Akaike's information criterion and Bayesian information criterion ----------------------------------------------------------------------------- Model | N ll(null) ll(model) df BIC -------------+--------------------------------------------------------------- all | 46,771 -23181.92 -21956.55 29 44224.94 **** all_trust | 46,781 -23191.15 -22408.74 23 45064.8 all_age | 46,861 -23238.22 -22024.43 24 44306.98 all_sex | 46,822 -23205.76 -22007.41 28 44315.93 all_ethnic | 46,790 -23190.31 -22005.3 26 44290.19 all_ia_sex | 46,771 -23181.92 -21934.73 42 44321.08 all_ia_eth~c | 46,752 -23160.87 -21845.93 66 44401.54 all_ia_trust | 46,759 -23168.03 -21467.84 87 43871.17 ** all_ia_age | 46,743 -23174.38 -21891.81 89 44740.58 ----------------------------------------------------------------------------- I have looked now at model performance. The first line is with all covariates inlcuded. Then, I take trust out, then trsut back in and age out, then age back in and sex out, then sex back in and ethnic out. You see all terms are needed. The bottom part is where I look at interactions. None is needed except there is an imporvement for interaction of mask with trust. So, I did an analysis stratified by trust: -> trust = East of England note: 6.mask != 0 predicts success perfectly 6.mask dropped and 3 obs not used Logistic regression Number of obs = 4,012 LR chi2(20) = 112.33 Prob > chi2 = 0.0000 Log likelihood = -1613.8567 Pseudo R2 = 0.0336 ----------------------------------------------------------------------------------------- fit | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] ------------------------+---------------------------------------------------------------- mask | Alpha Solway 3030V | 5.578858 2.583301 3.71 0.000 2.2511 13.82598 Alpha Solway HX-3 | .9304839 .1623277 -0.41 0.680 .6610166 1.309801 Alpha Solway S-3V | 2.763856 2.874921 0.98 0.328 .3598392 21.22864 Dräger 1730 | 1.178618 .1759554 1.10 0.271 .879625 1.579242 Dräger 1730V | 1 (empty) GVS F31000 | 1 (base) Handanhy HY9330 | .7667149 .1225455 -1.66 0.097 .5605117 1.048777 Handanhy HY9632 | 1.835163 .2777786 4.01 0.000 1.364058 2.468973 Honeywell Super One | .420678 .5192759 -0.70 0.483 .0374321 4.727753 Medium Kolmi | .5924349 .0916737 -3.38 0.001 .4374467 .8023356 Meixin MX-2016V | 2.30286 .4739923 4.05 0.000 1.538391 3.447215 Small Kolmi | .882567 .256673 -0.43 0.668 .4991103 1.560626 Valmy Spireor VSP352TF | .4773351 .236949 -1.49 0.136 .1804211 1.262873 ----------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------- -> trust = London Logistic regression Number of obs = 6,488 LR chi2(21) = 289.91 Prob > chi2 = 0.0000 Log likelihood = -2508.9587 Pseudo R2 = 0.0546 ----------------------------------------------------------------------------------------- fit | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] ------------------------+---------------------------------------------------------------- mask | Alpha Solway 3030V | 17.03455 7.778399 6.21 0.000 6.960666 41.68794 Alpha Solway HX-3 | .6806441 .0856363 -3.06 0.002 .5318937 .8709943 Dräger 1730 | .5461107 .0617581 -5.35 0.000 .437543 .6816173 Dräger 1730V | 1.347058 1.42338 0.28 0.778 .1698078 10.686 Fang Tian FT-045A | .2723134 .1726963 -2.05 0.040 .0785692 .9438128 GVS F31000 | 1 (base) Handanhy HY9330 | .9851746 .128861 -0.11 0.909 .7623878 1.273065 Handanhy HY9632 | 1.041109 .1609259 0.26 0.794 .7689967 1.409508 Honeywell Super One | .0574275 .0705911 -2.32 0.020 .0051618 .6389045 Medium Kolmi | .4752258 .0655229 -5.40 0.000 .3626925 .622675 Meixin MX-2016V | 2.180575 .5217709 3.26 0.001 1.364252 3.485361 Small Kolmi | .6599371 .0959914 -2.86 0.004 .4962387 .8776359 Valmy Spireor VSP352TF | 1.379999 .3793407 1.17 0.241 .8051861 2.365163 ----------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------- -> trust = Midlands note: 11.mask != 0 predicts success perfectly 11.mask dropped and 1 obs not used Logistic regression Number of obs = 12,242 LR chi2(21) = 418.26 Prob > chi2 = 0.0000 Log likelihood = -5889.8074 Pseudo R2 = 0.0343 ----------------------------------------------------------------------------------------- fit | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] ------------------------+---------------------------------------------------------------- mask | Alpha Solway 3030V | 5.013844 .7928917 10.19 0.000 3.677574 6.835656 Alpha Solway HX-3 | .9689565 .0670337 -0.46 0.649 .8460909 1.109664 Alpha Solway S-3V | 1.542935 .3600035 1.86 0.063 .9766566 2.437548 Dräger 1730 | 1.600613 .1480191 5.09 0.000 1.335273 1.91868 Dräger 1730V | 2.465783 .8283407 2.69 0.007 1.27646 4.763241 Fang Tian FT-045A | 1.440641 .8997555 0.58 0.559 .4235806 4.899769 GVS F31000 | 1 (base) Handanhy HY9330 | .8359664 .0680376 -2.20 0.028 .7127074 .9805424 Handanhy HY9632 | 1.003663 .0873826 0.04 0.967 .8462119 1.19041 Honeywell Super One | 1 (empty) Medium Kolmi | .6237546 .0650113 -4.53 0.000 .5085067 .7651223 Meixin MX-2016V | .7263493 .0805772 -2.88 0.004 .5844103 .9027618 Small Kolmi | .5494767 .0662265 -4.97 0.000 .4338673 .6958917 Valmy Spireor VSP352TF | .3866526 .0762785 -4.82 0.000 .2626616 .5691742 ----------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------- -> trust = North East and Yorkshire note: 7.mask != 0 predicts failure perfectly 7.mask dropped and 2 obs not used Logistic regression Number of obs = 8,301 LR chi2(20) = 164.70 Prob > chi2 = 0.0000 Log likelihood = -3421.0889 Pseudo R2 = 0.0235 ----------------------------------------------------------------------------------------- fit | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] ------------------------+---------------------------------------------------------------- mask | Alpha Solway 3030V | .2003666 .103058 -3.13 0.002 .0731159 .5490837 Alpha Solway HX-3 | .7688099 .1012982 -2.00 0.046 .5938337 .9953436 Dräger 1730 | .5533573 .0550325 -5.95 0.000 .4553568 .672449 Dräger 1730V | .1922115 .119155 -2.66 0.008 .0570303 .6478181 Fang Tian FT-045A | 1 (empty) GVS F31000 | 1 (base) Handanhy HY9330 | .4953621 .0470383 -7.40 0.000 .4112396 .5966925 Handanhy HY9632 | .7215101 .1517472 -1.55 0.121 .4777697 1.089598 Honeywell Super One | .2349279 .2889032 -1.18 0.239 .0210944 2.616386 Medium Kolmi | .741868 .1002128 -2.21 0.027 .5693048 .9667371 Meixin MX-2016V | .3827202 .0570449 -6.44 0.000 .2857648 .5125709 Small Kolmi | .9473863 .1811671 -0.28 0.777 .6512583 1.378164 Valmy Spireor VSP352TF | .2526925 .0466238 -7.46 0.000 .1760106 .3627821 ----------------------------------------------------------------------------------------- Note: _cons estimates baseline odds. ----------------------------------------------------------------------------------------------------------------------------------------------------- -> trust = North West Logistic regression Number of obs = 3,770 LR chi2(19) = 122.49 Prob > chi2 = 0.0000 Log likelihood = -1417.8889 Pseudo R2 = 0.0414 ----------------------------------------------------------------------------------------- fit | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] ------------------------+---------------------------------------------------------------- mask | Alpha Solway 3030V | 4.401927 1.288151 5.06 0.000 2.480578 7.811472 Alpha Solway HX-3 | .8112697 .1148428 -1.48 0.140 .6147092 1.070683 Dräger 1730 | 1.13227 .1720144 0.82 0.414 .8406897 1.524982 Dräger 1730V | .2296306 .0916 -3.69 0.000 .1050713 .5018515 GVS F31000 | 1 (base) Handanhy HY9330 | .5389246 .1095274 -3.04 0.002 .3618558 .8026394 Handanhy HY9632 | .4834398 .1439315 -2.44 0.015 .269724 .8664935 Medium Kolmi | .4985255 .1614161 -2.15 0.032 .2642891 .9403628 Meixin MX-2016V | .5045381 .1014529 -3.40 0.001 .3401995 .7482629 Small Kolmi | .5296493 .3546904 -0.95 0.343 .1425489 1.967945 Valmy Spireor VSP352TF | .5442534 .2128296 -1.56 0.120 .2528948 1.171284 ----------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------- -> trust = South East Logistic regression Number of obs = 11,415 LR chi2(22) = 1283.19 Prob > chi2 = 0.0000 Log likelihood = -6244.1489 Pseudo R2 = 0.0932 ----------------------------------------------------------------------------------------- fit | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] ------------------------+---------------------------------------------------------------- mask | Alpha Solway 3030V | 4.382854 1.118746 5.79 0.000 2.657562 7.228206 Alpha Solway HX-3 | .7884737 .0687786 -2.72 0.006 .6645641 .9354866 Alpha Solway S-3V | 14.51059 10.37177 3.74 0.000 3.574945 58.89802 Dräger 1730 | .3696205 .0306491 -12.00 0.000 .3141768 .4348486 Dräger 1730V | .8005018 .4001466 -0.45 0.656 .3005194 2.132319 Fang Tian FT-045A | .2821943 .0956752 -3.73 0.000 .1451967 .5484534 GVS F31000 | 1 (base) Handanhy HY9330 | .2676049 .0211887 -16.65 0.000 .2291378 .3125297 Handanhy HY9632 | .2453973 .0203396 -16.95 0.000 .208602 .288683 Honeywell Super One | .0139278 .0044433 -13.40 0.000 .0074529 .0260278 Medium Kolmi | .8142534 .1055539 -1.59 0.113 .6315619 1.049792 Meixin MX-2016V | .2050702 .018601 -17.47 0.000 .1716698 .244969 Small Kolmi | 1.100668 .1747472 0.60 0.546 .8063353 1.50244 Valmy Spireor VSP352TF | .4111264 .0415323 -8.80 0.000 .3372766 .5011462 ----------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------- -> trust = South West (this is problematic as there are not many masks used) Logistic regression Number of obs = 531 LR chi2(11) = 62.51 Prob > chi2 = 0.0000 Log likelihood = -308.77398 Pseudo R2 = 0.0919 ------------------------------------------------------------------------------------- fit | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] --------------------+---------------------------------------------------------------- mask | Alpha Solway 3030V | 1 (empty) Alpha Solway HX-3 | .1320404 .0386991 -6.91 0.000 .0743417 .2345207 Alpha Solway S-3V | 1 (empty) Dräger 1730 | 1 (empty) GVS F31000 | 1 (base) Meixin MX-2016V | .6729545 .1598452 -1.67 0.095 .4224759 1.071937 | ------------------------------------------------------------------------------------- I think the results give you quite a consistent picture what masks are good and which are not fitting well.