# Control lmercontrolopt optimx optctrl listmethod

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Control: lmerControl(opt = "optimx", optCtrl = list(method = "nlminb"))REML criterion at convergence: 3685.8Scaled residuals:Min1QMedian3QMax-2.5791 -0.6337 -0.04040.59144.8761Random effects:GroupsNameVariance Std.Dev. Corrplayer_id (Intercept)2.61510 1.6171minutes0.01789 0.1337-0.98home1.06872 1.0338-0.580.73c_opp_av0.01635 0.1279-0.540.36 -0.37Residual18.30500 4.2784Number of obs: 631, groups:player_id, 20
8.2.GENERAL MODEL WITHPPREDICTORS225Fixed effects:Estimate Std. Error t value(Intercept) -3.252950.72662-4.477minutes0.499710.0390012.814c_opp_av-0.061080.05285-1.156home0.574150.413551.388Correlation of Fixed Effects:(Intr) minuts c_pp_vminutes-0.883c_opp_av -0.1640.151home-0.3550.317 -0.095> logLik(wnba.rcr2)’log Lik.’ -1842.915 (df=15)The (REML) estimates variance-covariance matrix forβiis obtained from the variances, standard de-viations, and correlations of the estimated random effects.ˆV{βj}= ˆσ2βjˆ{COV}{βjjprime}= ˆσβjjprime= ˆρˆσjˆσjprimeˆΣβ=2.61510-0.21188-0.96962-0.11169-0.211880.017890.100900.00616-0.969620.100901.06872-0.04892-0.111690.00616-0.048920.016358.2.2Tests Regarding Elements ofΣβTo test whether variance components (variances of regression coefficients) are 0, fit the model with andwithout the random effect(s) for the component(s) of interest. Obtain the log-likelihood with and withoutthe random effect(s) of interest, along with the degrees of freedom.In R, these are obtained using thelogLik()function. A conservative test is conducted as follows.H0:σ2βj=· · ·σ2βk= 0TS:X2LR=-2 [lnLR-lnLC]RR:X2LRχ2α,dfC-dfRP:P(χ2dfC-dfRX2LR)In R, thelmerTestpackage takes the output of thelmerfunction, and conducts the Likelihood-Ratiotest, one-at-a-time for the regression coefficients (not including the intercept). To test multiple coefficientssimultaneously (and/or the intercept), multiple models need to be fit, and their log-likelihoods can becompared using the test above.Example: Women’s NBA Player’s Points per Game
226CHAPTER 8.RANDOM COEFFICIENT REGRESSION MODELSminutespoints0102030010203040Angel McCoughtryBecky Hammon010203040Bria HartleyCourtney Paris010203040Danielle AdamsDanielle RobinsonDewanna BonnerErin PhillipsEssence Carson0102030Janel McCarville0102030Kayla McBrideKelsey BoneKelsey GriffinNicole PowellPenny TaylorSandrine Gruda010203040Sue BirdSylvia Fowles010203040Tanisha Wright0102030Tina CharlesFigure 8.3: WNBA Data - Points versus Minutes with Simple Linear Regression
8.2.GENERAL MODEL WITHPPREDICTORS227Random EffectsRandom CoefficientsPlayer IDˆβi0-ˆβ0ˆβi1-ˆβ1ˆβi2-ˆβ2ˆβi3-ˆβ3ˆβi0ˆβi1ˆβi2ˆβi34-2.18040.20961.8547-0.0405-5.43340.7093-0.10162.42885-2.97620.21380.23740.2387-6.22920.71350.17760.811621-1.31470.14301.6428-0.0916-4.56770.6427-0.15272.2170220.3516-0.0301-0.1817-0.0085-2.90140.4696-0.06960.3925300.5435-0.03560.0648-0.0574-2.70950.4641-0.11850.6389320.3003-0.0383-0.55320.0437-2.95260.4614-0.01740.021033-1.35580.11300.60180.0455-4.60880.6127-0.01561.176034-2.38060.21941.7234-0.0056-5.63350.7191-0.06662.2975410.3893-0.0330-0.1914-0.0107-2.86360.4667-0.07180.3827420.7952-0.0694-0.4514-0.0141-2.45780.4303-0.07510.122744-0.05800.00730.1038-0.0081-3.31100.5070-0.06910.6779470.0862-0.0244-0.58470.0671-3.16680.47530.0061-0.0105490.4641-0.0717-1.25310.1186-2.78880.42800.0575-0.6790512.0034-0.1547-0.5020-0.1168-1.24960.3450-0.17790.0722720.5627-0.0412-0.0706-0.0418-2.69020.4585-0.10290.5036731.6616-0.1553-1.27220.0128-1.59140.3444-0.0483-0.6981851.2298-0.0877-0.0785-0.1012-2.02320.4120-0.16220.4956950.7575-0.0699-0.55020.0020-2.49540.4298-0.05910.02401021.9650-0.1701-1.0730-0.0402-1.28790.3297-0.1013-0.4989108-0.84440.07530.53330.0080-4.09730.5751-0.05311.1074Table 8.3: Random Effects and Random Coefficients for WNBA SampleThe following R program and output conducts Likelihood Ratio Tests regarding the variance componentsσ2βj

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Term
Fall
Professor
Ceryan