Have you got enough degrees of freedom to estimates your odds ratios with sufficient precision (small sampling variance)?

I decided to apply the logistic regression method to my categorical and quantitative data. So, I followed these steps:

• Eliminating the bad and inconsistent data.
• Preparing the target variable (categorical variable).
• Testing the dependencies between categorical variables and the target variable using the Ki-2 test for selecting the variables that are well linked with the target variable.
• Testing the correlation between quantitative variables to avoid the choice of two correlated variables at a time.
• Crossing some variables to improve their significance.

After all this I do not find any significant variables in my logistic regression model knowing that the base is well coherent and well cleaned.

I work with the R language and I used the glm function:

glm (formula, family = familytype (link = linkfunction), data =)

You can see my data base. Note that Achat_client is target variable:

> M=data.frame(Type_peau,PEAU_CORPS,SENSIBILITE,IMPERFECTIONS,BRILLANCE ,GRAIN_PEAU,RIDES_VISAGE,ALLERGIES,MAINS,PEAU_CORPS, + INTERET_ALIM_NATURELLE,INTERET_ORIGINE_GEO,Crois_Prior1_Milieu,Crois_Profil_Prio,Crois_ALL_AGE, + INTERET_VACANCES,INTERET_COMPOSITION, PEAU_CORPS,Nbre_gift,w,Achat_client) > str(M) 'data.frame': 836 obs. of 21 variables: $ Type_peau : Factor w/ 5 levels "","Grasse","Mixte",..: 3 4 5 3 4 3 3 3 2 3 ... $ PEAU_CORPS : Factor w/ 4 levels "","Normale","Sèche",..: 2 3 3 2 2 2 3 2 3 2 ... $ SENSIBILITE : Factor w/ 4 levels "","Aucune","Fréquente",..: 4 4 4 2 4 3 4 2 4 4 ... $ IMPERFECTIONS : Factor w/ 4 levels "","Fréquente",..: 3 4 3 4 3 2 3 4 3 3 ... $ BRILLANCE : Factor w/ 4 levels "","Aucune","Partout",..: 4 2 2 4 4 4 4 4 3 4 ... $ GRAIN_PEAU : Factor w/ 4 levels "","Dilaté","Fin",..: 4 4 4 2 4 2 4 4 2 4 ... $ RIDES_VISAGE : Factor w/ 4 levels "","Aucune","Très visibles",..: 2 2 2 4 4 2 4 2 4 2 ... $ ALLERGIES : Factor w/ 4 levels "","Non","Oui",..: 2 2 2 2 2 2 2 2 2 2 ... $ MAINS : Factor w/ 4 levels "","Moites","Normales",..: 3 4 4 3 3 3 3 4 4 4 ... $ PEAU_CORPS.1 : Factor w/ 4 levels "","Normale","Sèche",..: 2 3 3 2 2 2 3 2 3 2 ... $ INTERET_ALIM_NATURELLE: Factor w/ 4 levels "","Beaucoup",..: 2 4 4 4 2 2 2 4 4 2 ... $ INTERET_ORIGINE_GEO : Factor w/ 5 levels "","Beaucoup",..: 2 4 2 5 2 2 2 2 2 2 ... $ Crois_Prior1_Milieu : Factor w/ 14 levels "Per_nature_éclatante",..: 11 13 8 12 8 6 8 9 13 11 ... $ Crois_Profil_Prio : Factor w/ 294 levels "Eclatante / Hydratée_éclatante",..: 141 227 221 74 56 184 13 86 227 68 ... $ Crois_ALL_AGE : Factor w/ 6 levels "jeune_Avec_ALL",..: 2 4 2 4 2 2 4 4 6 2 ... $ INTERET_VACANCES : Factor w/ 6 levels "","À la mer",..: 3 4 2 2 3 2 3 2 3 2 ... $ INTERET_COMPOSITION : Factor w/ 4 levels "","Beaucoup",..: 2 2 2 4 2 2 2 2 4 2 ... $ PEAU_CORPS.2 : Factor w/ 4 levels "","Normale","Sèche",..: 2 3 3 2 2 2 3 2 3 2 ... $ Nbre_gift : int 1 4 1 1 2 1 1 1 1 1 ... $ w : num 0.25 0.25 0.5 0.25 0.5 0 0 0 0 0.75 ... $ Achat_client : num 0 0 0 0 0 0 1 0 0 0 ...

Then I split my data base into tow parts: 70% of data for modeling and 30% for testing then the model:

split = sample.split(M$Achat_client, SplitRatio = 0.70) final.train = subset(M, split == TRUE) final.test = subset(M, split == FALSE)

Then for application of logistic regression:

final.log.model summary(final.log.model) Call: glm(formula = Achat_client ~ . - 1, family = binomial(link = "logit"), data = final.train) Deviance Residuals: Min 1Q Median 3Q Max -1.60306 -0.26636 -0.04545 -0.00003 2.83714 Coefficients: (5 not defined because of singularities) Estimate Std. Error z value Pr(>|z|) Type_peauGrasse -7.530e+00 2.811e+00 -2.679 0.007383 ** Type_peauMixte -8.278e+00 2.535e+00 -3.265 0.001095 ** Type_peauNormale -7.902e+00 2.568e+00 -3.077 0.002087 ** Type_peauSèche -9.710e+00 2.583e+00 -3.759 0.000171 *** PEAU_CORPSSèche 8.639e-01 5.966e-01 1.448 0.147612 PEAU_CORPSTrès sèche 1.660e+00 8.959e-01 1.853 0.063843 . SENSIBILITEFréquente -1.978e-02 9.583e-01 -0.021 0.983531 SENSIBILITEOccasionnelle -1.123e-01 8.905e-01 -0.126 0.899640 IMPERFECTIONSOccasionnelle -2.825e-01 5.859e-01 -0.482 0.629712 IMPERFECTIONSRares -1.234e+00 9.116e-01 -1.353 0.175956 BRILLANCEPartout 1.720e+00 1.351e+00 1.273 0.202993 BRILLANCEZone T 2.942e-01 7.643e-01 0.385 0.700299 GRAIN_PEAUFin 1.901e+00 9.640e-01 1.972 0.048609 * GRAIN_PEAUMoyen 6.999e-01 6.976e-01 1.003 0.315696 RIDES_VISAGETrès visibles 2.350e+00 1.101e+00 2.134 0.032843 * RIDES_VISAGEVisibles -1.224e-02 5.696e-01 -0.021 0.982857 ALLERGIESOui -1.770e+01 4.714e+03 -0.004 0.997004 MAINSNormales 1.767e+00 1.055e+00 1.675 0.093963 . MAINSSèches 1.679e+00 1.073e+00 1.565 0.117595 PEAU_CORPS.1Sèche NA NA NA NA PEAU_CORPS.1Très sèche NA NA NA NA INTERET_ALIM_NATURELLEPas du tout -6.929e-01 1.490e+00 -0.465 0.641833 INTERET_ALIM_NATURELLEUn peu -1.801e+00 7.381e-01 -2.441 0.014666 * INTERET_ORIGINE_GEOPas du tout 1.025e+00 1.293e+00 0.793 0.427673 INTERET_ORIGINE_GEOUn peu -4.041e-01 6.494e-01 -0.622 0.533728 Crois_Prior1_MilieuPer_nature_hydratée -7.592e-01 2.015e+00 -0.377 0.706322 Crois_Prior1_MilieuPer_nature_lisse -3.454e-01 1.756e+00 -0.197 0.844073 Crois_Prior1_MilieuPer_nature_matifiée -1.509e-01 2.495e+00 -0.060 0.951761 Crois_Prior1_MilieuPer_nature_nourrie -1.860e+01 6.608e+03 -0.003 0.997754 Crois_Prior1_MilieuPer_nature_purifiée -3.315e-01 1.611e+00 -0.206 0.837001 Crois_Prior1_MilieuPer_nature_reposée 1.284e+00 1.883e+00 0.682 0.495542 Crois_Prior1_MilieuPer_urbain_éclatante -1.819e-02 1.534e+00 -0.012 0.990538 Crois_Prior1_MilieuPer_urbain_hydratée 3.449e-01 1.356e+00 0.254 0.799243 Crois_Prior1_MilieuPer_urbain_lisse 1.080e+00 1.334e+00 0.810 0.418107 Crois_Prior1_MilieuPer_urbain_matifiée 1.051e+00 1.398e+00 0.752 0.452290 Crois_Prior1_MilieuPer_urbain_nourrie 3.070e+00 1.627e+00 1.887 0.059226 . Crois_Prior1_MilieuPer_urbain_purifiée -1.456e+00 1.430e+00 -1.018 0.308601 Crois_Prior1_MilieuPer_urbain_reposée 2.520e+00 1.493e+00 1.688 0.091498 . Crois_Profil_PrioLisse / Eclatante_éclatante 2.472e+00 1.486e+00 1.663 0.096222 . Crois_Profil_PrioMatifiée / Eclatante_éclatante 2.845e+00 1.631e+00 1.744 0.081110 . Crois_Profil_PrioNourrie / Eclatante_éclatante -1.685e+01 7.795e+03 -0.002 0.998276 Crois_Profil_PrioPurifiée / Eclatante_éclatante 1.182e+00 1.523e+00 0.776 0.437707 Crois_Profil_PrioReposée / Eclatante_éclatante -1.895e+01 5.224e+03 -0.004 0.997106 Crois_Profil_PrioEclatante / Hydratée_hydratée -1.763e+01 2.457e+03 -0.007 0.994276 Crois_Profil_PrioLisse / Hydratée_hydratée -1.409e-02 1.625e+00 -0.009 0.993081 Crois_Profil_PrioMatifiée / Hydratée_hydratée -1.623e+01 4.667e+03 -0.003 0.997225 Crois_Profil_PrioNourrie / Hydratée_hydratée 1.917e+00 1.854e+00 1.034 0.301226 Crois_Profil_PrioPurifiée / Hydratée_hydratée 1.841e+00 1.417e+00 1.299 0.193915 Crois_Profil_PrioReposée / Hydratée_hydratée -1.581e+01 7.573e+03 -0.002 0.998334 Crois_Profil_PrioEclatante / Lisse_lisse 1.464e+00 1.427e+00 1.026 0.305064 Crois_Profil_PrioHydratée / Lisse_lisse -1.757e+01 3.171e+03 -0.006 0.995578 Crois_Profil_PrioMatifiée / Lisse_lisse 3.308e+00 1.879e+00 1.760 0.078343 . Crois_Profil_PrioNourrie / Lisse_lisse 1.318e+00 1.829e+00 0.721 0.471155 Crois_Profil_PrioPurifiée / Lisse_lisse -1.844e+01 3.417e+03 -0.005 0.995695 Crois_Profil_PrioReposée / Lisse_lisse -1.627e+01 6.889e+03 -0.002 0.998115 Crois_Profil_PrioEclatante / Matifiée_matifiée -1.651e+01 4.405e+03 -0.004 0.997010 Crois_Profil_PrioHydratée / Matifiée_matifiée 3.058e+00 1.669e+00 1.832 0.066970 . Crois_Profil_PrioLisse / Matifiée_matifiée 2.699e+00 1.761e+00 1.533 0.125319 Crois_Profil_PrioNourrie / Matifiée_matifiée 3.910e+00 2.316e+00 1.688 0.091412 . Crois_Profil_PrioPurifiée / Matifiée_matifiée -1.614e+01 3.076e+03 -0.005 0.995814 Crois_Profil_PrioReposée / Matifiée_matifiée -1.751e+01 1.235e+04 -0.001 0.998868 Crois_Profil_PrioEclatante / Nourrie_nourrie 2.304e+00 1.620e+00 1.422 0.154909 Crois_Profil_PrioHydratée / Nourrie_nourrie -1.622e+01 3.909e+03 -0.004 0.996688 Crois_Profil_PrioLisse / Nourrie_nourrie 4.018e+00 2.082e+00 1.931 0.053542 . Crois_Profil_PrioMatifiée / Nourrie_nourrie -1.683e+01 9.424e+03 -0.002 0.998575 Crois_Profil_PrioPurifiée / Nourrie_nourrie 2.889e+00 1.891e+00 1.528 0.126629 Crois_Profil_PrioEclatante / Purifiée_purifiée 1.983e-01 1.773e+00 0.112 0.910932 Crois_Profil_PrioHydratée / Purifiée_purifiée -1.700e+00 2.025e+00 -0.840 0.401098 Crois_Profil_PrioLisse / Purifiée_purifiée -1.741e+01 5.381e+03 -0.003 0.997419 Crois_Profil_PrioMatifiée / Purifiée_purifiée -1.840e+01 4.515e+03 -0.004 0.996749 Crois_Profil_PrioReposée / Purifiée_purifiée -1.771e+01 1.039e+04 -0.002 0.998640 Crois_Profil_PrioEclatante / Reposée_reposée 2.290e+00 1.796e+00 1.275 0.202363 Crois_Profil_PrioHydratée / Reposée_reposée -1.609e+01 3.890e+03 -0.004 0.996699 Crois_Profil_PrioLisse / Reposée_reposée 2.916e+00 1.552e+00 1.879 0.060212 . Crois_Profil_PrioMatifiée / Reposée_reposée -1.625e+01 9.461e+03 -0.002 0.998629 Crois_Profil_PrioNourrie / Reposée_reposée -1.724e+01 8.232e+03 -0.002 0.998329 Crois_Profil_PrioPurifiée / Reposée_reposée 6.497e-01 1.724e+00 0.377 0.706274 Crois_ALL_AGEjeune_Sans_ALL -7.512e-01 7.326e-01 -1.025 0.305170 Crois_ALL_AGEsenior_Avec_ALL 1.664e+01 4.714e+03 0.004 0.997183 Crois_ALL_AGEsenior_Sans_ALL 3.611e-01 6.555e-01 0.551 0.581703 Crois_ALL_AGEvieux_Avec_ALL 1.930e+01 4.714e+03 0.004 0.996733 Crois_ALL_AGEvieux_Sans_ALL NA NA NA NA INTERET_VACANCESÀ la montagne 1.208e+00 5.537e-01 2.182 0.029090 * INTERET_VACANCESEn ville 2.452e+00 9.143e-01 2.682 0.007317 ** INTERET_COMPOSITIONPas du tout -1.763e+01 4.579e+03 -0.004 0.996929 INTERET_COMPOSITIONUn peu 4.350e-01 8.082e-01 0.538 0.590461 PEAU_CORPS.2Sèche NA NA NA NA PEAU_CORPS.2Très sèche NA NA NA NA Nbre_gift 2.144e-01 1.520e-01 1.411 0.158265 w 1.796e+00 1.027e+00 1.749 0.080317 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 812.37 on 586 degrees of freedom Residual deviance: 170.68 on 501 degrees of freedom AIC: 340.68 Number of Fisher Scoring iterations: 19

I think you have got a problem of multicollinearity, residual's deviance 812-170=642 is distributed approx. as a chi2(85). The 1% threshold is approx equalt to 120 i.e. your pvalue is approx. 0. So you have a model with good fit overall but none of the effects turns up significant. If, as it seem, your objective is not just prediction but also the estimation of the ORs, then try to simplify your model, also to make results more interpretable .