function maximum_likelihood_models($opps, $debugML = false)
{
if ($debugML) {
echo "Grades for this student and KC:\n";
foreach ($opps as $j => $opp) {
$yy = reset($opp);
$gg = $yy['grade'];
echo " {$gg}";
}
echo "\n";
}
$maxll = false;
$allll = array();
$allGain = array();
// Step through possible chances for learning skill.
for ($step = 0; $step < count($opps); $step++) {
$cbl = 0;
$wbl = 0;
$cal = 0;
$wal = 0;
foreach ($opps as $j => $opp) {
$yy = reset($opp);
if ($j < $step) {
if ($yy['grade'] == 'correct') {
$cbl++;
} else {
$wbl++;
}
} else {
if ($yy['grade'] == 'correct') {
$cal++;
} else {
$wal++;
}
}
}
// Values for guess and slip are from maximum likelihood.
$pg = $cbl + $wbl > 0 ? $cbl / ($cbl + $wbl) : false;
$ps = $cal + $wal > 0 ? $wal / ($cal + $wal) : false;
$allSlip[$step] = $ps;
// Calculate the log likelihood for model with step at $step.
// Note that this number is negative (so we are trying to maximize it)
// Also, note that the case $step=0 corresponds to not learning.
$ll = 0;
$ll += $cbl > 0 ? $cbl * log($pg) : 0.0;
$ll += $wbl > 0 ? $wbl * log(1.0 - $pg) : 0.0;
$ll += $wal > 0 ? $wal * log($ps) : 0.0;
$ll += $cal > 0 ? $cal * log(1.0 - $ps) : 0.0;
$allll[$step] = $ll;
// Maximum likelihood estimator for the learning gain 1-g-s
$allGain[$step] = $ps !== false && $pg !== false ? 1 - $ps - $pg : false;
// Find maximum value.
if ($maxll === false || $ll > $maxll) {
$maxll = $ll;
// Only count cases where step occurs inside student data
$maxv = array('logLike' => $ll, 'learn' => $step, 'pg' => $pg, 'ps' => $ps);
if ($step == 0) {
$maxv0 = $maxv;
}
}
if ($debugML) {
echo ' (' . $step . ',' . print2($pg) . ',' . print2($ps) . ',' . number_format($ll, 3) . ',' . ')';
// echo " <$cbl,$wbl,$cal,$wal>";
}
}
if ($debugML) {
echo "\n";
}
// Find relative probabilities for learning on each step.
//
// We are are going from "the probability of producing seen behavior
// for a given L" to "the probablitiy of a certain L given the
// seen behavior." Thus, we are assuming that the
// prior p.d.f. for a given L is constant. See Section 33.1.4 of
// http://pdg.lbl.gov/2011/reviews/rpp2011-rev-statistics.pdf
//
// Elements where learning cannot be determined are left empty.
//
// In fact, we use AIC to determine the relative probability
// of different models with various values of L. When there
// is a fit with a step, there are two model parameters. When no
// learning is found ($i=0), there is one model parameter.
// See http://en.wikipedia.org/wiki/Akaike_information_criterion
$maxv['opps'] = count($opps);
$maxv['learnHereProb'] = array();
$sum = 0;
// Include no learning case.
// There is no way to measure learning on last step.
for ($i = 0; $i < count($allll); $i++) {
// Using AIC, to determing the relative probability.
$val = exp($allll[$i] - ($i == 0 ? 1 : 2));
$maxv['learnHereProb'][$i] = $val;
$sum += $val;
}
// Next, normalize probabilities;
for ($i = 0; $i < count($allll); $i++) {
$maxv['learnHereProb'][$i] /= $sum;
}
// If no significant model-weighted gain is seen, then
// model has failed, "point of learning" doesn't exist.
// There are two possible strategies to determine learning:
// 1. The best fit parameters predict positive learning or
// 2. The model predicts positive learning with probability
// greater than some confidence level.
//
// The model weighted gain is about 1/2 for any data
// where the initial rate cbl/(cbl+wbl) is equal to the
// final rate cal/(cal+wal).
// This includes all correct, all wrong, or some
// random rate of correctness.
// get all fits where there is enough data to fit.
$maxv['valid'] = count($opps) >= 3;
// Otherwise, use the value from learn=0
if (!$maxv['valid']) {
$maxv['learn'] = 0;
$maxv['pg'] = false;
$maxv['ps'] = $maxv0['ps'];
$maxv['logLike'] = $maxv0['logLike'];
}
// Associated learning gains
$maxv['learnGain'] = $allGain;
$maxv['slip'] = $allSlip;
if ($debugML) {
if ($maxv['valid']) {
echo ' model with pg=' . number_format($pg, 3) . ', ps=' . number_format($ps, 3) . ', logLike=' . number_format($maxv['logLike'], 3);
} else {
echo ' no learning: ps=' . number_format($ps, 2);
}
echo "\n";
}
return $maxv;
}
function GetPage($res = '', $tab)
{
if ($tab == 1) {
$data = '
<fieldset id="fiel_bank">
<legend>ბარათები</legend>
<div class="inner-table">
<div id="dt_example" class="ex_highlight_row">
<div id="container" class="overhead_container">
<div id="button_area"></div>
<div id="dynamic">
<table class="display" style="width: 900px" id="table-3">
<thead>
<tr id="datatable_header">
<th>ID</th>
<th class="min">ბარათის ნომერი</th>
<th style="width: 150px">თარიღი </th>
<th style="width: 150px">თანხა</th>
<th style="width: 150px">ფილიალი</th>
<th style="width: 150px">შენიშვნა</th>
</tr>
</thead>
<thead>
<tr class="search_header">
<th class="colum_hidden">
<input type="text" name="search_id" value="ფილტრი" class="search_init" />
</th>
<th>
<input type="text" name="search_aleter" value="ფილტრი" class="search_init" />
</th>
<th>
<input type="text" name="search_client" value="ფილტრი" class="search_init" />
</th>
<th>
<input type="text" name="search_client" value="ფილტრი" class="search_init" />
</th>
<th>
<input type="text" name="search_client" value="ფილტრი" class="search_init" />
</th>
<th>
<input type="text" name="search_client" value="ფილტრი" class="search_init" />
</th>
</tr>
</thead>
<tfoot>
<tr>
<th> </th>
<th> </th>
<th><p align="right">ჯამი:<br/>სულ ჯამი:</th>
<th align="left"> </th>
<th> </th>
<th> </th>
</tr>
</tfoot>
</table>
</div>
</div>
</div>
</div>
</fieldset>
<input type="hidden" id="inv_id" value="' . $_REQUEST['id'] . '">
</div>
<div class="inner-table" >
</div>';
} else {
global $sum;
$later = 'b';
$reQ = mysql_fetch_assoc(mysql_query("\n\t\t\tSELECT\n\t\t\t\t\t CONCAT('ბ–',`a_letter`.`id`) AS id,\n\t\t\t\t\ta_letter.request_date as start_date,\n\t\t\t\t\t`a_letter`.`finish_date` as end_date,\n\t\t\t\t\trequest_sources.`name` as source,\n\t\t\t\t\tCONCAT(`client`.`name`,' (',`client_objects`.`name`, ')') AS `client`,\n\t\t\t\t\t`client_objects`.`id` as `obj_id`,\n\t\t\t\t\t`a_letter`.`b_letter_status` as `b_letter_status`,\n\t\t\t\t\t`a_letter`.`b_letter_overhead_id` as `overhead_id`,\n\t\t\t\t\tclient_object_persons.`name` as client_p,\n\t\t\t\t\tpersons.`name` as obj_p\n\t\t\tFROM\t\t\t`a_letter`\n\t\t\tLEFT JOIN\t\t`client_objects` ON `a_letter`.`client_object_id` = `client_objects`.`id`\n\t\t\tLEFT JOIN\t\t`client` ON `client`.`id` = `client_objects`.`client_id`\n\t\t\tLEFT JOIN \trequest_sources ON request_sources.id=a_letter.source\n\t\t\tLEFT JOIN \tpersons ON a_letter.receiver=persons.id\n\t\t\tLEFT JOIN \tclient_object_persons ON client_object_persons.id=a_letter.requester\n\t\t\tWHERE\t\t\t`a_letter`.`id` = '{$res['id']}'\nUNION\n\t\t\tSELECT CONCAT('ე–',`d_letter`.`id`) AS id,\n\t\t\t\t\t\td_letter.request_date as start_date,\n\t\t\t\t\t\t`d_letter`.`finish_date` as end_date,\n\t\t\t\t\t\trequest_sources.`name` as source,\n\t\t\t\t\t\tCONCAT(`client`.`name`,'(',`client_objects`.`name`, ')') AS `client`,\n\t\t\t\t\t\t`client_objects`.`id` as `obj_id`,\n\t\t\t\t\t\t`d_letter`.`e_letter_status` as `e_letter_status`,\n\t\t\t\t\t\t`d_letter`.`e_letter_overhead_id` as `overhead_id`,\n\t\t\t\t\t\tclient_object_persons.`name` as client_p,\n\t\t\t\t\t\tpersons.`name` as obj_p\n\t\t\tFROM\t\t\t`d_letter`\n\t\t\tLEFT JOIN\t\t`client_objects` ON `d_letter`.`client_object_id` = `client_objects`.`id`\n\t\t\tLEFT JOIN\t\t`client` ON `client`.`id` = `client_objects`.`client_id`\n\t\t\tLEFT JOIN \trequest_sources ON request_sources.id=d_letter.source\n\t\t\tLEFT JOIN \tpersons ON d_letter.receiver=persons.id\n\t\t\tLEFT JOIN \tclient_object_persons ON client_object_persons.id=d_letter.requester\n\t\t\tWHERE\t\t\t`d_letter`.`id` = '{$res['id']}'"));
$m = "\n\t\t</table>\n\t\t</fieldset>\n\n\t\t\t<fieldset style='margin-top: 4px;'>\n\t\t\t<legend></legend>\n\t\t\t\t<table width='90%'>\n\t\t\t\t<tr>\n\t\t\t\t<td>მიმწოდებელი: {$reQ['client_p']}</td>\n\t\t\t\t<td></td>\n\t\t\t\t<td>მიმღები: {$reQ['obj_p']}</td>\n\t\t\t\t<td></td>\n\t\t\t\t</tr>\n\t\t\t\t</table>\n\t\t\t</fieldset>\t";
$data = "\n\t\t<div id='dialog-form'>\n\t\t\t\t<fieldset>\n\t\t\t\t\t<legend>{$reQ['client']}</legend>\n\t\t\t\t\t<table width='100%'>\n\t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t<td>შეკვეთის N: {$res['id']}</td>\n\t\t\t\t\t\t\t<td></td>\n\t\t\t\t\t\t\t<td>შეკვეთის დრო: {$reQ['start_date']}</td>\n\t\t\t\t\t\t\t<td></td>\n\t\t\t\t\t\t</tr>\n\t\t\t\t\t\t<tr>\n\t\t\t\t\t\t\t<td>შეკვეთის ფომა: {$reQ['source']}</td>\n\t\t\t\t\t\t\t<td></td>\n\t\t\t\t\t\t\t<td>მიტანის დრო: {$reQ['end_date']}</td>\n\t\t\t\t\t\t\t<td></td>\n\t\t\t\t\t\t</tr>\n\n</table>\n\t\t\t\t</fieldset>\n\t\t\t\t<div style='padding: 2px;'></div>\n\t\t\t\t<fieldset>\n\t";
if (substr($reQ[id], 0, 3) == 'ე') {
if ($_REQUEST['rw'] == 'wr' & $_REQUEST['tab'] == 0) {
$data .= '<table class="display dataTable" style="width: 550px !important; border:1px solid black !important;" cellpadding="0" cellspacing="0">
<tr class="ui-widget-header" style="border:1px solid black !important; color: white !important;">
<td style="width: 25% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>მოდელი</span></td>
<td style="width: 20% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;">რაოდენობა</td>
</tr>';
$data .= print4($res['id']);
$data .= $m;
} elseif ($_REQUEST['rw'] == 'wr' & $_REQUEST['tab'] == 1) {
$data .= '<table class="display dataTable" style="width: 550px !important; height:25px; border:1px solid black !important;" cellpadding="0" cellspacing="0">
<tr class="ui-widget-header" style="border:1px solid black !important; color: white !important;">
<td style="width: 45% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>შტრიხკოდი</span></td>
<td style="width: 25% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>მოდელი</span></td>
<td style="width: 20% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;">სტატუსი</td>
</tr>';
$data .= print5($res['id']);
$data .= $m;
} else {
$data .= '<table class="display dataTable" style="width: 550px !important; border:1px solid black !important;" cellpadding="0" cellspacing="0">
<tr style="background-color: black !important; border:1px solid black !important; color: white !important;">
<td style="width: 45% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>სერვისი</span></td>
<td style="width: 25% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>მოდელი</span></td>
<td style="width: 20% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;">შტრიხკოდი</td>
<td style="width: 10% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;">ფასი</td>
</tr>';
$data .= print2($res['id']);
}
} else {
if ($_REQUEST['rw'] == 'wr' & $_REQUEST['tab'] == 0) {
$data .= '<table class="display dataTable" style="width: 550px" cellpadding="0" cellspacing="0">
<thead class="ui-widget-header">
<tr style="border:1px !important; height:25px; color: white !important;">
<td style="width: 25% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>მოდელი</span></td>
<td style="width: 20% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;">რაოდენობა</td>
</tr>
</thead>';
$data .= print3($res['id']);
$data .= $m;
} elseif ($_REQUEST['rw'] == 'wr' & $_REQUEST['tab'] == 1) {
$data .= '<table class="display dataTable" style="width: 550px !important; border:1px solid black !important;" cellpadding="0" cellspacing="0">
<thead class="ui-widget-header">
<tr class="ui-widget-header" style="border:1px solid black !important; color: white !important;">
<td style="width: 45% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>შტრიხკოდი</span></td>
<td style="width: 25% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>მოდელი</span></td>
<td style="width: 20% !important; font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;">სტატუსი</td>
</tr>
</thead>';
$data .= print5($res['id']);
$data .= $m;
} else {
$data .= '
<table style="width: 550px !important; border:1px solid black !important;" cellpadding="0" cellspacing="0">
<tr style="background-color: #D9D9D9;border:1px solid black !important;">
<td style="background-color: #D9D9D9; font-size: 100% !important; border:1px solid black !important;"> </td>
<td style="background-color: #D9D9D9; font-size: 100% !important; border:1px solid black !important;"> </td>
<td colspan="9" style="background-color: #D9D9D9; font-size: 100% !important; border:1px solid black !important; text-align: center;">ჩატარებული სამუშაოები</td>
<td style="background-color: #D9D9D9; font-size: 100% !important; border:1px solid black !important;"> </td>
<td style="background-color: #D9D9D9; font-size: 100% !important; border:1px solid black !important;"> </td>
</tr>
<tr style="background-color: #D9D9D9;!important; border:1px solid black !important;">
<td style="width: 170px;font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>შტრიხკოდი</span></td>
<td style="width: 110px;font-size: 9pt; border:1px solid black !important; vertical-align: middle !important; text-align: center;"><span>მოდელი</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">ტონერი</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">ბარაბანი</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">მაგნიტ. ლილ.</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">რეზინის PCR</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">გამწ. რაკელი</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">დოზ. რაკელი</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">ჩიპი</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">კორპუსი</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">სერვ გარაშე</span></td>
<td style="width: 25px !important; border:1px solid black !important;"><span style="writing-mode: tb-rl; -webkit-transform: rotate(270deg); white-space: nowrap; display: block;width: 8px; margin-top: 80px; margin-left: 4px;">საგარანტიო</span></td>
<td style="font-size: 100% !important; width: 110px !important; vertical-align: middle !important; text-align: center;"> ფასი </td>
</tr>';
$data .= print1($res['id']);
$data .= '</table>
<table >
<div style="text-align: right; font-size: 10pt; margin-top: 4px;">
<p>თანხა სულ : <span style="border-bottom: 1px solid #000; padding: 0 30px; margin-left: 0px;">' . addNull($sum) . ' ლარი</span></p>
</div>
</table>';
}
}
$data .= '
</div>
<div class="inner-table" >
</div>';
}
return $data;
}
if (false) {
ksort($allKCStudent);
foreach ($allKCStudent as $kc => $ss) {
foreach ($ss as $thisSection => $st) {
foreach ($st as $thisName => $xx) {
echo "{$kc} {$thisSection} {$thisName}\n";
foreach ($xx as $yyy) {
$yy = reset($yyy);
// return first element.
$g = $yy['grade'];
$dt = $yy['dt'];
$id = $yy['id'];
$tt = $yy['timeStamp'];
$clientID = $yy['clientID'];
$err = isset($yy['error']) ? $yy['error'] : '';
echo " ({$g}," . print2($dt) . ",{$err})\n";
}
echo "\n";
}
}
}
}
function skipKC($kc)
{
// none: entries where assigment of blame failed
// select-mc-answer answer multiple-choice questions
return $kc == 'none' || $kc == 'select-mc-answer';
}
// For each student and KC, Print out the model parameters.
// this was used to compare with Anirudh fits to logistic model.
if (false) {