Passing–Bablok regression

[JulienBohy]

Hello,

Is it possible to add Passing–Bablok regression in this lib?
src : https://en.wikipedia.org/wiki/Passing%E2%80%93Bablok_regression

thanks

[Beakerboy]

In an initial glance, this seems like the Theil-Sen regression, but with Confidence Intervals. Is it similar?

[JulienBohy]

The Passing-Bablok and Theil-Sen regression are closely related non-parametric methods to
estimate the regression coefficients and build tests on the relationship between the dependent
and independent variables. Both methods rely on the slopes of the connecting lines between
pairwise measurements. While Theil and Sen assume no measurement errors in the independent
variable, the method from Passing and Bablok accounts for errors in both variables

src: https://arxiv.org/pdf/1905.07649.pdf

I'm not a mathematician but here's what I found
;)

[Beakerboy]

I’m not a mathematician either ...scientist/engineer. As an aside...neither of your links are working correctly.

[JulienBohy]

Hello,

Links are updated sorry

[JulienBohy]

What do you think of this proposal?
Do you think it deserves to be added to this wonderful library?

[Beakerboy]

All submissions are welcome.

[JulienBohy]

Hi,

A trainee wrote us a function, but the code is not very clear and does not really correspond to PHP standards.
So i cant make a pull request.

I've never been in open source projects and honestly don't really have time.

I found also Python implementation on this link

you will find below the code of our intern

<?php
        /**
         * @param array $dataPoints
         * @return array
         */
        public static function passingBablok($dataPoints)
        {
            $x = [];
            $y = [];
            $ic = [];
            $ic_low = [];
            $ic_upp = [];
            $S = [];

            foreach ($dataPoints as $point) {
                $x[] = (float)$point[0];
                $y[] = (float)$point[1];
            }

            $n = count($x);

            if ($n != count($y)) {
                throw new Exception('passingBablok(): Number of elements in coordinate arrays do not match.');
            }

            $x_min = min($x);
            $x_max = max($x);

            $x_sum = array_sum($x);
            $y_sum = array_sum($y);

            $xx_sum = 0;
            $xy_sum = 0;
            $yy_sum = 0;

            for ($i = 0; $i < count($x); ++$i) {
                $xy_sum += ($x[$i] * $y[$i]);
                $xx_sum += ($x[$i] * $x[$i]);
                $yy_sum += ($y[$i] * $y[$i]);
            }
            $r = ($xy_sum - ((1 / $n) * $x_sum * $y_sum)) / (sqrt(
                (($xx_sum) - ((1 / $n) * (pow($x_sum, 2)))) * (($yy_sum) - ((1 / $n) * (pow($y_sum, 2))))
              ));
            $r2 = $r * $r;

            $cgamma = 1.95996 * pow(($n * ($n - 1) * (2 * $n + 5) / 18), 0.5);

            $k = 0;
            for ($i = 0; $i < $n; ++$i) {
                for ($j = 0; $j < $n; ++$j) {
                    $var = null;
                    if ($i < $j && !($x[$i] == $x[$j] && $y[$i] == $y[$j])) {
                        $dx = $x[$j] - $x[$i];
                        $dy = $y[$j] - $y[$i];
                        if (0.00 !== $dx) {
                            $var = $dy / $dx;
                        }
                        if (0 == $dx) {
                            $var = MathUtils::Sgn($dy) * 99999;
                        }
                        if (!empty($var)) {
                            $S[] = $var;
                            ++$k;
                        }
                    }
                }
            }

            $nn = $k;
            sort($S);

            $k = 0;
            while ($S[$k] < -1) {
                ++$k;
            }

            $N_CIlow = round(($nn - $cgamma) / 2, 0);

            $N_CIupp = $nn - $N_CIlow + 1 + $k;

            $N_CIlow = $N_CIlow + $k;

            $nr = round($nn / 2, 0);
            if ($nn / 2 == $nr) {
                $odd_even = 1;
                $n_med = $nn / 2 + $k;
            } else {
                $odd_even = 2;
                $n_med = ($nn + 1) / 2 + $k;
            }

            $b = $S[$n_med];

            $b_CI95upp = 0;
            $b_CI95low = 0;
            $slope_b = 0;
            for ($i = 0; $i < $nn; ++$i) {
                if (1 == $odd_even && $i == $n_med) {
                    $slope_b = $S[$i] / 2;
                }
                if (1 == $odd_even && $i == $n_med + 1) {
                    $slope_b = $slope_b + $S[$i] / 2;
                }
                if (2 == $odd_even && $i == $n_med) {
                    $slope_b = $S[$i];
                }
                if ($i == $N_CIlow) {
                    $b_CI95low = $S[$i - 1];
                }
                if ($i == $N_CIupp) {
                    $b_CI95upp = $S[$i];
                }
            }

            for ($i = 0; $i < $n; ++$i) {
                $ic[$i] = $y[$i] - $slope_b * $x[$i];
                $ic_low[$i] = $y[$i] - $b_CI95upp * $x[$i];
                $ic_upp[$i] = $y[$i] - $b_CI95low * $x[$i];
            }

            $a_CI95upp = Average::median($ic_upp);
            $intercept_a = Average::median($ic);
            $a_CI95low = Average::median($ic_low);

            $results = [];
            $results['SLOPE'] = $slope_b;
            $results['R2'] = $r2;
            $results['INTERCEPT'] = $intercept_a;
            $results['B_CI95LOW'] = $b_CI95low;
            $results['B_CI95UPP'] = $b_CI95upp;
            $results['A_CI95LOW'] = $a_CI95low;
            $results['A_CI95UPP'] = $a_CI95upp;
            $results['REGRESSION_LINE_X_MIN'] = $x_min;
            $results['REGRESSION_LINE_X_MAX'] = $x_max;

            return $results;
        }
		?>

Can all of this information be useful?

[markrogoyski]

Hi @JulienBohy,

Thank you for sharing your code. Even if it is not a formal pull request, it is still helpful.

We'll update this thread if there is any progress on an official MathPHP implementation.

Thanks again,
Mark