Fitting a Multinomial Logistic Regression (MLR)

Asian Research Journal of Mathematics 3(4): 1-9, 2017; Article no.ARJOM.30651 ISSN: 2456-477X

SCIENCEDOMAIN international www.sciencedomain.org

Fitting a Multinomial Logistic Regression (MLR) Model to Need Assessment Survey on E-learning in Kenya Lameck Ondieki Agasa1*, Anakalo Shitandi1, Wycliffe Cheruyout2, Wycliff Ombasa3 and Onsongo Wycliff Nyaundi3 1

Research and Extension Office, Kisii University, P.O.Box 408-402000, Kenya. 2 Maasai Mara University, P.O.Box 861-20500, Kenya. 3 Kenya Revenue Authority, P.O.Box 8240-00100, Kenya. Authors’ contributions

This work was carried out in collaboration between all authors. Authors LOA, AS and WC designed the study, performed the statistical analysis and wrote the first draft of the manuscript. Authors WO and OWN managed the analyses of the study. All authors read and approved the final manuscript. Article Information DOI: 10.9734/ARJOM/2017/30651 Editor(s): (1) Gongxian Xu, Associate Professor, Department of Mathematics, Bohai University, Jinzhou, China. Reviewers: (1) Radosław Jedynak, Kazimierz Pulaski University of Technology and Humanities, Poland. (2) B. Chametzky, Washington & Jefferson College, USA and Ozarks Technical Community College, USA and City University of Seattle, USA. (3) Jong-Wuu Wu, National Chiayi University, Taiwan. (4) Eduardo Mario Lacues Apud, Universidad Católica del Uruguay, Uruguay. Complete Peer review History: http://www.sciencedomain.org/review-history/18752

Received: 23rd November 2016 Accepted: 10th April 2017 Original Research Article Published: 22nd April 2017 _______________________________________________________________________________________

Abstract Information Communication Technology (ICT) advances have reduced the world to a small village. The use of technology to meet societal need has increased in developing countries. It’s from this perspective that technology should find its way to developing countries classroom through e-learning to replace the traditional methods of teaching .This research aimed at addressing the needs an e-learning class should have by fitting a model. The study was based on the Taskforce Report on Implementation of ElectronicLearning at Kenya, Kisii University, Faculty of Education and Human Resource Development (FEHRD) 2013. Both primary and secondary data was obtained from Kisii University and was entered in SPSS version 22.0 for analysis. A Multinomial Logistic Model (MLM) showed a relationship between the level of education, level of preparedness, readiness and computer literacy of students. The adequacy of the model was tested using Deviance method which proved the model to be adequate. It was established that certificate and diploma holders need to be prepared with the necessary computer skills to enable them undertake an e-learning class. E-learning can be rolled out to degree holders and masters holders as it was established that they are prepared, ready and have the computer skills to undertake an e-learning classes. _____________________________________

*Corresponding author: E-mail: [email protected], [email protected];

Agasa et al.; ARJOM, 3(4): 1-9, 2017; Article no.ARJOM.30651

Keywords: E-learning; multinomial logistic regression; readiness; computer literacy; preparedness.

1 Introduction The rise of Information and Communication Technology (ICT) has brought great innovation in the education sector. Globally, eLearning has found wide acceptance like in United States of America (USA) where its embraced by public schools and private schools in which the environments can be a traditional classroom or virtual classrooms; Virtual School enable students to log into synchronous learning or asynchronous learning environment anywhere there is an internet connection. Technological kits are usually provided that include computers, printers, and reimbursement for home internet use. These models require students to use technology for school work only and must meet weekly work submission requirements [1]. Moreover, reports indicate online schools enable students to maintain their own pace, progress and course selection, in addition to providing students flexibility to create their own time for study. Higher learning institutions in USA also predominantly utilize e-learning in their curriculum. According to existing figures, fully online enrolment learning increased by an average of 12–14 percent annually between 2004–2009, compared with an average of approximately 2 per cent increases overall. In 2006, 3.5 million students participated in on-line learning at higher education institutions in the United State. Almost a quarter of all students in post-secondary education were taking fully online courses in 2008 In 2009, 44 percent of post-secondary students in the USA were taking some or all of their courses online, this figure is projected to rise to 81 percent by 2014. During the fall 2011 term, 6.7 million students enrolled in at least one online course. Over two-thirds of chief academic officers believe that online learning is critical for their institution. The Sloan Report, based on a poll of academic leaders, indicated that students are satisfied with on-line classes as with traditional ones [1]. [2] in his article he ranks countries globally on eLearning uptake as India 55%, China 52%, Malaysia 41%, Romania 38%, Poland 28%, Czech Republic 27%, and Brazil 26%. It was evident countries in sub-Saharan Africa had lower levels of eLearning. In Africa Rwanda has a government policy that seeks to have all students from primary schools given laptops to enable e-learning. Internet connectivity is high to allow virtual classes to be conducted. Teachers are trained on how to engage students using an e-learning interface and how to make their students active in an online platform like Moodle. Rwanda has moved some strides ahead in its education by decongesting classrooms and allowing students to learn from any location in the country provided there is internet connectivity. Also e-learning has improved the quality of education since homogenous content is taught throughout the country. E-Learning has found wide acceptance in Kenya’s education sector because of improved technology. The Kenyan government rolled out free laptops to pupils in primary schools to boost e-Learning. According to Daily Nation of 14 November 2013, the government anticipated to transform education system in the country to e-teaching and e-learning. Moreover, Kenya has one of the fastest internet speeds in Africa which boost e-learning, thus, integrating technology into education can be quite beneficial given the current global era. E- Learning is boosted by the increased use of internet across the board. According to Communication Commission of Kenya(CCK) statistics the total number of internet users stand at 17.3 million combining all mobile and data internet subscribers, terrestrial wireless subscribers, satellite subscription, fixed internet connections, fibre optics subscription and fixed cable modem users. Kenya internet penetration is estimated at 25.5 percent of the population which stands at 41 million people according to the World Internet statistics. World Bank report published in 2012 indicated that internet users in Kenya was gaining momentum in the country faster [3]. With the installation of the fibre optic network in Kenya there are high rates of internet connectivity. Various technologies are used to facilitate e-learning. Most e-learning uses combinations of these techniques, including blogs, collaborative software, portfolios, and virtual classrooms.

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Private primary schools in Kenya are geared to integrating e-learning in their schools; Kenya Private Schools Association (KEPSA) has indicated the need to implement e-learning systems with computer laboratories and e-boards. It has rolled out the plan to implement e-learning in phases with the first phase likely to cover 1000 private primary schools across the country out of the 12000 primary schools in the country. The association contacted a Chinese company, Haier to this effect [4] a good signal to e-learning.

2 Literature Review Technological innovation, deregulation of telecommunication sector and increased need for quality education has essentially led to emergence of online teaching and learning in Kenya. E-resources have got a great market for internet related activities. The modern generation will be access education system if put in social media as it can attract many people making it easier and faster. Uses of Facebook to teach, use of emails to send assignment which are forms of m-learning are widely used by students. E-learning is the transfer of academic work from paper work to internet (from face to face to use of internet). A needs analysis requires assessment of level of education, readiness, level of preparedness and computer to make eLearning possible. Evaluation should ideally be planned at the outset of any new development or modification. Initial plan include aims, questions, tasks, stakeholders, timescales and instruments/methods. It should define “that which you are trying to investigate but also how you are going to go about it” [5] He further said that the areas to consider in embedding e-learning effectively into a course include issues around [6]. Needs analysis is an element of designing (or reviewing) a curriculum. Its purpose is to establish key learning outcomes and requirements in the design and delivery of a course or learning activity. The analysis seeks to match possible or proposed techniques and materials to these needs and thus identify whether the design is appropriate to the intended goals. Good course design should separate ends from means. “We are constantly making the mistake of specifying the means of doing something rather than the results we want. This can only limit our ability to find better solutions to real problems” [7]. In most cases, reviewing a course and responding to current need is perhaps something done intuitively and without formal procedures. However, there is increasing pressure to update curriculum purposes and methods in response to changing government requirements (such as accessibility, employability and information and IT skills agendas). Developing a new course or changing an existing teaching approach is likely to feel daunting, time-consuming and risky, especially when technology is involved. These risks and concerns are likely to be significantly diminished if a more explicit approach is taken to evaluating needs. There is certainly the usual need to justify limited time available and to be aware of likely technical requirements. Looking at needs across different types of development models, [8,9] contends that: “Current approaches to teaching and learning in higher education are dominated by the following: the importance of interactivity in the learning process, the changing role of the teacher from sage to guide, the need for knowledge management skills and for team working abilities, and the move towards resource-based rather than packaged learning”.

3 Methodology This study was conducted in Kisii University, Kenya. The study employed sample-resample method in which data that was collected during the ELearning Taskforce report writing was sampled for this study. A sample of 65 participants was used. This data was entered in Excel spreadsheet after which it was imported to SPSS version 22.0 for cleaning and analysis [10]. The study employed MLR in which the dependent variable was the level of education and the independent variables are level of preparedness, readiness and computer literacy. Multinomial Logistic Regression (MLR) was used because it allows for consideration of more than two categories of the outcome variable. Level of education was categorised into Certificate and

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Agasa et al.; ARJOM, 3(4): 1-9, 2017; Article no.ARJOM.30651

below versus Doctor of Philosophy (PhD), Diploma and PhD, Degree and PhD and lastly Masters and PhD. PhD was used as a reference category because it has the highest numeric score. Each independent variable has two comparisons. MLR provides a set of coefficients for each of the comparison. The coefficient of the reference category are all zeros, similar to the coefficient’s for the reference group for a dummy-coded variable, thus there are three equations, one for each group defined by the dependent variable. The independent variables used were level of readiness, level of preparedness and computer literacy of the respondents. Level of readiness includes ability to undertake the ELearning regardless of its difficultness. Computer literacy means ability to use a computer devises. Level of preparedness implies access to eLearning materials like internet. All the independent variables had five Likert-scales response that ranged from strongly agree, agree undecided, disagree and strongly disagree. These categorical responses were coded from 5-1 respectively before the model was fitted. The weighted averages were calculated on each independent variable that was used to fit the model. Multinomial Logistic Regression model is presented as in the following illustration example: Consider a scenario where [11] an individual is faced with k choices an asset of variables characterized by the vector Xi= (Xi1, Xi2……Xim) contain variables like age, sex, and income. Consequently, Zir will denote the utility of the rth category individual i. Yi will denote the categorical response variable. A simple linear model for Zir is given by: Zir= βr0+Xiβri i=0,1,2…..m Where β= (βro,……….,βm) is a parameter vector. That implies that the preference of the rth alternative for ith individual is determined by Xi and the parameter βr depends on the category. Therefore, a parameter that depends on the category will be called specific, the variable Xi are called global. Assuming only global variable Xi the MLR is given by:

exp( β ro + Xi β r ) P (Yi=r) =

1+

∑ exp(

Bro + XiBr )

i=1, 2, 3; r=1,2,3

This can be written equivalently as: Log

P(Yi = r ) =βr0+Xiβr P (Yj = k )

i=1, 2, 3; r=1,2,3

Hence Xi is the vector of covariates determining the log odds for category r with respect to the category k; we fit an MLR to the need assessment data by taking the level of education (PhD) as the reference category of Y P (Yi=r) =

1

i=1, 2, 3;r=1,2,3

m

1 + ∑ exp( β ro + Xiβ r ) s =1

According to the equation above, the models can be written as; Log

p(Yi = 1) =β10+Xiβ1 p(Yi = 5)

i=r-1, 2, 3;

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Agasa et al.; ARJOM, 3(4): 1-9, 2017; Article no.ARJOM.30651

Log

p(Yi = 2) =β20+Xiβ2 p(Yi = 5)

Log

p(Yi = 3) p(Yi = 5)

Log

p(Yi = 4) =β40+Xiβ4 p(Yi = 5)

=β30+Xiβ3

4 Results and Discussion This notation will be used in interpretation of the results: The response variable is

1iflevelofeducationcertificate    Yi= 2iflevelofeducationdiploma  3iflevelofeducation deg ree    4iflevelofeducationmasters  1 − Levelof Pr eparedness    3 − Computerproficiency 

Xi = 2 − Levelofreadiness

 0 − Cons tan t 1 − Coeffecientofpreaparedness  βi =    2 − Coeffecienofreadness   3 − Coeffecientofcomputerliteracy Multiple logistic regression model [12] was fitted as indicated in Table 1 below: Table 1. Model fitting information Model Intercept only Final

Model fitting criteria -2 log likelihood 674.390 1 45.045

Likelihood ratio tests Chi-square d.f

Sig.

39.346

0.010

36

The presence of a relationship between the dependent variable (level of education) and combination of independent variables (preparedness, readiness and computer literacy) is based on statistical significant of the final model chi-square value. The probability of the model Chi-square (39.46) was 0.01 less than the significance level of 0.05. Thus there exists evidence of a relationship between the independent variable and the dependent variable at 5% level of significance. Overall, there is a statistical significant relationship between the level of education and level of preparedness, level of readiness and computer literacy to undertake eLearning.

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Further the individual independent variables were tested to see their significance as in Table 2 below: Table 2. Likelihood ratio tests Effect

Intercept x1(Readiness) X2(Preparedness) X3(Computer literacy)

Model fitting criteria -2 log likelihood of reduced model 45.045 52.637 49.597 54.925

Likelihood ratio tests Chi-square D.f

Sig.

.000 7.592 4.552 9.880

. 0.016 0.004 0.034

0 12 8 12

Table 2 above indicates the chi-square statistic which is the difference in -2log likelihood between the final model and the reduced model. The reduced model is formed by omitting an effect from the final model. Thus there exists a strong evidence to suggest a statistical relationship between independent variable (preparedness, readiness and computer literacy) and the dependent variable (level of education) since the significance values are less than 0.05. The probability of the chi-square (7.592) was 0.016 less than significance level of 0.05 for level preparedness thus indicating there exist evidence to show that preparedness affects e-learning, for readiness the probability of the chi-square (4.552) was 0.04 less than that of significance level of 0.05 indicating readiness affects e-learning and for computer literacy has a chisquare value of 9.88 and probability of 0.034 less than the significance level of 0.05 indicating that computer literacy affects e-learning. This implies that the independent variables are highly statistically significant hence considerable in the model [13]. Person and deviance were used to test the goodness of fit for the model as in Table 3. Table 3. Goodness-of-fit

Pearson Deviance

Chi-square 32.413 33.248

Df 32 32

Sig. .902 .882

The Pearson and Deviance are used to test whether the data adequately fits the model. In this case the significance level is 5% thus indicating the model adequately fits the model since the significance level from Chi-Square computation is higher than the level of significance. Thus the data are consistent with the model assumptions. Assuming the assumption that the null hypothesis is the data adequately fits the model versus the alternative that the data does not adequately fit the model. From the Table 4 the multinomial regression coefficients, Wald test and odds ratio for each predictor variable in all the four categories under study are shown. Using a 0.05 level of significance, the level of readiness for e-learning is statistically significant at all the categories while computer literacy and preparedness are not statistically significant in the first and secondary category of certificate and diploma holders but in the category of degree and that of masters its statistically significant. The exponent coefficients in the last column of the output are interpretable as multiplicative effects on the level of education. The multinomial logistic regression for the first category is: Log

p(Yi = r ) =βr0+Xiβr, p (Yi = k )

Where P(Yi=r) is the probability of being a certificate , A diploma, a degree, masters or PhD holder the rth category with reference to kth category.

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Table 4. Model results Level of education Intercept 1 X1 X2 X3 Intercept 2 X1 X2 X3 Intercept 3 X1 X2 X3 Intercept 4 X1 X2 X3

B 1.696 0.023 0.032 -12.562 2.098 0.765 0.345 -0.013 6.031 .087 -1.234 2.567 14.981 0.056 3.082 12.034

Std. error 0.277 2.341 2.04 0.089 0.465 0.765 0.543 0.023 0.098 0.432 0.459 0.009 0.043 0.021 0.003 0.093

Wald 1.76 0.465 7.893 1.233 0.087 1.542 11.424 0.342 1.230 3.409 2.341 5.098 10.981 5.132 8.943 17.854

Df 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sig. .002 0.134 0.002 0.567 0.008 0.125 0.003 0.089 0.004 0.001 0.004 0.003 0.001 0.002 0.001 0.000

Exp(B) 1.046 0.009 1.089 1.078 0.023 0.061 0.046 0.037 0.098 0.956 0.996 0.007

Model interpretation [14,15]. In the first category for Certificate holders, we develop the following model: Log

p (Yi = 1) =1.696+0.032X2 p (Yi = 5)

It implies that only readiness is statistically significant in the certificate category since its significance value is less than 0.05 the level of significance. Thus holding all other variables constant, an increase in the level of readiness increases the likelihood of a certificate holder to take e-learning by a factor of 0.032 on average i.e., an increase by 3.2%. The Wald statistics tests the unique contribution of each predictor in the context of the other predictor in each category .In this category (certificate), readiness has the highest value of 7.893. Second category of Diploma holders, we develop the following model: Log

P (Yi = 2) =2.098+0.345X1 P (Yi = 5)

In these categories, we observed that the level of preparedness that has the significance value 0.003 less than 0.05 meaning it’s statistically significant. Holding all other variables constant an increase in the level of readiness increases the likelihood of a diploma holder to take an e-learning by a factor of 0.345 on average i.e., an increase by 34.5%. The wald statistic tests (11.424) of the level of preparedness is higher than other predictor variables. In the third category of Degree holders, we develop the following model: Yi Log

P (Yi = 3) = 6.031+0.87X1-1.234X2+2.567X3 P (Yi = 5)

In these category, we observed that the level of preparedness, readiness and computer literacy have the significance value less than 0.05 hence they are statistically significant. Holding all other variables constant

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an increase in level of preparedness increases the likelihood of a degree holder to take an e-learning by a factor of 0.87 i.e., an increase by 87%, also an increase in the level of readiness reduces the chance of a degree holder taking an e-learning by a factor of -1 .23 and an increase in level of computer literacy increases the likelihood of a degree holder taking an e-learning by a factor of 2.56 i.e., an increase by 156%. The Wald test (5.098) of computer literacy is the highest. In the fourth category of Masters Holders, We develop the following model: Log

P(Yi = 4) =14.981+8.056X1+0.0082X2+12.034X3 P(Yi = 5)

In these category, we observed that the level of preparedness, readiness and computer literacy have the significance value less than 0.05 hence they are statistically significant. Holding all other variables constant an increase in level of preparedness increases the likelihood of a master’s holder to take an e-learning class by a factor of 8.056, level of readiness is at 0.0082 and for computer literacy by 12.043. The Wald test (17.854) of computer literacy is the higher.

5 Conclusion The study established that certificate and diploma holders need to be prepared with the necessary computer skills to enable them undertake an e-learning class. Also e-learning can be rolled out to degree holders and masters holders as it was established that they are prepared, ready and have the computer skills to undertake an e-learning classes.

Acknowledgement The authors wish to thank in a special way Kisii university for allowing them use the ELearning Taskforce Report to publish this paper.

Competing Interests Authors have declared that no competing interests exist.

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© 2017 Agasa et al.; This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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