The Ordinal Regression to Analyze Radical

This paper presents a result of research about the student’s radical intention related to their tolerance and personality type. The main research variable that is radical intention has a psychological construct that is theoretically built with a social approach and political point of view. As a big country, Indonesia has various pluralism i.e ethnic and religion, so that it requires a high tolerance attitude to live in a harmony. Students as the next generation and important elements in society are expected to avoid intolerance. The research subjects were 175 students from an Islamic university in Indonesia. The data were analyzed with Ordinal Regression which intention of radicalism (ordinal) as the dependent variable, personality type (nominal), and tolerance attitude level (ordinal) as independent variables. The majority of these students have good moral values so they can tolerate the difference. From the regression analysis, only a tolerance attitude has a significant effect on radicalism intention.


Introduction
What is the main factor which triggers a person to become radical?Is it because of external factors such as getting unfair treatment in the field of law and economics or internal factors such as personality type or mindset and parenting?In the psychological terminology, radically related to abnormal behavior (Sarwono, 1999).It is based on the statistical concept that individuals with radical thinking or behavior are fewer in number than those who think or behave radically.Hence the greater number are non-radical populations which are then classified as normal populations.Besides the abnormal personality, it is hypothesized that radicalism can be predicted from the attitude of individual tolerance.The more intolerant a person allegedly the higher radical potential.
Although this research was done in Indonesia, radicalism is a problem for all countries.Cause of that, some important things can be identified from this research that correlates with radicalism and the main factor which suspects relevant to it.Researchers are still interested in knowing further whether there is a relationship between personality type and the level of tolerance for radical intentions among students.Given that students are the millennial generation who interact intensely with the internet and the spread of radicalism occurs massively through social media (Ahmad and Nurhidaya, 2020).
The main issue that motivate this research was the statement from SETARA Institute which said that many campuses in Indonesia are already contaminated with radicalism.But there is no data that support this statement.Throughout 2021, the National Counterterrorism Agency (Badan Nasional Penanggulangan Terorisme/BNPT) noted that there had been a decline in radical intentions and an increasing level of tolerance.This is more or less the impact of BNPT's efforts to take down as many as 650 pieces of propaganda content that are indicated to be radical from hundreds of internet sites and social media.The process is in collaboration with the Director-General of Aptika, Ministry of Communication and Information (Kominfo).

Pakistan Journal of Statistics and Operation Research
As an archipelago country, Indonesia consists of 1331 ethnic groups each with a culture (BPS, 2015).Plurality in Indonesia is also in religion.There are six recognized religions in Indonesia i.e.Islam, Protestantism, Catholicism, Hinduism, Buddhism, and Confucianism, as presented in Table 1.This cultural diversity can be a capital for many things because it can a source of inspiration for the various joints of life but also as potentially a source of conflict if it fails to reduce the difference, caused by the low tolerance of society.Several factors are suspected can influence intolerant attitudes within society, especially among students, one of them is personality.Personality factors consist of many aspects those are genetics, gender, age, and emotional maturity, parenting and family patterns, and several other things.The study of personality and culture shows that there is a relationship between individual development and sociocultural setting (Pervin et al, 2004).Therefore, this study proposes that student tolerance is associated with personality type.Similar studies had been conducted by the Research and Development Agency and the Ministry of Religious Affairs Republic of Indonesia in seven public colleges in 2010.So that, this research was conducted in an Islamic university with the assumption that the students with better religious knowledge have better tolerance.
From a psychological perspective, terrorism is a product of the radicalism process.Research from Schmid and Jongman (Maskaliunate, 2002).find seven keywords which related to 'terrorism' those are violence (83,5%), politics (65%), fear and terror (51%), threat (47%), psychological effect and anticipate reaction (41,5%), differentiation of victim target (37,5%), purposeful, planned, systematic, and organized action (32%).These definitions have strengthened the previous argument which terrorism is an illegal action that full of violence to gain political towards and else.According to Dewi (Dewi, 2017), intolerance meets radicalism will give birth to terrorism.
As written in Milla and Faturochman's research (Mila and Faturochman, 2009) has found that in radicalism, individuals experience subordination of personal identity with group identity.Radicalism is not individual identity anymore.Although that, the research about internal psychological factors which stimulate an individual being radical is still interesting to do.
From this study are expected to know the psychological internal factors that contribute to one's radical intentions.The research's subjects are students from an Islamic university.This is an interesting thing because some students grow up in a fairly thick religious education environment.Today many terrorists appeared precisely from religious circles who use certain verses as encouragement of jihad.Being radical is experienced by some students in an educational environment with a religious background.On another side, Islam teaches about love and peace.From research, subjects are also explored whether religious teachings on love and peace can foster tolerance that is expected to prevent a person from being radical.

Respondent and Instruments.
The sample in this study was 175 students of an Islamic university in Bandung, Indonesia.Sampling is done randomly.This study uses primary data from three variables namely dependent variable (dv) is Radical Intention (Y) on an ordinal scale from 1 to 4. Next, there are two independent variables (iv) Personality Type ( 1 ) in nominal scale (category/classification) with four (4) categories and Tolerance attitudes ( 2 ) on an ordinal measure which divided into three levels i.e. low (1), middle (2), and high (3).

Big Five Personality Scale
The Big Five Personality Scale is an adaptation from the International Personality Item Pool (IPIP) that developed at the Eugene-Springfield Community Sample (ESCS) of the 1990s.Within the period, every year the gauge is piloted with many items.For example in 1994 tested 858 items, then continued with 285 items in 1995.While the Big Five Factor itself was developed by Goldberg, L.R. in 1992.Indicator for Big Five Personality Scale derived from IPIP.This instrument consists of 50 items with 10 items each to measure the five personality types.Each item is scored according to the Likert scale of 1 to 4 and we get the interval data.Data collecting is done using a measuring instrument that has been tested by Sari (Sari, 2010).

Tolerance Scale
The Tolerance Scale was compiled by van der Walt, J.L. (Van der Walt, 2016) consisting of 42 items.This measuring tool was developed based on several categories of religious attitudes in addressing the differences put forward by Bennett (Bennet, 1993) namely denial of difference, acceptability of difference, adaptation to difference, and integration on the difference.These categories are arranged into items that score with a Likert scale of 1-5, 1 expressing attitude Strongly Agree to 5 stating Strongly Disagree.Data were obtained on an interval scale.Because this instrument is the result of adaptation then before being used for data retrieval, firstly done the testing process (Try Out).The reliability coefficient was calculated with the Cronbach Alpha technique of α = 0.795.It provides information that the instrument is quite reliable.

Radical Intention Scale
Remember that Silber and Bhatt (Silber and Bhatt, 2007) identified four stages of radical intention namely preradicalization → self-identification →indoctrination → jihadization (holy war).Because the research subjects are the Muslim community then this study is associated with the efforts of the Muslims to do the sharia jihad which is encouraged by the verses in the Quran among them QS At Taubah verse 73 which means "O Prophet, do jihad (fight) people unbelievers and hypocrites and be harsh with them.Their place is hell.And that is the worst place to return." The four aspects identified by Silber and Bhatt are constructed onto a scale with Likert scoring, measuring device containing four (4) options, scoring 1 to 4 (unfavorable items) and scoring of 4 to 1 (favorable items).This measuring instrument consists of 32 items then the range of scores ranges from 32 to 128 with the greater the score indicating the more intense radical in individual.

Data Analysis
In this research, the data analysis technique is Ordinal Regression where data analysis was carried out with Statistical Package for the Social Science (SPSS) software version 26.This technique is a method to find the relationship between the dependent variable (dv) or Y, which has an ordinal scale with independent variables.In this study, the goal is to see how much the influence of personality type and tolerant attitude towards radical intentions.
Ordinal (logistic) regression model are used to predict the dependent variable that has an ordinal type (Arfan & Sherwani, 2017).If the dependent variable is ordinal data, we can use Ordinal Regression (Agresti, 2007) Ordinal Regression describes the relationship between dependent variables with a set of independent variables, where the dependent variable is ordinal that has more than 2 categories and each category can be rated with free variables of each nominal scale and interval.Ordinal regression analysis is a statistical method that describes the relationship between a response variable (Y) with more than one predictor variable (X), where the response variable is more than two categories and the measurement scale is level (Hosmer and Lemeshow, 2000).
For this research, we use Ordinal Regression because the dependent variable has four levels are pre-radicalism, self-identification, indoctrination, and jihadism.Pre-radicalism is the lowest level and jihadism is the highest level of radical intention.The purpose of Ordinal Regression is to estimate the value of the probability of a particular event within a population as an explanatory function.This type of regression uses response variable (dv) shaped dummy variables for each level.Table 2 contains details of research variables.

Table 2. Dependent Variable and Independent Variables
From Agresti, Ordinal regression is supposed to count the probability of the event in a population as an explanatory function.Ordinal regression can be performed using a Generalized Linear Model (GLM) which fits a coefficient vector to a dataset.One of the models that use to find the Ordinal regression is the Logit model.This model is a cumulative logit model in which the ordinal nature of the dependent variable Y is expressed in the cumulative probability.The model for ordinal regression is expressed by equation (1).If it is assumed that the dependent variable Y consists of j categories, the probability for a certain X can be expressed by equation (2).This results in a cumulative logit model obtained by comparing the cumulative probability with a greater chance than the response category to j. Next, the cumulative probability form, (1) where X is the success probability for an event and   are parameter values and  = 1, 2, … ,  the level of respon categorical.This function is linear so must transform to logit form to see the relationship between dv and iv.With do the logit transformation for (), we find the more simplified equation for Equation (1) as follow (2) where is a risk from  − 1 for particular .
Next do 3 (three) testing that is the overall test, partial test, and fitness model.The final section is the interpretation of the results associated with the value of each predictor.

Descriptive Results
Before looking at the results of ordinal logistic regression analysis, the three research variables will be described with their proportion, those are Radicalization Intention (Figure 1a), Type of Personality (Figure 1b), and Tolerance (Figure 1c). [a] [b] [c] The results of data analysis appear only 4 (four) personality types on the subject of this study are type E (n = 6), type C (n = 93), type ES (n = 47), and type I (n = 29).The facts that in this research found only four of five personality types from 175 respondents.
In Figure 1 (a) we can see that more than half of respondents 58% are in the lowest level Pre Radicalism, only 2% are in the second level, Identification, 3% are in Indoctrination, the third level, and 37% are in the highest level, Jihadization.These results provide an illustration that what is 'suspected' of Islamic educational institutions as a place to grow the seeds of radicalism is not found.
Figure 1 (b) say that more than half of respondent (54%) have a Conscientiousness personality.Indicator said that these respondents have a regular, systematic, thorough, neat, efficient, careful, steady, earnest, and timely manner.Although the facts on the ground indicate the possibility that the response has a normative attitude considering the respondent comes from the environment of religious institutions.Figure 1 (c) shows that the level of tolerance most respondents are in the middle state (84%).The rest (16%) have a low and high tolerance.These results show that the majority of students in Islamic-based universities can accept differences, even though they are in the moderate category.

Regression Results
After getting some descriptions from three variables, we find some inference results.Begin with an analysis of the correlation between radical intention and tolerance level.Table 3 is a cross tabulation containing the number of subjects at low, medium and high levels of radical intensity, as well as their tolerance level.for example, the contents of the cells in row 1 and column 1 are 7 people, this is the number of subjects who have low radical intention and also have a low tolerance level.Because according to the purpose of cross tabulation is to present two quantities or characteristics in one value.

N of Valid Cases
From approximation significance, we can see the result is 0.028 < 0.05 (Gamma test), i.e. p-value less than alpha.So, we can reject the  0 .The conclusion is that the correlation between Radical Intention and Tolerance Level is significant.

a. The Proportional Odds Model (POM)
Furthermore, we presented the results of data analysis with ordinal logistic regression with the model is Proportional Odds.The first result is shown in Model Fitting Information.-2log Likelihood explains that without entering the independent variable (intercept only) the value is 89.500.However, by entering the independent variable into the model there is a decline in value to 61.426.This changed the Chi-Square to 28.075 and was significant at a 5% real level (sig.0.00).The Goodness of Fit with Chi-Square in Table 6 shows the model's equity test with the data found that Deviance is 34,460 with significance 0.059 > 0.05.This means that the model corresponds to empirical data or a model is worth using.
These three equations i.e.Equation (3), Equation ( 4), and Equation ( 5) are called Classification Functions (Hosmer and Lemeshow, 2000).These functions have the same coefficients for the independent variables, in this case, only the second variable is significant that is the tolerance level, whereas the constants have different values.This value of constants is a cut point that will be differentiated the three classification functions.
The classification function formed strengthens the Logit Model which is a distinguishing function.If there is a category in the non-free variable then the classification function is formed as much as  − 1.For this research the dependent variable (Radical Intention) consist of four categories/levels i.e.Pre Radicalism (PR = 1), Identification (Id = 2), Indoctrination (In = 3), and Jihadization (J = 4) so that the Classification Function formed there are 3 i.e.Equation (3) to (5).  9 is used to test the assumption that each category has the same parameters.Hence the result of significance (pvalue = 0.087 > 0.05) causing the assumption can be  0 accepted.This means that the selection of the link function i.e.Logit is correct.

b. The Partial Proportional Odds Model (PPOM)
In an ordinal logistic regression model that fulfills the proportional odds assumption, the regression coefficient of each logit function is formed the same, and the intercept value of each logit function is different (Kleinbaum & Klein, 2010).From equations (3), (4), and (5) it can be seen that the intercept is different for each logit function, as the coefficient of the first variable.While the coefficient for the second variable is the same.Thus the assumption of proportional opportunity presented by Kleinbaum & Klein is not fulfilled.Therefore the Partial Proportional Opportunity Model (PPOM) is more suitable here.The PPOM is an extension of the Proportional Odds Model (POM) which allows some predictors to be modeled with the assumption of proportional increase and for other variables where this assumption is not fulfilled, certain parameters are entered into different models for the various categories being compared (Siqueira, Cardoso, Caiaffa, Abreu & Natali, 2008).Data analysis was repeated for PPOM using SPSS software by selecting the Complex Samples procedure.The analysis was carried out per category of the dependent variable which consisted of 4 categories.But a warning appears from the software that says the log-likelihood value is approaching zero.There may be a complete separation in the data.The maximum likelihood estimates do not exist.The CSORDINAL procedure continues despite the above warning(s).Subsequent results shown are based on the last iteration.The validity of the model fit is uncertain.

Conclusions
In the conclusion of this study, there is a significant contribution of the level of tolerance to radical intentions.This rational logic makes sense because it has been discussed in the introduction that tolerance, radicalism, and terrorism are three interrelated words.The more intolerant one is, the greater the potential to become a radical individual.
Whereas personality type variables do not make a significant contribution to radical intentions.This is understandable because research subjects are students who have a well religious education background so that has a good and objectively understanding of how to be tolerant.This is not correlated with their type of personality.
Taking the students from Islamic university as the subjects of research based on curiosity whether the type of personality and tolerance level together affect the radical intention due to the increase of radicalism among the people who learn religion.Moreover, the age of students is still in the phase of searching for an identity that allows shelter under the cover of religion makes them comfortable although misguided or has little religious insight in interpreting the verses of jihad in the Qur'an as a frontal movement that leads to radicalism.This hypothesis is proven significantly from the Ordinal Regression Model used.However, not significant for the first independent variable, Type of Personality.Suggestion, the variable personality type will be removed from the model because it doesn't significant.Then re-done Ordinal Regression testing as a whole.Some arguments may be proposed for the rejection of the first independent variable that is the type of personality.One of the arguments is the insight of knowledge about religion is good enough among respondents to cause them to know how to be tolerant, however, that attitude has nothing to do with their personality type.
Suggestion, the next research can be started by conducting in-depth research on the instrument to measure the variable, especially the radical intention considering the items contains a sensitive topic.The respondents may be careful not to be detected have a deviating attitude from the norm.It can rise a bias in the measurement.Need to be checked from a Psychometric point of view whether there are Common Method Variance and Bias on measurement.This research is a response-based research and uses 175 subjects as a sample.Actually, the number of subjects involved in this study was initially around 400 people, but most of the data was invalid.So only 175 subjects were used.Because of that, it is suggested for future studies that are interested in continuing this topic, to increase the number of subjects so that the conclusions obtained are stronger and more representative.
In the future, this research wants to be developed by applying the catastrophic mathematical model which is to see two people with different types of personalities but who have the same level of tolerance will be at the same stage of radical intention.If the tolerance level of one subject is increased (added a little), the two subjects will be at a different stage of radical intention.

Table 1 .
Composition of Religion in Indonesia The bad incidents happened in the past years.The motto of Bhinneka Tunggal Ika (Indonesian motto, Unity in Diversity) was tested by various conflicts that divide the unity.Discrimination attitudes towards certain ethnicities in political matters, as well as the election of regional leaders, became the source of disunity.A very strong idea of Primordial and Ethnocentrism emerged in a society where it was feared that Indonesia would become a country prone to horizontal conflict.The number of cases of intolerance increases.In 2014 has recorded 74 cases of intolerance and in 2015 has 87 cases and in 2016 almost 100 cases (The Wahid Institute, 2014).The types of intolerance include prohibiting certain religious activities, destroying houses of worship, discriminating against adherents of certain religions, intimidating and forcing the faith to the other.

Table 3 .
Radical Intention vs Tolerance LevelBecause these two variables have ordinal measures, we use the Gamma test to examine that the correlation between the two qualitative ordinal variables.The result is present in Table4.

Table 5 .
Model Fitting Information

Table 7 .
Pseudo R-Square Square in Table7shows how independent variables (Type of Personality and Tolerance Level) can explain the dependent variable (Radical Intention).These values are like the coefficient of determination on regression analysis.Cox and Snell values were 0.148 (14.8%),Nagelkerke 0.217 (21.7%), and McFadden 0.140 (14%).

Table 8
shows the results of the Wald test and its significance.Variable Tolerance Level 29.22 has p-value significance of 0.000 < 0.05 and variable Type of Personality has p-value 0.547 > 0.05.These results show that the Tolerance Level affects Radical Intention but the Type of Personality does not affect Radical Intention.From Table8we can construct the Ordinal Regression equation for Radical Intention as follow

Table 9 .
Test of Parallel Lines