Modeling of waiting time to first employment of graduates at wolkite university, Ethiopia: Application of accelerated failure time models

Abstract In Sub-Saharan African countries like Ethiopia, the waiting time for graduates before having their first job is very high. This study aimed at predicting the waiting time to get their first job and the effects of the associated factors. A retrospective study was conducted based on the 2021 graduate tracer survey data at Wolkite University. By considering the complete information on the total of 2069 graduates, the accelerated failure time model was used to identify the different factors. The median waiting time to first employment for the graduates was 17 months. The Weibull accelerated failure time model was the most efficient model to examine the waiting time among other survival models. It revealed that graduates from all colleges had shorter waiting times when compared to colleges of agriculture and natural resource. Graduates who scored lower have been waiting longer to get their first employment when compared to the high scorer. Graduates who were from Amhara, Oromia, Tigray, and other regions have been waiting for about 1.30, 1.18, 1.93, and 1.38 times longer, respectively, compared to those who were from Addis Ababa. Also, graduates who search for a job through relations and others had shorter waiting times when compared to those searching through public advertisements. College of graduates, CGPA, region, ways of searching for a job, and numbers of applications were statistically significant factors identified. So considering these factors is vital to produce labor market-oriented professionals hired within a short time.

Belete Adelo Wobse received his First Degree in statistics from Arbaminch University, Ethiopia, in 2011, and Master's Degree in statistics from Addis Ababa University, Ethiopia, in 2014. Also, he awarded Higher Diploma in Teaching in Higher Education from Wollo University, Ethiopia in 2016. He had more than 9 years teaching experience. Belete is currently teaching undergraduate Statistics courses at Wolkite University, Ethiopia. He has published more than three articles in both national and international journals. His research interest include, research design and data analysis, modeling and applying statistical concepts to support and strengthen the various policies and decisionmaking activities in the areas of Economics, Public Health, Agriculture and Education-related areas.
Yohannes Haile Menuta is currently employed as lecturer and researcher at the department of statistics in Wolkite University. Yohannes had started teaching learning experience on higher education institution from 2 November 2008 to the present time. He delivered different statistics courses for under graduate students, did different research and community service projects. He was participated in different academic leadership as tracer study coordinator. But now in addition to research, community service and teaching-learning activities he is a head of statistics department. Finally, his research interest basically focused on public health, agriculture, and economics and finance-related issues.
Abebe Debu Liga is a lecturer at the department of statistics at Wokite University, Wolkite, Ethiopia. Abebe Debu is well interested in health care, agricultural development, and educational change-related disciplines.

PUBLIC INTEREST STATEMENT
Employability can be defined differently for different purposes. It is usually related to immediate employment which is full-time employment within 6 months. The purpose of this study is to predict the waiting time of new graduates to get their first job and the effects of the associated factors. The existing literature relates waiting time to secure first job with transition to employment and relevant factors that affect graduates' waiting time to first employment. Accelerated failure time model was used to identify the different factors based on the new graduate's information. Hence, the knowledge we obtained from the statistical modeling of waiting time to get first employment and understanding the effects of these factors is vital in developing educational program for producing labor market-oriented professionals that can be hired within a short time.

Introduction
Employability is a chameleon concept for the simple reason that can be defined differently for different purposes (Knight & Yorke, 2004). Some relate it to immediate employment which is fulltime employment of graduates within 6 months. However, from the international higher education policies and strategies perspective, the issue of higher education and the graduate labor market is treated much deeper and broader. It is often related and studied with multiple factors like sociobiographic background data, the study conditions of higher education, the curriculum, the individual study behaviors and competencies (hard skills and soft skills), job searching methods, and transition period of graduates (Arruda et al., 2018;Dania et al., 2014;Garcia, 2003;Getie Ayaneh et al., 2020;Gines, 2014;Jackson, 2014;Jun, 2017;Demissie et al., 2021;Niragire & Nshimyiryo, 2017;Schomburg, 2003).
The challenge of new graduates to be hired immediately after graduation is increasing. The lack of timely employment remains the most consistent problem for both developed and developing countries (CA, 2019;Eita, 2010). In Sub-Saharan African countries like Ethiopia, the waiting time of graduates before having the first job is very high and many graduates in Ethiopian universities challenged a lot in securing a job immediately after graduation (Reda & Gebre-Eyesus, 2018). Many university graduates were waiting long to be hired or staying unemployed (Gebretsadik, 2016;Yibeltal, 2016). Though entering the workforce and making a professional transition depends on personal effort and determination, academia must develop its curriculum in such a way that the possible waiting time for new graduates to get their first employment is reduced. To shorten the waiting time of new graduates to get their first job, revising academic curriculum programs based on labor market demand and research findings that are related to the time spent to secure their first job and the associated factors can be paramount.
In Ethiopia, there were rapid expansions of programs in higher education institutions and a number of students were graduated from the institutions (Akalu, 2016). However, the labor market in the country absorbed only a limited number of graduates, thereby thousands of fresh graduates remain unemployed (Batu, 2016;Yibeltal, 2016). Due to the low employment rate of new university graduates, they wait longer to get timely employment. In turn, the country was challenged by the unemployment of new graduates (Tessema et al., 2011).
Though many students were coming to the university by expecting skills and experiences that enable them to access graduate employment opportunities (Korka, 2010), they do not focus on key activities to engage in while attending college. However, every single decision regarding the choice of the right major, getting a quality internship, and decision on the best extracurricular activities plays an important role in one's future. Encouraging students to focus on their right major and engage in quality internships while attending college and equipping them with entrepreneur skills during their study is important to get timely employment (Groh et al., 2012;Majid et al., 2012;Shakir, 2009;Sławińska & Villani, 2014). One can mention many possible factors that can prolong the graduates' employment. For instance, discipline type, graduate's achievement, gender, residence, family background, and graduates' job hunting skills can be possible factors that can affect the employment of graduates (Arruda et al., 2018;Dania et al., 2014;Getie Ayaneh et al., 2020;Jackson, 2014;Jun, 2017;Molla Demissie et al., 2021;Niragire & Nshimyiryo, 2017).
These days the issue of graduate unemployment draws the attention of many scholars. This is because it affects the unemployed graduates, their families, and the country as a whole (Hossain et al., 2018;Hwang, 2017;Mohamedbhai, 2015). In this study, the waiting time to first employment is of particular interest because predicting the time spent to get the first job and the effects of the associated factors with the timing of first employment of new graduates in Wolkite University. Since such issues are vital in higher education policies and strategies to produce effective and labor market-oriented manpower.
Despite many studies on the prevalence of unemployment and associated factors in Ethiopia (Batu, 2016;Molla Demissie et al., 2021;Reda & Gebre-Eyesus, 2018), the assessment of the employment of university graduates and the underlying factors that affect the timely transition of undergraduate students into the labor market is still limited. Though some Ethiopian public universities have been trying to explore the factors associated with graduate unemployment (Gebretsadik, 2016;Getie Ayaneh et al., 2020;Molla Demissie et al., 2021;Siraye et al., 2018;Yibeltal, 2016;Yizengaw, 2018), it is not sufficient and inclusive. So, conducting some more research by using emerging statistical methods in the area may be appreciated. Thus, this study intends to predict the waiting time of bachelor's degree graduates of WKU to get their first employment and determine the associated factors using parametric and semi-parametric survival models. Specifically, the aim of this study was to compare the efficiency of the Cox PH and AFT survival models and identify the best model that describes the waiting time to first employment based on the AIC criterion.

Literature Review
This section reviews previous literature regarding employment of new graduates that includes transition to employment and relevant factors that affect graduates' waiting time to first employment such as sex of graduate, graduate's region, college of graduates, CGPA, the status of having an internship during the study, ways of searching for a job, number of companies/institutions contacted and some other variables studied in the section to understand the current study comprehensively. Meanwhile, study findings regarding factors that affect the employability of graduates from different countries would be compared. P. Knight and M.Yorke (Knight & Yorke, 2004) defined employability as a chameleon concept that can be defined differently for different purposes. Some relate it to immediate employment which is full-time employment of graduates within 6 months. However, from the international higher education policies and strategies perspective, the issue of higher education and the graduate labor market is treated much deeper and broader. Many authors, for instance, Gines, A. C (Gines, 2014).; Schomburg, H (Schomburg, 2003).; Garcia M (Garcia, 2003).; E. F. Arruda et al (Arruda et al., 2018); F. Niragire and A. Nshimyiryo (Niragire & Nshimyiryo, 2017); K. Jun (Jun, 2017); D. Jackson (Jackson, 2014); J. Dania et al (Dania et al., 2014); Muluye G. A. et al (Getie Ayaneh et al., 2020); Mesfin M. D. et al (Molla Demissie et al., 2021) studied and often relate employability with multiple factors like socio-biographic background data, the study conditions of higher education, the curriculum, the individual study behaviors and competencies (hard skills and soft skills), job searching methods and transition period of graduates.
Usually, universities conduct a tracer study to understand the current employment situations of their graduate as well as the labor market. This can be justified by Gines, A.C (Gines, 2014) who have undertaken a tracer study and concluded that tracer results are a powerful tool to document the employment characteristics, transition to employment, and the level of satisfaction of graduates in terms of the level of satisfaction of the university services, learning environment and facilities as well as the skills and competencies of the different bachelors' degree programs. Also, Schomburg, H (Schomburg, 2003) suggested that one need to consider graduate's information regarding their professional success (career, status, income) and information on the relevance of knowledge and skills (relationship between knowledge and skills and work requirements, area of employment, professional position) in conducting a tracer survey of graduates.
Another study by Garcia, M (Garcia, 2003) pointed out that tracer studies are an important source of information in Philippine to know what happened to graduates of academic programs in higher education institutions and to tackle social problems in relation to unemployment and underemployment. Moreover, the findings of tracer studies can be used to define/redefine higher education institutions' mission and market niche and show how academic programs can be adjusted to reflect institutional goals.
Researchers usually consider different factors of unemployment in their academic research articles on unemployment. For instance, Elano F. Arruda, et al. (Arruda et al., 2018) analyzed gender, age, race, residence, education level, and the region as determinants of long-term unemployment in Brazil. The finding revealed that Brazilian workers were unemployed for more than a year and it was found that women take longer to find work than men, indicating some gender discrimination in the Brazilian labor market. Similarly, some other academic research articles on unemployment were done by F. Niragire and A. Nshimyiryo (Niragire & Nshimyiryo, 2017); K. Jun (Jun, 2017); D. Jackson (Jackson, 2014); J. Dania (Dania et al., 2014) also considered discipline type, graduate's achievement, gender, residence, family background, and graduates' job hunting skills as determinants of graduates' employment. F. Niragire and A. Nshimyiryo (Niragire & Nshimyiryo, 2017) analyzed these factors using logistic regression analysis when they studied determinants of graduates' employment in Rwanda.
K. Jun (Jun, 2017) considered college reputation, major fields, grade average, gender, noncognitive skills, and graduate's internship status when he studied factors that affect employment and unemployment for fresh graduates in Shandong province in China. His finding showed that the higher the reputation of the college the higher is the possibility of a graduate finding a job. Also, he showed that many graduates find jobs and are hired simply because of their successful completion of an internship. Moreover, his findings revealed that economics and management, and engineering graduates find jobs more easily and there was no significant difference in job search between the female and male graduates.
A study by D. Jackson (Jackson, 2014) indicated that industry selection decisions in Australia broadly align with constitutes of graduate employability such as technical expertise, generic skill mastery, and a successfully formed graduate identity. Furthermore, it was indicated that demographic factors such as age, residency status, study mode, full-or part-time status, discipline, and the awarding institution enhance employment prospects, such as skill and identity development, engage in effective job search strategies, and provide high-quality courses through effective teaching and learning.
Dania et al (Dania et al., 2014) pointed out that students' employability in Malaysia was found to be correlated with gender, industrial training, involvement in extracurricular activities, and their participation in career development activities. Findings of Harry, T., Chinyamurindi, W.T., & Mjoli, T (Harry et al., 2018) showed that poor socio-economic status, a poor education system, curriculum issues, the choice of higher education institution, and social connections were identified as factors that influence graduates employability. In addition, the study suggested that policymakers should consider student perceptions towards employability when addressing the issue of unemployment.
Often universities face a series of challenges originating in their relationship with the labor market as stated by Korka (Korka, 2010). He explored a variety of education mismatches in the graduate labor market: from over-education to skill mismatches and their impact on employability though many students were coming to the university by expecting skills and experiences that enable them to access graduate employment opportunities. Thus, university curricula should align with industry expectations, and strengthening stakeholder links, enforcing industry-centric university curricula, improving graduate work experience, honing graduate soft skills, and their attitude to work is much more important to improve graduates work readiness as stated by Hardin-Ramanan, S., Gopee, S., Rowtho, V., & Charoux, O (Hardin-Ramanan et al., 2020). (Nicholaus & Eliafura, 2016) studied many curricula factors such as knowledge of technology, language (English), practical and technical skills, practical experience and class of degree obtained, and demographic characteristics like sex, age, marital status, level of education, residence and the like that may influence employability of fresh higher learning graduates in Tanzania, and their result revealed that sex of graduates and knowledge of practical experience were the only significant factors of employability of fresh higher learning graduates. Moreover, promoting internships, placements, and work-based learning was suggested as a measure to be taken to address employability in the study area. This may be because every single decision regarding the choice of the right major, getting quality internships and the decision on the best extracurricular activities plays an important role in one's future.
As stated by Gill, R (Gill, 2018)., employability skills, particularly interpersonal skills such as networking, job application, time management, and effective work habits can be developed through participation in an educational forum that may increase the professional employability of recent graduates. Also, many authors (e.g., R. Shakir (Shakir, 2009), M. Groh, et al. (Groh et al., 2012), S. Majid, et al. (Majid et al., 2012), and K. Sławińska and C. S. Villani (Sławińska & Villani, 2014)) believe that encouraging students to focus on their rights major and engage in quality internships while attending college and equipping them with entrepreneur skills during their study is important to get timely employment.
According to Joel Hinaunye Eita (Eita, 2010) who investigated the determinants of unemployment from a macroeconomic perspective rather than a microeconomic perspective indicated that the lack of timely employment remains the most consistent problem in both developed and developing countries. Furthermore, the challenge of new graduates to be hired immediately after graduation has been increasing globally as indicated by Patric OW CA (CA, 2019). The same thing has happened in Sub-Saharan African countries like Ethiopia.
Though there was a reduction in overall unemployment in Ethiopia, the percentage of graduate unemployment has been increasing which might create potential ground for social and political unrest. According to N. W. Reda and M. T. Gebre-Eyesus (Reda & Gebre-Eyesus, 2018), graduate unemployment in Ethiopia has reached its limit, and its increase could be perceived as a "red flag" to higher education expansion. They suggest that the expansion of higher education in Ethiopia must be aligned with market demand. Also, J. Yibeltal (Yibeltal, 2016) and D. Gebretsadik (Gebretsadik, 2016) confirmed that many graduates in Ethiopian universities were challenged a lot due to prolong waiting time before having their first job.
In Ethiopia, G. A. Akalu (Akalu, 2016) points out that a number of students were graduated from universities year by year due to the massification of students joining higher education and the rapid expansion of programs in higher education. However, J. Yibeltal (Yibeltal, 2016) and M. M. Batu (Batu, 2016) showed that the labor market in the country would absorb only a limited number of graduates and thereby thousands of fresh graduates remain unemployed. This might be due to graduates' skill gaps. J. Y. Yizengaw (Yizengaw, 2018) investigated that skills gaps and mismatches of graduates in Ethiopian universities result in very limited graduate employment. He stated that the skill gaps were largely caused by the poor design of the higher education curriculum and corrupted recruitment practices. A study by Z. Siraye et al. (Siraye et al., 2018) also revealed that Ethiopian public university graduates were unable to secure their employment shortly in the labor market due to problems of solving skills, information technology skills, and so on.
Also, it was noted that one of the challenges of new graduates in Ethiopia is the low employment rate of new graduates (Tessema et al., 2011). Muluye et al (Getie Ayaneh et al., 2020) have conducted a study regarding the waiting time to first employment of new graduates in the case of Debre Markos University graduates, Ethiopia. He pointed out that gender, age, college; cumulative grade point average (CGPA), the region where the graduates were from and place of residence was identified as significant factors that affect the graduates' average time span of unemployment based on the log-logistic model. Also, his finding showed that only 50% of the graduates managed to find their first job by 15 months after their graduation date.
Additionally, the findings of Mesfin Molla Demissie et al (Molla Demissie et al., 2021) showed that demographic characteristics, curriculum characteristics, institutional culture, graduate characteristics, economic and labor market conditions, and global and emerging issues can all significantly predict the fate of graduates' employment outcomes in Ethiopia. Based on his result from multinomial logistic regression analysis, he has drawn a lesson that except for their demographic characteristics, almost all independent variables predict the graduates' employment outcomes.
Nowadays, due to an increment in graduates' unemployment in many countries, the issues of graduate unemployment draw the attention of many researchers, for example, M. I. Hossain, et al. (Hossain et al., 2018), G. Mohamedbhai (Mohamedbhai, 2015), and Y. Hwang (Gines, 2014) who have studied the cause of graduates' unemployment and its effect. They believe that graduate unemployment affects the unemployed graduates, their families, and the country as a whole. Thus, the issue of graduate unemployment has to be researched timely.
Based on the above reviewed literatures, the main factors like gender, age, race, residence, graduate's region, college of graduates, discipline type (major fields), graduate's achievement, education level, study mode, full or part-time status, family background, and graduates' job hunting skills, the status of having an internship during the study, ways of searching for a job, number of companies/institutions contacted, interpersonal skills, study conditions of higher education, the curriculum, the individual study behaviors and competencies (hard skills and soft skills), student perceptions towards employability, industrial training, involvement in extracurricular activities, and their participation in career development activities were identified as candidate factors which affect the waiting time to first employment in this study.

Data source and population
This study was conducted by using 2021 graduate tracer survey data of all graduates in WKU. The target population of the survey was all WKU regular graduates in 2019. A total of 2505 students were graduated from 42 undergraduate regular programs in WKU in 2019. However, in this study a total of 2069 graduates with complete information were considered and analyzed.
The principal objective of the 2021 tracer was to assess the employment profile of the 2019 graduates after they obtained their first degree. In the graduate tracer survey, detailed information about the graduate was collected on issues such as their college/faculty, field of study, gender, cumulative grade point average (CGPA), region of graduates, ways of searching for a job, number of applications contacted, graduates internship status, their current employment status, waiting time for first employment, hiring organizations, area of work assignment, the extent of the field of study and work relationship, the importance of internship for finding a job, and other related variables using a structured questionnaire adapted from a nationally designed questionnaire for conducting tracer studies in all Ethiopian universities and through a telephone interview. That means the baseline information of the graduates was collected from the form that was required to be filled by the graduates immediately after their graduation date and the rest information related to graduates' current employment status and other related variables was obtained by contacting the graduates through their phone. In the graduate tracer survey, a total of 30 trained data collectors were recruited to collect the data.

Study Design
This particular study was a kind of retrospective cross-sectional study conducted based on data of all graduates with complete information. That means, among 2505 eligible university graduates invited to participate in the 2021 Graduate Tracer Survey (GTS), a total of 2069 graduates were analyzed since they provided complete information during the survey.

Variables in the Study
The Response Variable: The primary outcome of interest (response variable) was waiting time until employment, which was assessed using the question, "How long have you been waiting till your first employment in months?" according to the 2021 GTS survey questionnaire. Thus the waiting time to first employment is the response variable, which was measured as the length of time in months from graduation date to first employment. During the survey, all graduates were asked a series of questions regarding their employment status and how long they have been waiting till their first employment. The response to this question constitutes the waiting time of the graduate till first employment and graduates who had not yet employed result in right censoring of the data.
Explanatory Variables: In the study, several predictors were considered by asking the graduates about potential demographic and environment-related predictors of waiting time to employment such as sex of graduate (female, male), graduate's region, the current region where the graduate lives, college/faculty (AGRI, BECO, CI, ET, MHS, NCS, and SSH), CGPA, the status of having an internship during the study (yes or no), number of companies/institutions contacted and major means for searching a job (Public advertisements, Social media (internet), Relatives, Others) were considered as explanatory variables.

Methods of Data Analysis
We have used descriptive statistics to describe graduate's baseline information in relation to waiting time till first employment in order to show the distribution of graduates by the key variables. Also, we have used the Kaplan-Meier method (Kaplan et al., 1958) to estimate the unemployment curve and the survival modeling approach such as Cox PH and parametric AFT models to investigate the extent of variations and the factors associated with the variable of interest. That means we have fitted a survival model for estimating factors associated with waiting time to first employment by using STATA 14.

Survival models
This study was considered two types of survival models namely, Cox PH and AFT models to determine the correlates of waiting time to first employment of graduates from WKU. Cox PH is a widely applicable survival analysis technique that makes no assumption about the functional form of the baseline hazard, λ 0 t ð Þ. It is given by (Cox, 1972) Where, λ t; X; β ð Þ is hazard function at time t with covariates, X ¼ X 1 ; X 2 ; . . . ::; X p À �0 , λ 0 t ð Þ is the arbitrary baseline hazard function that characterizes how the hazard function changes as a function of survival time, and β ¼ β 1 ; β 2 ; . . . ; β p À �0 is a column vector of p regression parameters associated with explanatory variables. The Cox PH model is popular because it allows a flexible choice of Covariates and also does not require estimation of the baseline hazard rate, λ 0 t ð Þ to estimate the regression parameters. However, these days using parametric survival models like AFT models which assume some function form for λ 0 t ð Þ, and hence for the baseline survival function,S 0 t ð Þ have increased greatly due to software advancement to support certain probability distribution families for the survival time that can be used with this model. For instance, STATA (Streg) supports parametric families such as exponential, loglogistic, Weibull, lognormal, and generalized gamma.
Thus researchers can apply parametric models like the accelerated failure time model to analyze survival data as an alternative to the Proportional hazards model for the analysis of survival time data (Orbe et al., 2002;Pourhoseingholi et al., 2007). Under AFT models, we measured the direct effect of the explanatory variables on the survival time instead of hazard. This characteristic allows for an easier interpretation of the results because the parameters measure the effect of the correspondent covariate on the mean survival time (Gelfand et al., 2016).
The AFT model states that the survival function of an individual with covariate X at time t is the same as the survival function of an individual with a baseline survival function at a time is a vector of regression coefficients. In other words, the accelerated failure-time model is defined by the relationship (Klein & Moeschberger, 2003).
The effect size for the AFT model is measured using the time ratio (TR) which is a ratio of the survival time of an individual with an exposure to the survival time of an individual without the exposure for a given survival probability. The effects of the covariates in the AFT model either accelerate or decelerate the event time by some constants (Khanal et al., 2014). Suppose, T i is a random variable representing the survival time for the, individual. The representation of the relationship between covariate values and survival time in the AFT model is linear relationship between log time and the covariate values and expressed as: where μ is an intercept, β 0 ¼ β 1 ; β 2 ; . . . ; β p � � is a vector of regression coefficients, δ is a scale parameter and is a random error which is assumed to have a particular probability distribution.
Among commonly adopted parametric AFT models like Weibull, log-normal, and log-logistic in terms of the distribution of survival time, in this study we have considered Weibull AFT Model. For model selection and comparison purpose, the Akaike's information criterion (AIC) was used which is defined as: Where k is the number of covariates and c the number of model specific distributional parameters. Lower values of the AIC suggest a better model.

Descriptive statistics
The graduate tracer survey data of 2069 graduates of Wolkite University in 2019 academic year have been reviewed of which 672 (32.5%) were unemployed and the remaining 1397 (67.5%) were employed. As shown in Table 1, the proportion of employment for females is not differing that much compared to males. Out of 825 female and 1244 male graduates, 274 (33.2%) and 398 (32.0%) were not employed yet since their graduation, respectively. The distributions of graduate's employment status as per colleges were showed in the table. The maximum unemployment proportion was 48.2% from college of Agriculture and Natural Resource.
With regard to CGPA Category, majority of the graduates had a CGPA of 2.00 to 2.74 with maximum unemployment rate, about 40.0 percent. When we look the graduates' region of origin, about 10.9% of the graduates were from Addis Ababa, 21.9% from Amhara, 33.0% from Oromia, 31.9% from SNNP, 0.5% from Tigray, and the rest 1.7% from others regions. More than half (61.0%) of the graduates had internship experience when they were in the university. Of the total graduates, 55.8% of the graduates were searching a job through public advertisements, whereas the remaining 20.1%, 21.4% and 2.8% were through social Media, Relations and other ways, respectively. The overall median waiting time to first employment for the graduates was 17 months with 95% CI; (16, 18). Among employed graduates, about 46.5% were responded as they got their first job after a year as shown in Table 2. The majority of employed graduate, about 57.2% were hired in governmental organization while the remaining 4.4%, 19.6%, 4.5%, 0.2%, and 14.0% were hired in non-profit organization/NGO, private enterprise, public enterprise, consultancy firm and self-employed, respectively.
Regarding their area of work assignment, the majority of employed graduates, about 29.3% believed as they were assigned in elementary occupation, but the rest 8.7%, 5.8%, 15.8%, 17.9%, 7.7%, and 14.9% were assigned as managers, consultant, teacher, service and sales worker, plant and machine operator, and others, respectively. Moreover, about 53.3% of employed graduates confirmed as there were a very high extent of relationship between their field of study and area of work. With regard to importance of internship for finding a job, about 53.4% were responded as they have not got any importance from internship for finding a job.

Non-Parametric survival analysis
In any data analysis, it is commonly advisable to use univariate statistical analysis before doing multivariate analysis. In survival analysis it is highly recommended to look at the Kaplan-Meier curves for all the categorical predictors. This would provide insight into the shape of the survival function for each group and give an idea of whether or not the survival functions for the group are approximately parallel.
To have insight into the shape of the survival function of the waiting time to first employment for each group of covariate, Kaplan-Meier curves were drawn. The graph of the estimate of overall Kaplan-Meier survivor function showed that most of the graduates hired after they stayed a year and above (Figure 1).
To compare the waiting time to first employment among the different groups of covariates, the separate graphs of the estimates of the Kaplan-Meier survivor functions were produced for different categorical covariates. In the graph, the survivorship pattern of one lying above another means the group defined by the upper curve has a much waiting time to first employment (many unemployed) than the group defined by the lower curve.
Most of the graph shows the existence of differences in survival experience (waiting time to first employment) between different categories. For instance, the survival curves of the Kaplan-Meier survivor functions were depicted in Figure 2 (i-vi) for covariates like college of graduates, internship status, CGPA categories, region, ways of searching job, and number of applications, respectively.
The KM survival curves of covariates in Figure 2 indicate that the survival estimate of graduates' unemployment for each group of covariate was different. For instance, the survival curves in Figure 2(i) shows that graduates from college of medical and health science have better timing of first employment as compared to all other colleges whereas graduates from college of agriculture waiting long till they get their first employment. Also, the survival curves shown in Figure 2 (ii) tells that graduates who have had internship experience when they were in the university have lower waiting time to first employment as compared to graduates without internship experience.
To test whether the survival function for the waiting time to first employment is equal across group of covariates, log-rank tests were conducted besides to the Kaplan-Meier curves. Primarily, the log-rank tests of equality across strata have been considered to explore whether or not to include the predictor in the final model. The log-rank test results in Table 3 revealed that the covariates like college of graduates, CGPA category, religion of graduates, ways of searching a job, number of applications contacted and internship status during study were significant at 5% level of significance but the covariate sex of graduate is insignificant. Therefore, all the covariates that were showing a significant difference regarding graduates waiting time to first employment in Kaplan-Meier survival analysis were included in the multivariable survival analysis (final model).

Results of the Cox proportional hazard model
As in any model building procedure, the first step in survival modeling is exploring the relationship between each covariate and time to event through univariate analysis like Kaplan-Meier survival analysis and log-rank tests. In order to identify the relative contribution of different factors to the waiting time to first employment, it is important to check the significance of all the factors through such analysis before proceeding to more complicated models.
The Kaplan-Meier survival analyses that have been used previously were used for every factor separately as a result they do not control the effect of the other covariates. However, the results are important for selecting candidate variables for multivariable models. Based on results obtained from Kaplan-Meier survival analysis for categorical variables and log-rank tests, those significant variables at 25% level of significance like college of graduates (P < 0.001), CGPA category (P < 0.001), religion of graduates (P < 0.001), ways of searching a job (P = 0.001), number of applications contacted (P < 0.001) and internship status during (P = 0.001) were included in the multivariate Cox proportional hazard model and the following result were obtained (Table 4).

Test of the assumption of proportional hazards
Before using and interpreting a fitted Cox proportional hazards model, the proportional hazard assumption, which asserts the hazard ratios remain constants over time, must be tested. This is because incorporating variable(s) violating the proportional hazard assumption leads to an inferior fit of a Cox model since the power of test for the variables will be reduced with constant and nonconstant hazard ratio in the model (Achilonu et al., 2019).
In this study, the graphical methods and statistical test like likelihood based Wald test to the proportional-hazards assumption were used. We have checked whether curves are parallel or not for testing the proportionality assumption by visualizing the plots of estimated log(-log(survival)) against survival time for two groups. If we saw a parallel curves, the proportionality assumption of the proportional hazards model is satisfied. To tell how the curves are close enough to parallel visually may be difficult. However, this method gives some clue about the proportionality of the proportional hazards model for each covariate over time. The Figure 3(a-f) below depicts that the parallelity assumption is not met, more or less for all covariates.
The results of the test global test result (P-value<0.001) for testing the proportional-hazards assumption in Table 5 reveal violation of the proportionality assumption. This is because some of the P-values for testing whether the correlation between Schoenfeld residual for some covariates and ranked survival time is less than 0.05. To test proportionality assumption of proportional hazards assumption, generate time varying covariate by creating interactions of the predictors  and a function of survival times, and include these in the model. If any of time covariates is significant then those predictors do not have a constant proportionality over time. In this case we can conclude the proportional hazards assumption is violated. The estimated parameter value for some of the covariates like college, ways of searching a job and number of application contacted were having a small p-value smaller than 0.05 when they were used in a model as time dependent. This also shows these covariates are time dependent and hence they support evidence of deviation from the proportionality assumption in the model.
In general, both the graphical method and statistical test confirmed the violation of proportional-hazards assumption. Thus due to the violation of proportional-hazards assumption, we have used an alternative survival models like accelerated failure time models with different distributional assumptions were built to examine the waiting time to first employment.

Results of accelerated failure time models
To model the waiting time to first employment and estimate the relative contribution of different factors, parametric models such as Weibull, log-normal, log-logistic, and exponential models were carried out. Among these candidate models, a model that fits the data better was identified by using Akaike's information criterion (AIC). The rule is that any model with a smaller AIC is adequate to be used for fitting the observed data. The summary of log-likelihood and Akaike's information criterion (AIC) statistic for the survival models were presented in Table 6.
According to the results obtained, the Weibull model appears to be with minimum AIC and BIC values among all other competing survival models, revealing that it is the most efficient model to examine and estimate the relative contribution of different factors associated with the waiting time to first employment. The result for Weibull AFT Model is presented in Table 4, with the estimated values of the coefficients and its standard errors (Std.Err), time ratio (TR) and its 95% CI, and p value.
Even though the proportional hazard assumption was violated, the results of the results of Cox PH model were also included in the table alongside for comparison purpose. The results of the Weibull AFT model were similar to that of the Cox PH model in detecting the significant predictors of time to first employment. Though both models detect the same significant predictors, the interpretation of their effect is not the same. Since the assumption of proportional hazard assumption was violated, we have interpreted the results of the Weibull AFT model only.
Accordingly, the Weibull AFT model reflects that college of graduates, CGPA category, region of graduates, ways of searching a job, and numbers of applications contacted were identified as a statistically significant contributing factor for the graduates' waiting time to first employment at 5% level of significance. While internship status were not a contributing factor for the waiting time to first employment.
The estimated coefficients of predictors with a positive sign (i.e. time ratio above 1) imply that these variables prolong or accelerate the waiting time to first employment. Based on the  Wobse et al., Cogent Education (2022), 9: 2143032 https://doi.org/10.1080/2331186X.2022.2143032 estimated Weibull AFT model, those graduates from all colleges had shorter waiting times for first employment as compared to the college of agriculture and natural resource. However, the difference in the waiting time of first employment between college of social science and humanity and college of agriculture and natural resource were not statistically significant (TR = 0.91, p-value = 0.253). When comparing graduates with their CGPA categories, graduates who have scored a CGPA of 2.00-2.74, 2.75-3.24, and 3.25-3.74 have been waiting 1.58, 1.42, and 1.29 times longer to get their first employment as compared to the high scorer (3.75-4.00) graduates, respectively. Regarding to the region of graduates, graduates who were originally from Amhara, Oromia, Tigray and other regions had to wait 1.30 times (p-value<0.001), 1.18 times (p-value = 0.002), 1.93 times (p-value = 0.014), and 1.38 times (p-value = 0.017) longer to find their first job, respectively, as compared to those who were from Addis Ababa. However, the difference in the waiting time of first employment between graduates from SNNP and Addis Ababa were not statistically significant (TR = 1.06, p-value = 0.314).
When comparing graduates who were searching a job through public advertisements to those who were searching a job through relations like parents, relatives and friends, and to those who were searching a job other than this ways, graduates who were searching a job through relations and others had shorter (0.87 times with p-value = 0.001) and (0.78 times with p-value = 0.003) waiting time to first employment, respectively, as compared to those searching through public advertisements. However, graduates who were searching a job through social media had statistically insignificant difference (TR = 0.98, p-value = 0.557) in the waiting time of first employment as compared to those searching through public advertisements.
As compared to graduates who had 0 to 4 number of application contacts, graduates who had 5 to 9 and those who had more than 10 number of application contacts had a longer waiting time, about 1.17 (p-value< 0.001) and 1.25 (p-value<0.001) times, respectively, to find their first job. This result reveals that increasing the number of application contacts does not make the graduates to get their first job sooner though it was expected. Lastly, the results in Table 4 also showed that graduates who have had an internship experience during their study and those who did not have an internship experience were not statistically different (TR = 1.02, p-value = 0.682) in the waiting time to get their first job.

Discussions
In Ethiopia, the waiting time of graduates before having the first job is very high. This study revealed that the median waiting time to first employment for the WKU graduates was 17 months which is slightly longer compared to the finding obtained by Muluye et al. (2020) that was about 15 months. This shows many graduates wait long to get timely employment which is supported by other finding too (Eita, 2010;Reda & Gebre-Eyesus, 2018;Yibeltal, 2016). The difference in waiting time to get first employment may be due to college variation and ways of searching a job after graduation.
Since the proportional hazard assumption was violated in this research, the accelerated failure time (AFT) model was used to analyze time to first employment data and the Weibull AFT model was selected and discussed among the other parametric AFT models based on AIC criterion. This research showed that graduates from all colleges had shorter waiting times for first employment as compared to the college of agriculture and natural resource. Among graduates of all colleges, graduates from college of medical and health science had shorter waiting times for first employment which is consistent with the previous finding in Ethiopia (Getie Ayaneh et al., 2020). This may be due to the luck of skills in searching a job and limited number of absorbance of new graduates in labor market from the graduating programs (Akalu, 2016;Eita, 2010;Reda & Gebre-Eyesus, 2018).
The result also revealed that graduates who achieved a lower CGPA have been waiting longer to get their first employment as compared to the high achievers which is supported with other findings (Getie Ayaneh et al., 2020;Jun, 2017). This is probably due to imbalance between the number of vacancies contacted and number of job applicants. Moreover, graduates who were searching a job through relations like parents, relatives and friends, and other methods had shorter waiting time to first employment, respectively, as compared to those searching through public advertisements. This result is supported by findings of D. Jackson (Jackson, 2014) who have indicated that engaging in effective job search strategies would significantly determine the graduates waiting time to get their first employment.
Regarding gender, this study showed that male and female was not differ significantly in their survival function for the waiting time to first employment on the basis of log rank test result. This result was not supported by other findings (Dania et al., 2014;Getie Ayaneh et al., 2020;Molla Demissie et al., 2021;Nicholaus & Eliafura, 2016). For instance, Muluye et al (Getie Ayaneh et al., 2020) revealed that males had shorter waiting time to get their first employment than that of females. Mesfin Molla Demissie et al (Molla Demissie et al., 2021) also indicated that sex of graduate significantly predict the fate of graduates' employment outcomes in Ethiopia. In addition, a study by Nicholaus E. Nikusekela & Eliafura M. Pallangyo (Nicholaus & Eliafura, 2016) showed that employability of fresh higher learning graduates were significantly affected by their sex and knowledge of practical experience. However, it is in line with K. Jun (Jun, 2017) finding which reveals there was no remarkable gap in finding job between female and male graduates.
Regarding the effect of graduates' internship experience, many researchers have showed that a number of graduates find jobs and hired simply because of their successful completion of internship (Gill, 2018;Groh et al., 2012;Hardin-Ramanan et al., 2020;Harry et al., 2018;Majid et al., 2012;Nicholaus & Eliafura, 2016;Shakir, 2009;Siraye et al., 2018;Sławińska & Villani, 2014;Yizengaw, 2018). However, this study showed that graduates who have had an internship experience during their study and those who did not have an internship experience were not statistically different in the waiting time to get their first job. This may be due to unsuccessful internship practices which were incorporated in their study program.
In general, the result from Weibull AFT model revealed that the covariates such as college of graduates, CGPA category, region of graduates, ways of searching a job, and numbers of applications were identified as a statistically significant contributing factor at 5% level of significance.

Conclusions, Limitations, And Future Research
This study was carried out based on the WKU graduate tracer survey data of graduates in the 2019 academic year to model the waiting time to first employment of the graduates. The study revealed that the majority of graduates were employed. That means the majority reported as they have gotten their first job. Weibull AFT model was the best model that describes the waiting time to first employment compared to the other survival models based on AIC. According to the result of the Weibull AFT, college of graduates, CGPA category, region of graduates, ways of searching for a job, and numbers of applications were statistically significant contributing factors at a 5% level of significance. Therefore, we suggest the university consider these factors in developing its educational program for producing labor market-oriented professionals that can be hired within a short time.
This study has some limitations since it focused only on modeling and relied on secondary data of graduates of WKU. Thus, the study provides only some insights regarding factors influencing graduate waiting time to first employment as a result it was difficult to pinpoint all possible factors associated with the employability of graduates. Furthermore, the secondary data considered were obtained from graduates of a single university, and thus the findings cannot be generalized to the entire graduates in the country. Therefore, given this limitation, it is more important to conduct more detailed further research regarding the employability of graduates by considering the contribution of some other variables.

Funding
No, any funding was received from any organization.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Availability of data and materials
All result-based data are available within the manuscript and anyone can access the data set from the university tracer coordinating office or from corresponding author upon request.

Ethics approval and consent to participate
For this study ethical approval was not required since this is a secondary analysis. But, we have got permission from Wolkite university graduate tracer coordinating office to use the data.

Consent for publication
Not applicable.