer articles n.e.c. Wholesale of packaging
Wholesale of washing, polishing and cleaning products
Wholesale on a fee or contract basis of agricultural products, live animals and textile and food raw materials
Wholesale trade of marine and fishing supplies Wholesale trade of mineral oil products (no fuels) Wholesale trade of paints and dyes
C
Descriptive Analysis
Figure 7: Average time interval between violations per punishment on previous violation type. This shows that the average time between violations is longer if the punishment on the previous violation is severe and shorter if the punishment was very severe or mild.
Figure 8: Average time interval between violations per previous violation type. The average duration of the time between violations per previous violation type are very close to each other, thus it seems that this variable might not matter to the duration between violations.
Figure 9: Average time interval between violations per middle industry type. Manufacture of primary met-als industries have a low average time between violations, whereas remediation and other waste management industries have a long average duration.
Figure 10: Time between violations by the number of inspections at that point. This shows a steep decrease in time between violations as the number of inspections increases, which suggests that more inspections results in the company making violations faster, which is an artificial effect.
Figure 11: Time between violations by the length of the trajectory at that point. This shows a doubtful relation between length of trajectory at t and the time between violations. Although the correlation is a bit unclear, there do is an upwards line visible.
Figure 12: Time between violations by the amount of workers working for the companies. This leads to believe that bigger companies have a shorter time between violations.
D
Feature Selection
Figure 13: Selected features using Boruta R package for data without censoring. The green columns are the relevant features
Figure 14: Selected features using Boruta R package for data with censoring. The green columns are the relevant features
No Censoring Stepwise Method With Censoring Stepwise Method
Feature Coefficient Feature Coefficient length trajectory at t 0.15 length trajectory at t 0.196 number of inpsections at t -5.8 number of inspections at t -7.04 number of workers -0.014 unknown violation 93.2 Middle industry type: Manufacture of
primary metals
-100.8 unknown enforcement 66.6
Middle industry type: Remediation and other waste management
507.6 Low industry type: Manufacture of ba-sic iron and steel and of ferro-alloys
215.05
Low industry type: Management and operation of electricity, natural gas and hot water transmission networks
339.3 Low industry type: Manufacture of plastic plates, films, tubes and profiles
248.2
Low industry type: Manufacture of alu-minium
626.6 Low industry type: Brokerage of fuels, ores, metals and chemical products
365.6
Low industry type: Manufacture of ba-sic iron and steel and of ferro-alloys
427.8 Low industry type: Management and operation of electricity, natural gas and hot water transmission networks
149.5
Low industry type: Manufacture of metal structures and parts thereof
1356 Low industry type: Technical design and advice for earth, water and road construction
448
Low industry type: Manufacture of synthetic rubber in primary form
836.5 Low industry type: Manufacture of metal structures and parts thereof
439.1
Middle industry type: Financial in-stitutions (not insurance and pension funds)
30.6
