Fits a negative binomial regression model (for over-dispersed counts) via MASS::glm.nb().
Arguments
- formula
A formula, e.g.
count ~ x1 + x2.- data
A data frame.
- step
Logical. Always
FALSEfor negative binomial.- ...
Additional arguments passed to
MASS::glm.nb().
Value
A named list analogous to reg_poisson(), plus:
- theta
Estimated dispersion parameter for the negative binomial distribution.
- residuals
DataFrame of observed, fitted, Pearson residual.
Details
Note: The glm.nb family does not support stepwise selection.
Set step = FALSE.
For comparison with Poisson, inspect the dispersion ratio. NB is appropriate when dispersion >> 1.
Examples
set.seed(42)
x1 = rnorm(100)
mu = exp(1 + 0.3*x1)
y = rnbinom(100, size = 1, mu = mu)
reg_negbin(y ~ x1, data = data.frame(y, x1))
#> $model
#>
#> Call: MASS::glm.nb(formula = formula, data = data, init.theta = 1.065048329,
#> link = log)
#>
#> Coefficients:
#> (Intercept) x1
#> 0.9066 0.3223
#>
#> Degrees of Freedom: 99 Total (i.e. Null); 98 Residual
#> Null Deviance: 118
#> Residual Deviance: 107.8 AIC: 426.8
#>
#> $coefficient
#> # A tibble: 2 × 7
#> term estimate std.error statistic p.value conf.low conf.high
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 0.907 0.117 7.74 1.01e-14 0.674 1.14
#> 2 x1 0.322 0.116 2.78 5.52e- 3 0.0918 0.553
#>
#> $theta
#> [1] 1.065
#>
#> $residuals
#> observed fitted_val pearson_residual
#> 1 10 3.8515662 1.45813385
#> 2 3 2.0637798 0.38022455
#> 3 1 2.7832389 -0.56232217
#> 4 0 3.0360630 -0.88795154
#> 5 1 2.8203934 -0.56751176
#> 6 1 2.3925412 -0.49966195
#> 7 0 4.0300920 -0.91783383
#> 8 2 2.4013999 -0.14357779
#> 9 33 4.7454403 5.55301204
#> 10 0 2.4262552 -0.86031816
#> 11 0 3.7703837 -0.91129668
#> 12 7 5.1739838 0.33167912
#> 13 2 1.5822978 0.21062114
#> 14 0 2.2630181 -0.85100611
#> 15 1 2.3716583 -0.49583057
#> 16 1 3.0390864 -0.59585138
#> 17 1 2.2590357 -0.47416026
#> 18 1 1.0515664 -0.03567073
#> 19 1 1.1273871 -0.08362003
#> 20 15 3.7889557 2.69786926
#> 21 0 2.2427936 -0.84978084
#> 22 2 1.3942773 0.33757935
#> 23 1 2.3423351 -0.49035498
#> 24 3 3.6623436 -0.16427734
#> 25 1 4.5606361 -0.72545730
#> 26 0 2.1550342 -0.84426394
#> 27 3 2.2787702 0.26964147
#> 28 3 1.4024563 0.88626526
#> 29 1 2.8716086 -0.57447784
#> 30 7 2.0142924 2.06595728
#> 31 2 2.8673102 -0.26656014
#> 32 1 3.1073243 -0.60399201
#> 33 0 3.4563744 -0.90231357
#> 34 0 2.0345661 -0.83611636
#> 35 2 2.9134322 -0.27688530
#> 36 5 1.4234773 1.96109809
#> 37 0 1.9226440 -0.82787765
#> 38 2 1.8819006 0.05175445
#> 39 1 1.1369703 -0.08933592
#> 40 6 2.5047980 1.20627363
#> 41 9 2.6457802 2.09283292
#> 42 3 2.2037950 0.30614483
#> 43 3 3.1611981 -0.04551360
#> 44 0 1.9587721 -0.83061279
#> 45 3 1.5928291 0.70579639
#> 46 0 2.8464685 -0.88037002
#> 47 6 1.9060239 1.77545306
#> 48 2 3.9434531 -0.45130120
#> 49 2 2.1543556 -0.06048681
#> 50 1 3.0584438 -0.59819232
#> 51 2 2.7465179 -0.23811235
#> 52 1 1.9230283 -0.39738454
#> 53 3 4.1143681 -0.24912731
#> 54 1 3.0459013 -0.59667844
#> 55 0 2.5484818 -0.86668161
#> 56 5 2.7066395 0.74075383
#> 57 0 3.0818395 -0.88966913
#> 58 4 2.5485411 0.49359889
#> 59 3 0.9434328 1.54183614
#> 60 0 2.7139188 -0.87457392
#> 61 2 2.1994111 -0.07680247
#> 62 0 2.6281275 -0.87057839
#> 63 16 2.9865226 3.86085409
#> 64 7 3.8874613 0.73207187
#> 65 4 1.9584014 0.86587018
#> 66 1 3.7675566 -0.66936135
#> 67 3 2.7588717 0.07661481
#> 68 3 3.4601674 -0.12001412
#> 69 0 3.3312663 -0.89834871
#> 70 3 3.1234326 -0.03521845
#> 71 0 1.7688413 -0.81533789
#> 72 4 2.4048645 0.56987244
#> 73 7 3.0269319 1.16504470
#> 74 2 1.8206708 0.08074079
#> 75 2 2.0783795 -0.03164632
#> 76 1 2.9857264 -0.58926414
#> 77 0 3.1714202 -0.89291385
#> 78 2 2.8750079 -0.26830323
#> 79 1 1.8608672 -0.38074327
#> 80 0 1.7368276 -0.81252843
#> 81 2 4.0316317 -0.46253599
#> 82 2 2.6904349 -0.22416264
#> 83 0 2.5473973 -0.86662725
#> 84 2 2.3811759 -0.13732277
#> 85 0 1.6846934 -0.80779124
#> 86 2 3.0157114 -0.29880618
#> 87 0 2.3084385 -0.85369807
#> 88 2 2.3341654 -0.12243090
#> 89 4 3.3448429 0.17604688
#> 90 0 3.2266845 -0.89484243
#> 91 3 3.8779239 -0.20694160
#> 92 4 2.1235179 0.74422353
#> 93 9 3.0532239 1.73073029
#> 94 1 3.8766667 -0.67827549
#> 95 1 1.7306757 -0.34281067
#> 96 2 1.8759138 0.05452016
#> 97 1 1.7190279 -0.33919417
#> 98 3 1.5468187 0.74612093
#> 99 0 2.5404619 -0.86627870
#> 100 4 3.0560358 0.27450815
#>
#> $diagnostics
#> # A tibble: 3 × 2
#> metric value
#> <chr> <dbl>
#> 1 aic 427.
#> 2 bic 435.
#> 3 theta 1.06
#>
#> $model_info
#> # A tibble: 1 × 2
#> aic bic
#> <dbl> <dbl>
#> 1 427. 435.
#>
#> $formula
#> y ~ x1
#> <environment: 0x00000224a26c3038>
#>
#> $input
#> y x1
#> 1 10 1.37095845
#> 2 3 -0.56469817
#> 3 1 0.36312841
#> 4 0 0.63286260
#> 5 1 0.40426832
#> 6 1 -0.10612452
#> 7 0 1.51152200
#> 8 2 -0.09465904
#> 9 33 2.01842371
#> 10 0 -0.06271410
#> 11 0 1.30486965
#> 12 7 2.28664539
#> 13 2 -1.38886070
#> 14 0 -0.27878877
#> 15 1 -0.13332134
#> 16 1 0.63595040
#> 17 1 -0.28425292
#> 18 1 -2.65645542
#> 19 1 -2.44046693
#> 20 15 1.32011335
#> 21 0 -0.30663859
#> 22 2 -1.78130843
#> 23 1 -0.17191736
#> 24 3 1.21467470
#> 25 1 1.89519346
#> 26 0 -0.43046913
#> 27 3 -0.25726938
#> 28 3 -1.76316309
#> 29 1 0.46009735
#> 30 7 -0.63999488
#> 31 2 0.45545012
#> 32 1 0.70483734
#> 33 0 1.03510352
#> 34 0 -0.60892638
#> 35 2 0.50495512
#> 36 5 -1.71700868
#> 37 0 -0.78445901
#> 38 2 -0.85090759
#> 39 1 -2.41420765
#> 40 6 0.03612261
#> 41 9 0.20599860
#> 42 3 -0.36105730
#> 43 3 0.75816324
#> 44 0 -0.72670483
#> 45 3 -1.36828104
#> 46 0 0.43281803
#> 47 6 -0.81139318
#> 48 2 1.44410126
#> 49 2 -0.43144620
#> 50 1 0.65564788
#> 51 2 0.32192527
#> 52 1 -0.78383894
#> 53 3 1.57572752
#> 54 1 0.64289931
#> 55 0 0.08976065
#> 56 5 0.27655075
#> 57 0 0.67928882
#> 58 4 0.08983289
#> 59 3 -2.99309008
#> 60 0 0.28488295
#> 61 2 -0.36723464
#> 62 0 0.18523056
#> 63 16 0.58182373
#> 64 7 1.39973683
#> 65 4 -0.72729206
#> 66 1 1.30254263
#> 67 3 0.33584812
#> 68 3 1.03850610
#> 69 0 0.92072857
#> 70 3 0.72087816
#> 71 0 -1.04311894
#> 72 4 -0.09018639
#> 73 7 0.62351816
#> 74 2 -0.95352336
#> 75 2 -0.54282881
#> 76 1 0.58099650
#> 77 0 0.76817874
#> 78 2 0.46376759
#> 79 1 -0.88577630
#> 80 0 -1.09978090
#> 81 2 1.51270701
#> 82 2 0.25792144
#> 83 0 0.08844023
#> 84 2 -0.12089654
#> 85 0 -1.19432890
#> 86 2 0.61199690
#> 87 0 -0.21713985
#> 88 2 -0.18275671
#> 89 4 0.93334633
#> 90 0 0.82177311
#> 91 3 1.39211638
#> 92 4 -0.47617392
#> 93 9 0.65034856
#> 94 1 1.39111046
#> 95 1 -1.11078888
#> 96 2 -0.86079259
#> 97 1 -1.13173868
#> 98 3 -1.45921400
#> 99 0 0.07998255
#> 100 4 0.65320434
#>