class: center, middle, inverse, title-slide # Student drop-out modelling ## using Virtual Learning Environment behaviour data ### Jakub Kuzilek, Jonas Vaclavek, Viktor Fuglik and Zdenek Zdrahal ### 2018-09-05 --- class: center, middle ## Presentation available at: [https://bit.ly/2wzVXlk](https://bit.ly/2wzVXlk)  --- # Introduction - patterns leading to drop-out or passive withdrawal - (absorbing) Markov chains - 3 cases: - whole cohort, - first assessment submitting students, - first assessment non-submitting students - open dataset - OULAD - all codes available at [https://bit.ly/2JrY5zv](https://bit.ly/2JrY5zv) --- # Motivation - simplify previous approach  --- background-image: url(figs/logo_oulad.png) background-position: 50% 50% # Data - contains data from the [Open University](http://www.open.ac.uk/) from years 2013 and 2014 - detailed information about dataset can be found in paper [Open University Learning Analytics dataset](https://www.nature.com/articles/sdata2017171) --- # Data cont. - selected course `FFF`, presentation `2014J` - course is approximately 38 weeks long - 5 assessments during the presentation - selected course is on STEM subject - approximately 1/3 of the students withdrawn  --- # Methods - every week student should interact with recommended resources: - 0 - not interacted with planned resources - E - did something recommended - A - did everything recommended - student can visit other resources: - 0 - did not interacted with any other resources - E - visited some of the other materials - we can then define 7 student weekly states: ## `$$00,E0,A0,0E,EE,AE,Withdrawn$$` * the state `\(Withdrawn\)` is absorbing --- # Methods cont.  --- # Methods cont. 2 Simplifications: - the probability of transition from state to state does not change over time, - student cannot return to a course when withdrawn, - the probability of changing the student state depends only on current week ## Student weekly states → MCH transition matrix --- # Results - Markov chain of the whole cohort <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> 00 </th> <th style="text-align:right;"> 0E </th> <th style="text-align:right;"> EE </th> <th style="text-align:right;"> AE </th> <th style="text-align:right;"> Withdrawn </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> 00 </td> <td style="text-align:right;"> 66 </td> <td style="text-align:right;"> 29 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 2 </td> </tr> <tr> <td style="text-align:left;"> 0E </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 75 </td> <td style="text-align:right;"> 9 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> EE </td> <td style="text-align:right;"> 5 </td> <td style="text-align:right;"> 46 </td> <td style="text-align:right;"> 37 </td> <td style="text-align:right;"> 11 </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> AE </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 25 </td> <td style="text-align:right;"> 63 </td> <td style="text-align:right;"> 9 </td> <td style="text-align:right;"> 0 </td> </tr> <tr> <td style="text-align:left;"> Withdrawn </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 100 </td> </tr> </tbody> </table> <div id="htmlwidget-b3581842e1b771b76a20" style="width:504px;height:288px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-b3581842e1b771b76a20">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [len = \"1.5\",\n color = \"gray40\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"00\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"2\" [label = \"0E\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"3\" [label = \"EE\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"4\" [label = \"AE\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"5\" [label = \"Withdrawn\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n\"1\"->\"1\" [id = \"1\", weight = \"66\", label = \"66\"] \n\"1\"->\"2\" [id = \"2\", weight = \"29\", label = \"29\"] \n\"1\"->\"5\" [id = \"3\", weight = \"2\", label = \"2\"] \n\"2\"->\"1\" [id = \"4\", weight = \"13\", label = \"13\"] \n\"2\"->\"2\" [id = \"5\", weight = \"75\", label = \"75\"] \n\"2\"->\"5\" [id = \"6\", weight = \"1\", label = \"1\"] \n\"3\"->\"2\" [id = \"7\", weight = \"46\", label = \"46\"] \n\"3\"->\"3\" [id = \"8\", weight = \"37\", label = \"37\"] \n\"3\"->\"4\" [id = \"9\", weight = \"11\", label = \"11\"] \n\"3\"->\"5\" [id = \"10\", weight = \"1\", label = \"1\"] \n\"4\"->\"2\" [id = \"11\", weight = \"25\", label = \"25\"] \n\"4\"->\"3\" [id = \"12\", weight = \"63\", label = \"63\"] \n\"5\"->\"5\" [id = \"13\", weight = \"100\", label = \"100\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> --- # Results - Markov chain of submitting students <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> 00 </th> <th style="text-align:right;"> 0E </th> <th style="text-align:right;"> EE </th> <th style="text-align:right;"> AE </th> <th style="text-align:right;"> Withdrawn </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> 00 </td> <td style="text-align:right;"> 63 </td> <td style="text-align:right;"> 34 </td> <td style="text-align:right;"> 2 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 1 </td> </tr> <tr> <td style="text-align:left;"> 0E </td> <td style="text-align:right;"> 13 </td> <td style="text-align:right;"> 78 </td> <td style="text-align:right;"> 8 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 0 </td> </tr> <tr> <td style="text-align:left;"> EE </td> <td style="text-align:right;"> 6 </td> <td style="text-align:right;"> 60 </td> <td style="text-align:right;"> 34 </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 0 </td> </tr> <tr> <td style="text-align:left;"> AE </td> <td style="text-align:right;"> 1 </td> <td style="text-align:right;"> 32 </td> <td style="text-align:right;"> 60 </td> <td style="text-align:right;"> 7 </td> <td style="text-align:right;"> 0 </td> </tr> <tr> <td style="text-align:left;"> Withdrawn </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 100 </td> </tr> </tbody> </table> <div id="htmlwidget-9fa2e821115726554e5e" style="width:504px;height:288px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-9fa2e821115726554e5e">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [len = \"1.5\",\n color = \"gray40\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"00\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"2\" [label = \"0E\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"3\" [label = \"EE\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"4\" [label = \"AE\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"5\" [label = \"Withdrawn\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n\"1\"->\"1\" [id = \"1\", weight = \"63\", label = \"63\"] \n\"1\"->\"2\" [id = \"2\", weight = \"34\", label = \"34\"] \n\"1\"->\"5\" [id = \"3\", weight = \"1\", label = \"1\"] \n\"2\"->\"1\" [id = \"4\", weight = \"13\", label = \"13\"] \n\"2\"->\"2\" [id = \"5\", weight = \"78\", label = \"78\"] \n\"3\"->\"2\" [id = \"6\", weight = \"60\", label = \"60\"] \n\"3\"->\"3\" [id = \"7\", weight = \"34\", label = \"34\"] \n\"4\"->\"2\" [id = \"8\", weight = \"32\", label = \"32\"] \n\"4\"->\"3\" [id = \"9\", weight = \"60\", label = \"60\"] \n\"5\"->\"5\" [id = \"10\", weight = \"100\", label = \"100\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> --- # Results - Markov chain of non-submitting students <table> <thead> <tr> <th style="text-align:left;"> </th> <th style="text-align:right;"> 00 </th> <th style="text-align:right;"> 0E </th> <th style="text-align:right;"> EE </th> <th style="text-align:right;"> Withdrawn </th> </tr> </thead> <tbody> <tr> <td style="text-align:left;"> 00 </td> <td style="text-align:right;"> 95 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 2 </td> </tr> <tr> <td style="text-align:left;"> 0E </td> <td style="text-align:right;"> 51 </td> <td style="text-align:right;"> 41 </td> <td style="text-align:right;"> 3 </td> <td style="text-align:right;"> 5 </td> </tr> <tr> <td style="text-align:left;"> EE </td> <td style="text-align:right;"> 38 </td> <td style="text-align:right;"> 38 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 25 </td> </tr> <tr> <td style="text-align:left;"> Withdrawn </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 0 </td> <td style="text-align:right;"> 100 </td> </tr> </tbody> </table> <div id="htmlwidget-3b5bc1d820a559f4fefc" style="width:504px;height:288px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-3b5bc1d820a559f4fefc">{"x":{"diagram":"digraph {\n\ngraph [layout = \"neato\",\n outputorder = \"edgesfirst\",\n bgcolor = \"white\"]\n\nnode [fontname = \"Helvetica\",\n fontsize = \"10\",\n shape = \"circle\",\n fixedsize = \"true\",\n width = \"0.5\",\n style = \"filled\",\n fillcolor = \"aliceblue\",\n color = \"gray70\",\n fontcolor = \"gray50\"]\n\nedge [len = \"1.5\",\n color = \"gray40\",\n arrowsize = \"0.5\"]\n\n \"1\" [label = \"00\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"2\" [label = \"0E\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"3\" [label = \"EE\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n \"4\" [label = \"Withdrawn\", fillcolor = \"#F0F8FF\", fontcolor = \"#000000\"] \n\"1\"->\"1\" [id = \"1\", weight = \"95\", label = \"95\"] \n\"1\"->\"4\" [id = \"2\", weight = \"2\", label = \"2\"] \n\"2\"->\"1\" [id = \"3\", weight = \"51\", label = \"51\"] \n\"2\"->\"2\" [id = \"4\", weight = \"41\", label = \"41\"] \n\"2\"->\"4\" [id = \"5\", weight = \"5\", label = \"5\"] \n\"3\"->\"1\" [id = \"6\", weight = \"38\", label = \"38\"] \n\"3\"->\"2\" [id = \"7\", weight = \"38\", label = \"38\"] \n\"3\"->\"4\" [id = \"8\", weight = \"25\", label = \"25\"] \n\"4\"->\"4\" [id = \"9\", weight = \"100\", label = \"100\"] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> --- # Conclusions 1. students tends to do less next week 2. those who did nothing have larger probability to withdraw 3. students who did not submitted first assessment and did nothing after the cut-off, tends to do nothing and are passive for the whole course --- class: middle, center, inverse # Thank you!