如何解决Python Statsmodels Mixedlm随机斜率+截距R2
我根据以下内容在 Statsmodels 中安装了一个混合模型：
# Final model with random intercept and slopes
final_volume_model = smf.mixedlm("Transformed_Volume ~ score",data = final_model_data,groups = final_model_data['Stock'],missing = 'drop',re_formula = 'score')
final_volume_fit = final_volume_model.fit()
print(final_volume_fit.summary())
################## Output ##################
Mixed Linear Model Regression Results
================================================================
Model: MixedLM Dependent Variable: Transformed_Volume
No. Observations: 181 Method: REML
No. Groups: 13 Scale: 8698.0110
Min. group size: 13 Log-Likelihood: -1098.8257
Max. group size: 15 Converged: Yes
Mean group size: 13.9
----------------------------------------------------------------
Coef. Std.Err. z P>|z| [0.025 0.975]
----------------------------------------------------------------
Intercept 330.777 74.894 4.417 0.000 183.989 477.566
score 39.102 16.390 2.386 0.017 6.979 71.224
Group Var 71886.612 333.046
Group x score Cov 2161.829 70.984
score Var 65.015 18.319
================================================================
我已经检查了模型假设（一切都很好！），现在想计算 R2。 我是根据中川和 Shielzeth these 中的 article 公式完成的：
边际 R2
条件 R2
var(f) = 固定效应的方差
var(r) = 随机效应的方差
var(epsilon) = 模型残差的方差
我担心的是，在获取等式的不同部分时，我不确定我是否正确理解了 Statsmodels 的输出：
n = 181
# Obtain values for fixed- & random effects and model-residuals
fixed_effects = final_volume_fit.bse_fe
random_effects = final_volume_fit.bse_re
residuals = final_volume_fit.resid
# The fixed-,random- and residual variance
fixed_effect_variance = ((fixed_effects[0]**2)+(fixed_effects[1]**2))*n
random_effect_variance =((random_effects[0]**2)+(random_effects[1]**2)+(random_effects[2]**2))*n
residual_variance = [x**2 for x in residuals]
residual_variance = sum(residual_variance)/(n-2)
# Final calculation
marginal_R2 = (fixed_effect_variance)/(fixed_effect_variance+random_effect_variance+residual_variance)
conditional_R2 = (fixed_effect_variance+random_effect_variance)/(fixed_effect_variance+random_effect_variance+residual_variance)
############### Output #################
# marginal_R2: 0.04809224194663527
# conditional_R2: 0.9996329364055776
使用的数据：
fixed_effects:
Intercept 74.893656
score 16.389560
dtype: float64
random_effects:
Group Var 333.046398
Group x score Cov 70.984066
score Var 18.318524
dtype: float64
resiudals: [-44.02577774345405,-55.380815476000116,0.5551467914537653,24.419222256545936,42.52322225654595,76.3520335938154,-31.849853208546236,105.17222225654595,-27.640777743454052,-51.66681547600012,-21.619353208546244,-14.458027743454053,11.573071326361514,-43.89796640618461,-69.08432706508967,-200.8790151463973,-182.85991117349982,3.370054168867682,67.1446234841327,107.94783882650017,153.20901951123517,306.1360195112352,55.49401951123525,-22.14232706508966,-39.88522309219218,-19.779896380354614,-79.91794583113233,-61.767980488764806,5.717034491288729,-29.142006764681184,34.48203449128873,14.700034491288726,-5.011996450688734,-10.371746450688732,-6.738965508711274,-13.568965508711273,-23.234965508711273,-18.699455194718766,14.789158259198526,3.562117003228554,-5.04891393874885,3.3811170032285567,-27.641953808982805,-66.36607124278095,-94.03709472954057,-65.42876591490577,-84.23611821630024,-64.98961821630024,-38.10307124278091,128.52799921749795,168.35397573073828,-39.511000782502094,-42.02502426926168,5.048405270459455,57.2352961910172,128.52230454537312,38.089999217497905,-106.04053228102975,-73.08653228102969,-24.877435800848502,159.11346771897024,88.34987123878909,17.58627475860783,-6.228339320667374,-35.52553228102977,-14.282532281029717,-19.540207642298128,-11.820532281029728,17.10387123878911,34.88846771897033,40.36946771897033,-25.464942333496936,-5.803702846965834,-59.52094233349693,-39.34190241907507,36.23101775208124,121.74305766650309,54.648057666503064,-5.887902419075061,37.327858094393804,-53.3540221623406,-51.998062076762466,-46.35052216234061,-30.763862504653233,46.17545681072153,91.05194042624845,-57.54153103307135,-43.76575935851281,-120.26098768395423,15.359183560126837,46.86751231604575,118.71112647876646,30.370012316045745,101.54201231604577,41.868012316045736,-5.847987683954216,-3.5777022771524116,-62.94548768395424,-61.81034498055334,-87.59611665511193,360.93789319100745,98.00389319100736,28.1565186696331,68.31170593032027,117.10220593032034,-175.8513886572747,-137.75841954830537,-139.35910680899258,-37.792886742772,-52.96679406967968,-2.265386742772023,-37.91710680899257,-69.1851068089926,-6.690960150112332,72.00073098054312,18.72625452828096,-22.20826901945688,2.0006367895917094,-27.18300724558796,-20.10026901945689,-11.944269019456883,-7.8190072455879545,14.98137501572279,-19.284269019456886,-16.00229256719473,-28.42400724558796,21.61203984988768,-152.35548955431472,-31.63262921834348,-5.634039434325018,-93.13854941032702,57.70544061367093,187.80198051767917,-38.91505938632906,-82.24903943432503,260.39147054167705,43.76947054167704,2.9439705416770607,-9.169799410327016,-37.88152945832297,-91.70699953031675,-45.5148254647398,-49.71843056261332,-79.5655897796251,-21.791615268992757,156.2490694373867,236.39789904589253,348.48417453526025,-18.588825464739784,-95.36961526899275,-85.24098468175158,-78.78222036686628,-105.44203566048682,-125.00464075836035,-59.44795919238399,-91.19556701864133,19.101933610284846,-62.31407142112448,-62.807817962030526,-111.32131984880891,-180.30782047773528,-140.59606764756745,29.005182037969462,300.02167889333873,89.2391820379695,132.92393172350648,166.37218203796954,-38.33056827649352,-12.545107025784759,-30.392742746214935,-12.845198095677233,-52.76883381610742,-9.628804049082262,1.3081959509177352,-16.484107025784752,49.67116618389258,103.54219595091774,-39.68083381610742,-27.600015955892317,-28.400410002487284,48.99186320719008]
我在 Jupyter Notebook 中使用 Python。
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