!g# dZddlZddlmZddlmZddlmZddl m Z m Z Gdd eZ Gd d eZ d Zd Zedk(r1ej"ddidedddZdZeegZej,gdgZej0dZeD]ZgZgZgZgZeeD]Z e\Z!Z"eZ#ee!jHe!jJe!jLe!jNe#e Z(e(jSZ*ee!jHe!jJe!jLe!jNe#e"Z(e(jSe*j8Z*e* e*jVs e,dde(j[z Z.ej_ej0e"j<e.fej_ej`e*j8ej_ej`e*jbe\Z!Z"eZ#ee!jHe!jJe!jLe!jNe#e"eefZ(e(jSZ*e* e*jVs e,de(jdZ3e3dZ4ej_e4ej,e5ee6ez Z7ejqde6eefzejqd e!jse7ej,eZejudZ;ejydZ=ej,eZejudZejqd!ejqd"ejqej|e;d#zejqd$ejqej|e!j8d#zejqd%ejqej|e;e!j8z d#zejqd&ejqej|e;e!j8z e!j8z d#zejqd#ejqd'ejqd"ejqej|e=d#zejqd$ejqej|ed#zejqd%ejqej|e=ez d#zejqd&ejqej|e=ez ez d#zejqd#ejejqd(ejqd)ejqej|ed#zejqd*ejqej|ed#zejqd+ejd,d-d,D]*ZAejqd.eeBeAe6ezeAfz,ejqd/ejyy)0z Assesment of Generalized Estimating Equations using simulation. This script checks Poisson models. See the generated file "gee_poisson_simulation_check.txt" for results. N)Poisson) GEE_simulator)GEE) Exchangeable Independencec eZdZdZdZdZdZy)Exchangeable_simulatora6 Simulate exchangeable Poisson data. The data within a cluster are simulated as y_i = z_c + z_i. The z_c, and {z_i} are independent Poisson random variables with expected values e_c and {e_i}, respectively. In order for the pairwise correlation to be equal to `f` for all pairs, we need e_c / sqrt((e_c + e_i) * (e_c + e_j)) = f for all i, j. By setting all e_i = e within a cluster, these equations can be satisfied. We thus need e_c * (1 - f) = f * e, which can be solved (non-uniquely) for e and e_c. ?c(tjd|dztjd|jdztjd|dztjd|jztjdy)Nz/Estimated common pairwise correlation: %8.4f rz/True common pairwise correlation: %8.4f /Estimated inverse scale parameter: %8.4f r/True inverse scale parameter: %8.4f  )OUTwritedparams scale_invself dparams_ests r/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/genmod/tests/gee_poisson_simulation_check.py print_dparamsz$Exchangeable_simulator.print_dparams%s} Da.! " D,,q/" # Da.! " D..! " $cggggf\}}}}tj|jdz}tjj tj t |jtj|j|j|z z \}}}|ddtj|dkDf} t|jD]} tjj|jd|jd} |j| g| ztjj| df} |j| tjj!dd} | d|j"dz z|j"dz }tjj%| }tjj%|| }||z}|j|tj&| |ztj(| z}tj||jtj|jdzz }tjjt || j*df}|tj,|| j.z }|j|tj0|d|_tj0||_tj0|d|_tj0||_y) Nư>rrsize )lowhighaxis)npsumparamslinalgsvdeyelenouter flatnonzerorangengroupsrandomrandintgroup_size_rangeappendnormaluniformrpoissonlogonesshapedotT concatenateexogendogtimegroup)rr=r<r?r>fusvtparams0igsizetime1e_cecommonuniqueendog1lprexog1emats rsimulatezExchangeable_simulator.simulate1sw#%r2r> tUD FF4;;> "rvvc$++&67!xx T[[AAE FG!BAbnnQX../t||$ AII%%d&;&;A&>&*&;&;A&>@E LL! &II$$5!*$5E KK ))###3Cq4<<?*+dll1o=AYY&&s+FYY&&q%0Ff_F LL &&q/BGGEN2CHHS$++. Q1GGE99###c(GMM!4D)E#FD RVVD')), ,E KK 3 6NN4a0 ^^E* NN4a0 ^^E* rN)__name__ __module__ __qualname____doc__rrrPrrr r s$I (+rr ceZdZdZdZdZy)Overdispersed_simulatora Use the negative binomial distribution to check GEE estimation using the overdispered Poisson model with independent dependence. Simulating X = np.random.negative_binomial(n, p, size) then EX = (1 - p) * n / p Var(X) = (1 - p) * n / p**2 These equations can be inverted as follows: p = E / V n = E * p / (1 - p) dparams[0] is the common correlation coefficient ctjd|dztjd|jztjdy)Nr rrr)rrrrs rrz%Overdispersed_simulator.print_dparamsosC Da.! " D..! " $rc2ggggf\}}}}tj|jdz}tjj tj t |jtj|j|j|z z \}}}|ddtj|dkDf} t|jD]O} tjj|jd|jd} |j| g| ztjj| df} |j| tjj| t |jf} |j| tj tj"| |j}||j$z}||z }||zd|z z }tjj'||| }|j|Rtj(|d|_tj(||_tj(|d|_tj(||_y)Nrrrrrr")r$r%r&r'r(r)r*r+r,r-r.r/r0r1r2r3expr9rnegative_binomialr;r<r=r>r?)rr=r<r?r>r@rArBrCrDrErFrGrNEVpnrLs rrPz Overdispersed_simulator.simulatews#%r2r> tUD FF4;;> "rvvc$++&67!xx T[[AAE FG!BAbnnQX../t||$ !AII%%d&;&;A&>&*&;&;A&>@E LL! &II$$5!*$5E KK II$$5#dkk2B*C$DE KK rvveT[[12ADNN"AAAAQAYY00Au=F LL ) !,NN4a0 ^^E* NN4a0 ^^E* rN)rQrRrSrTrrPrUrrrWrW\s$#+rrWct}tjd|_d|_dg|_|j |tfS)N@皙?rcggɿg333333?)r r$r_r&r.rrPrexss rgendat_exchangeablerhsA "C/0CJCK&CKLLN   rct}tjd|_d|_d|_g|_|j|tfS)Nrardrb) rWr$rer&r.rrrPrrfs rgendat_overdispersedrjsF ! #C/0CJCKCMCKLLN   r__main__allc d|zS)Nz%8.3frU)xs rros GaKrT) formattersuppressz gee_poisson_simulation_check.txtwzutf-8)encodingd)rrr)ru) start_paramszFailed to converger ) constraintzp-valuez:Results based on %d successful fits out of %d data sets. z Checking dependence parameters: zChecking parameter values: zObserved: rzExpected: zAbsolute difference: zRelative difference: zChecking standard errors z!Checking constrained estimation: zLeft hand side: zRight hand side: z+Observed p-values Expected Null p-values g?gQ?z%20.3f %20.3f zR================================================================================ )DrTnumpyr$statsmodels.genmod.familiesrgee_gaussian_simulation_checkr3statsmodels.genmod.generalized_estimating_equationsrstatsmodels.genmod.cov_structrrr rWrhrjrQset_printoptionsopenrnrepgendatsarraylhsrerhsgendatpvaluesr& std_errorsrr-jdavagar=r<r?r>mdfitmdf convergedprintestimate_scalerr2asarraystandard_errorsscore_test_resultsscorepvaluer%r* dparams_meanrrmeaneparamsstdsdparams array_strsortarangeqintcloserUrrrs/8CCI+]I+X>+m>+D zB5*?"@!%' 13 IC D"$89G "((%' (C %%+CZ% t" #AXFBBRXXrww"''2!^%B&&(CRXXrww"''2rBB&& &3C{3==*+R..00I NN255Y!67 8 MM*"**SZZ0 1   jbjj)<)<= >HEBrBRXXrww"''2r!$c ,B&&(C{3==*+))E9%F NN6 "E" #H rxxG s7| ;<  P\4() * 56 &&!++a.::a=RXXj) __Q'  01 )* ,",,w'$./ )* ,",,ryy)D01 )* ,",,w23d:; )* ,",,")) 3ryy@A  $ ./ )* ,",,x(4/0 )* ,",,z*T12 )* ,",,x*45<= )* ,",,: 5CD  $  67 %& ,",,s#d*+ &' ,",,s#d*+ @A3c* 9A II's1S\>23Q78 9 9 #$uZ%xIIKWr