Bayesian Model Averaging (BMA) examples
About
This notebook tries out some of the Bayesian Model Averaging (BMA) packages for R. For a nice introduction, see this paper. https://journals.sagepub.com/doi/full/10.1177/2515245919898657
To find packages, I searched at MetaCRAN: https://www.r-pkg.org/search.html?q=bayesian+model+averaging
There are 100s of packages. I chose 3 that are made for OLS BMA, the simplest case.
Of the three here, BMA is probably the best. Like BMS, it fits instantly, and provides lots of useful output. BAS is very slow. BMA has the advantage over BMS that it supports factor variables natively, for BMS one has to recode them manually. This solution results in a lack of group-wise selection, i.e., all dummy variables are not included or excluded together.
Init
options(
digits = 3
)
library(pacman)
p_load(
kirkegaard,
BMA,
BMS,
BAS,
formula.tools #easy formula use
)Data
We use the mpg dataset for this. It has a mix of numerical and categorical variables. We pick a numeric one, displ, as the outcome.
mpg#split the transmission variable
mpg %<>% mutate(
trans_auto = str_detect(trans, "auto"),
trans_type = str_match(trans, "\\((\\w+)")[, 2]
)
#change chr to fct
for (v in names(mpg)) {
if (is.character(mpg[[v]])) mpg[[v]] = mpg[[v]] %>% as.factor()
}
#summarize variables
map(mpg, function(x) {
if (is.numeric(x)) {
return(psych::describe(x))
} else {
return(table2(x))
}
})## $manufacturer
## # A tibble: 16 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 dodge 37 15.8
## 2 toyota 34 14.5
## 3 volkswagen 27 11.5
## 4 ford 25 10.7
## 5 chevrolet 19 8.12
## 6 audi 18 7.69
## 7 hyundai 14 5.98
## 8 subaru 14 5.98
## 9 nissan 13 5.56
## 10 honda 9 3.85
## 11 jeep 8 3.42
## 12 pontiac 5 2.14
## 13 land rover 4 1.71
## 14 mercury 4 1.71
## 15 lincoln 3 1.28
## 16 <NA> 0 0
##
## $model
## # A tibble: 39 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 caravan 2wd 11 4.70
## 2 ram 1500 pickup 4wd 10 4.27
## 3 civic 9 3.85
## 4 dakota pickup 4wd 9 3.85
## 5 jetta 9 3.85
## 6 mustang 9 3.85
## 7 a4 quattro 8 3.42
## 8 grand cherokee 4wd 8 3.42
## 9 impreza awd 8 3.42
## 10 a4 7 2.99
## # … with 29 more rows
##
## $displ
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 234 3.47 1.29 3.3 3.39 1.33 1.6 7 5.4 0.44 -0.91 0.08
##
## $year
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 234 2004 4.51 2004 2004 6.67 1999 2008 9 0 -2.01 0.29
##
## $cyl
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 234 5.89 1.61 6 5.86 2.97 4 8 4 0.11 -1.46 0.11
##
## $trans
## # A tibble: 11 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 auto(l4) 83 35.5
## 2 manual(m5) 58 24.8
## 3 auto(l5) 39 16.7
## 4 manual(m6) 19 8.12
## 5 auto(s6) 16 6.84
## 6 auto(l6) 6 2.56
## 7 auto(av) 5 2.14
## 8 auto(s4) 3 1.28
## 9 auto(s5) 3 1.28
## 10 auto(l3) 2 0.855
## 11 <NA> 0 0
##
## $drv
## # A tibble: 4 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 f 106 45.3
## 2 4 103 44.0
## 3 r 25 10.7
## 4 <NA> 0 0
##
## $cty
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 234 16.9 4.26 17 16.6 4.45 9 35 26 0.79 1.43 0.28
##
## $hwy
## vars n mean sd median trimmed mad min max range skew kurtosis se
## X1 1 234 23.4 5.95 24 23.2 7.41 12 44 32 0.36 0.14 0.39
##
## $fl
## # A tibble: 6 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 r 168 71.8
## 2 p 52 22.2
## 3 e 8 3.42
## 4 d 5 2.14
## 5 c 1 0.427
## 6 <NA> 0 0
##
## $class
## # A tibble: 8 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 suv 62 26.5
## 2 compact 47 20.1
## 3 midsize 41 17.5
## 4 subcompact 35 15.0
## 5 pickup 33 14.1
## 6 minivan 11 4.70
## 7 2seater 5 2.14
## 8 <NA> 0 0
##
## $trans_auto
## # A tibble: 3 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 TRUE 157 67.1
## 2 FALSE 77 32.9
## 3 <NA> 0 0
##
## $trans_type
## # A tibble: 11 x 3
## Group Count Percent
## <chr> <dbl> <dbl>
## 1 l4 83 35.5
## 2 m5 58 24.8
## 3 l5 39 16.7
## 4 m6 19 8.12
## 5 s6 16 6.84
## 6 l6 6 2.56
## 7 av 5 2.14
## 8 s4 3 1.28
## 9 s5 3 1.28
## 10 l3 2 0.855
## 11 <NA> 0 0#model formula
#got errors when trying all the variables...
#https://github.com/hanase/BMA/issues/4
# model_form = "displ ~ manufacturer + model + year + cyl + drv + cty + hwy + fl + class + trans_auto + trans_type" %>% as.formula()
#but this selection works
model_form = "displ ~ manufacturer + year + cyl + drv + cty + hwy + fl + class + trans" %>% as.formula()Examples
BMA
#fit
BMA_fit = BMA::bic.glm(model_form, data = mpg, glm.family = "gaussian")
#results
BMA_fit##
## Call:
## bic.glm.formula(f = model_form, data = mpg, glm.family = "gaussian")
##
##
## Posterior probabilities(%):
## manufacturer year cyl drv cty hwy
## 100.0 100.0 100.0 100.0 100.0 6.2
## fl class trans
## 100.0 100.0 0.0
##
## Coefficient posterior expected values:
## (Intercept) manufacturerchevrolet manufacturerdodge
## -3.13e+01 1.10e+00 7.90e-01
## manufacturerford manufacturerhonda manufacturerhyundai
## 7.59e-01 2.89e-01 3.55e-01
## manufacturerjeep manufacturerland rover manufacturerlincoln
## 6.57e-01 -8.50e-02 8.95e-01
## manufacturermercury manufacturernissan manufacturerpontiac
## 6.42e-01 6.67e-01 1.05e+00
## manufacturersubaru manufacturertoyota manufacturervolkswagen
## 5.02e-01 5.91e-01 3.14e-01
## year cyl drvf
## 1.64e-02 4.79e-01 -1.57e-01
## drvr cty hwy
## 1.60e-01 -4.60e-02 2.25e-04
## fld fle flp
## 4.39e-01 -4.86e-01 1.18e-01
## flr classcompact classmidsize
## -1.78e-02 -8.42e-01 -8.87e-01
## classminivan classpickup classsubcompact
## -8.79e-01 -6.78e-01 -8.66e-01
## classsuv transauto(l3) transauto(l4)
## -6.12e-01 0.00e+00 0.00e+00
## transauto(l5) transauto(l6) transauto(s4)
## 0.00e+00 0.00e+00 0.00e+00
## transauto(s5) transauto(s6) transmanual(m5)
## 0.00e+00 0.00e+00 0.00e+00
## transmanual(m6)
## 0.00e+00#summary
BMA_fit %>% summary()##
## Call:
## bic.glm.formula(f = model_form, data = mpg, glm.family = "gaussian")
##
##
## 2 models were selected
## Best 2 models (cumulative posterior probability = 1 ):
##
## p!=0 EV SD model 1 model 2
## Intercept 100 -3.13e+01 9.32242 -3.13e+01 -3.08e+01
## manufacturer 100.0
## .chevrolet 1.10e+00 0.15955 1.10e+00 1.11e+00
## .dodge 7.90e-01 0.14821 7.89e-01 7.97e-01
## .ford 7.59e-01 0.14317 7.59e-01 7.67e-01
## .honda 2.89e-01 0.18521 2.89e-01 2.98e-01
## .hyundai 3.55e-01 0.15858 3.54e-01 3.64e-01
## .jeep 6.57e-01 0.16197 6.56e-01 6.66e-01
## .land rover -8.50e-02 0.18564 -8.54e-02 -8.02e-02
## .lincoln 8.95e-01 0.23851 8.94e-01 9.03e-01
## .mercury 6.42e-01 0.19266 6.42e-01 6.50e-01
## .nissan 6.67e-01 0.13560 6.66e-01 6.77e-01
## .pontiac 1.05e+00 0.18075 1.05e+00 1.06e+00
## .subaru 5.02e-01 0.12956 5.01e-01 5.07e-01
## .toyota 5.91e-01 0.12616 5.90e-01 6.00e-01
## .volkswagen 3.14e-01 0.12018 3.13e-01 3.22e-01
## year 100.0 1.64e-02 0.00471 1.64e-02 1.61e-02
## cyl 100.0 4.79e-01 0.02684 4.79e-01 4.80e-01
## drv 100.0
## .f -1.57e-01 0.11059 -1.57e-01 -1.64e-01
## .r 1.60e-01 0.11141 1.60e-01 1.54e-01
## cty 100.0 -4.60e-02 0.01464 -4.58e-02 -4.92e-02
## hwy 6.2 2.25e-04 0.00500 . 3.61e-03
## fl 100.0
## .d 4.39e-01 0.36101 4.38e-01 4.44e-01
## .e -4.86e-01 0.32638 -4.87e-01 -4.68e-01
## .p 1.18e-01 0.30998 1.18e-01 1.33e-01
## .r -1.78e-02 0.30733 -1.87e-02 -5.20e-03
## class 100.0
## .compact -8.42e-01 0.20270 -8.43e-01 -8.31e-01
## .midsize -8.87e-01 0.19355 -8.88e-01 -8.79e-01
## .minivan -8.79e-01 0.24365 -8.80e-01 -8.62e-01
## .pickup -6.78e-01 0.21012 -6.79e-01 -6.60e-01
## .subcompact -8.66e-01 0.19635 -8.66e-01 -8.55e-01
## .suv -6.12e-01 0.18984 -6.13e-01 -5.96e-01
## trans 0.0
## .auto(l3) 0.00e+00 0.00000 . .
## .auto(l4) 0.00e+00 0.00000 . .
## .auto(l5) 0.00e+00 0.00000 . .
## .auto(l6) 0.00e+00 0.00000 . .
## .auto(s4) 0.00e+00 0.00000 . .
## .auto(s5) 0.00e+00 0.00000 . .
## .auto(s6) 0.00e+00 0.00000 . .
## .manual(m5) 0.00e+00 0.00000 . .
## .manual(m6) 0.00e+00 0.00000 . .
##
## nVar 7 8
## BIC -8.79e+02 -8.74e+02
## post prob 0.938 0.062#default plots
BMA_fit %>% plot()
#coefs, manually
tibble(
term = names(BMA_fit$postmean),
post_mean = BMA_fit$postmean,
post_sd = BMA_fit$postsd,
cond_post_mean = BMA_fit$condpostmean,
cond_post_sd = BMA_fit$condpostsd
) %>% print(n = Inf)## # A tibble: 40 x 5
## term post_mean post_sd cond_post_mean cond_post_sd
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -31.3 9.32 -31.3 9.32
## 2 manufacturerchevrolet 1.10 0.160 1.10 0.178
## 3 manufacturerdodge 0.790 0.148 0.790 0.197
## 4 manufacturerford 0.759 0.143 0.759 0.417
## 5 manufacturerhonda 0.289 0.185 0.289 0.433
## 6 manufacturerhyundai 0.355 0.159 0.355 0.330
## 7 manufacturerjeep 0.657 0.162 0.657 0.419
## 8 manufacturerland rover -0.0850 0.186 -0.0850 0.688
## 9 manufacturerlincoln 0.895 0.239 0.895 0.311
## 10 manufacturermercury 0.642 0.193 0.642 0.241
## 11 manufacturernissan 0.667 0.136 0.667 0.330
## 12 manufacturerpontiac 1.05 0.181 1.05 1.12
## 13 manufacturersubaru 0.502 0.130 0.502 0.192
## 14 manufacturertoyota 0.591 0.126 0.591 0.466
## 15 manufacturervolkswagen 0.314 0.120 0.314 0.295
## 16 year 0.0164 0.00471 0.0164 0.00471
## 17 cyl 0.479 0.0268 0.479 0.0268
## 18 drvf -0.157 0.111 -0.157 0.137
## 19 drvr 0.160 0.111 0.160 0.327
## 20 cty -0.0460 0.0146 -0.0460 0.0146
## 21 hwy 0.000225 0.00500 0.00361 0.0197
## 22 fld 0.439 0.361 0.439 0.429
## 23 fle -0.486 0.326 -0.486 0.681
## 24 flp 0.118 0.310 0.118 0.465
## 25 flr -0.0178 0.307 -0.0178 0.335
## 26 classcompact -0.842 0.203 -0.842 0.203
## 27 classmidsize -0.887 0.194 -0.887 0.200
## 28 classminivan -0.879 0.244 -0.879 0.252
## 29 classpickup -0.678 0.210 -0.678 0.269
## 30 classsubcompact -0.866 0.196 -0.866 0.202
## 31 classsuv -0.612 0.190 -0.612 0.310
## 32 transauto(l3) 0 0 0 0
## 33 transauto(l4) 0 0 0 0
## 34 transauto(l5) 0 0 0 0
## 35 transauto(l6) 0 0 0 0
## 36 transauto(s4) 0 0 0 0
## 37 transauto(s5) 0 0 0 0
## 38 transauto(s6) 0 0 0 0
## 39 transmanual(m5) 0 0 0 0
## 40 transmanual(m6) 0 0 0 0BMS
#fit
BMS_fit = BMS::bms(X.data = model_form, data = mpg)## Warning in mean.default(y): argument is not numeric or logical: returning NA## Error in y - mean(y): non-numeric argument to binary operator#oh dear, it appears the package does not support non-numerical predictors
#so we make a new formula with only numerical ones
mpg_num_vars = map_dbl(mpg, is.numeric)
model_form_numerical = str_glue("displ ~ {str_c(names(mpg_num_vars[mpg_num_vars==1 & names(mpg_num_vars) != 'displ']), collapse = ' + ')}") %>% as.formula()
model_form_numerical## displ ~ year + cyl + cty + hwy
## <environment: 0x55e82c1a66b0>#fit
BMS_fit = BMS::bms(model_form_numerical, data = mpg)## PIP Post Mean Post SD Cond.Pos.Sign Idx
## cyl 1.000 0.65365 0.03232 1 2
## hwy 0.758 -0.02272 0.01560 0 4
## year 0.436 0.00596 0.00816 1 1
## cty 0.345 -0.01078 0.02082 0 3
##
## Mean no. regressors Draws Burnins Time
## "2.5385" "16" "0" "0.00761 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "16" "16" "100" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "NA" "234" "random / 2" "UIP"
## Shrinkage-Stats
## "Av=0.9957"
##
## Time difference of 0.00761 secs#print
BMS_fit## PIP Post Mean Post SD Cond.Pos.Sign Idx
## cyl 1.000 0.65365 0.03232 1 2
## hwy 0.758 -0.02272 0.01560 0 4
## year 0.436 0.00596 0.00816 1 1
## cty 0.345 -0.01078 0.02082 0 3
##
## Mean no. regressors Draws Burnins Time
## "2.5385" "16" "0" "0.00761 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "16" "16" "100" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "NA" "234" "random / 2" "UIP"
## Shrinkage-Stats
## "Av=0.9957"#summary
BMS_fit %>% summary()## Mean no. regressors Draws Burnins Time
## "2.5385" "16" "0" "0.00761 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "16" "16" "100" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "NA" "234" "random / 2" "UIP"
## Shrinkage-Stats
## "Av=0.9957"#default plots
BMS_fit %>% plot()
#coefs
BMS_fit %>% coef()## PIP Post Mean Post SD Cond.Pos.Sign Idx
## cyl 1.000 0.65365 0.03232 1 2
## hwy 0.758 -0.02272 0.01560 0 4
## year 0.436 0.00596 0.00816 1 1
## cty 0.345 -0.01078 0.02082 0 3#alternatively, we can recode all the factors to binary manually
BMS_data = model.matrix(model_form, data = mpg) %>%
as.data.frame() %>%
bind_cols(displ = mpg$displ)
BMS_form = ("displ ~ `" + str_c(names(BMS_data)[-c(1, 41)], collapse = "` + `") + "`") %>% as.formula()
BMS_form## displ ~ manufacturerchevrolet + manufacturerdodge + manufacturerford +
## manufacturerhonda + manufacturerhyundai + manufacturerjeep +
## `manufacturerland rover` + manufacturerlincoln + manufacturermercury +
## manufacturernissan + manufacturerpontiac + manufacturersubaru +
## manufacturertoyota + manufacturervolkswagen + year + cyl +
## drvf + drvr + cty + hwy + fld + fle + flp + flr + classcompact +
## classmidsize + classminivan + classpickup + classsubcompact +
## classsuv + `transauto(l3)` + `transauto(l4)` + `transauto(l5)` +
## `transauto(l6)` + `transauto(s4)` + `transauto(s5)` + `transauto(s6)` +
## `transmanual(m5)` + `transmanual(m6)`
## <environment: 0x55e82d26f4f0>#fit
BMS_fit2 = BMS::bms(BMS_form, data = BMS_data)## PIP Post Mean Post SD Cond.Pos.Sign Idx
## manufacturerchevrolet 1.00000 0.483059 0.10120 1.0000 1
## cyl 1.00000 0.558532 0.02499 1.0000 16
## drvr 1.00000 0.439126 0.10019 1.0000 18
## classcompact 1.00000 -0.593211 0.10848 0.0000 25
## classmidsize 1.00000 -0.480104 0.12170 0.0000 26
## classsubcompact 1.00000 -0.603914 0.10511 0.0000 29
## manufacturerland rover 0.87867 -0.570335 0.27114 0.0000 7
## manufacturerpontiac 0.79633 0.452436 0.27684 1.0000 11
## drvf 0.67967 -0.160791 0.12689 0.0000 17
## fle 0.35700 -0.117626 0.17739 0.0000 22
## transauto(s4) 0.26100 0.134249 0.25414 1.0000 35
## manufacturerhonda 0.23367 -0.069989 0.14498 0.0000 4
## transauto(s5) 0.23067 0.106832 0.21835 1.0000 36
## manufacturersubaru 0.19633 0.037026 0.09493 1.0000 12
## classminivan 0.18367 -0.055012 0.12873 0.0000 27
## year 0.15067 0.001852 0.00485 1.0000 15
## manufacturernissan 0.09333 0.019610 0.06883 1.0000 10
## transauto(l4) 0.09067 -0.007028 0.02803 0.0000 32
## manufacturerdodge 0.06233 0.004570 0.02755 1.0000 2
## cty 0.05467 -0.000581 0.00401 0.0915 19
## flr 0.05267 -0.000820 0.01444 0.3734 24
## manufacturertoyota 0.05000 0.002604 0.01995 1.0000 13
## transauto(l5) 0.04700 -0.001754 0.01709 0.1489 33
## classsuv 0.04633 -0.001889 0.01734 0.0144 30
## hwy 0.03967 -0.000441 0.00332 0.0420 20
## manufacturervolkswagen 0.03867 -0.002978 0.02284 0.0000 14
## transauto(s6) 0.02500 0.001813 0.01947 1.0000 37
## manufacturermercury 0.02467 0.000897 0.02880 1.0000 9
## transmanual(m6) 0.02333 0.002655 0.02165 1.0000 39
## manufacturerford 0.01967 0.002586 0.02244 1.0000 3
## transauto(l3) 0.01800 -0.001685 0.03621 0.0000 31
## manufacturerhyundai 0.01600 -0.000732 0.01482 0.0000 5
## fld 0.01267 0.000657 0.01890 1.0000 21
## manufacturerjeep 0.01233 0.001253 0.01878 1.0000 6
## flp 0.01133 0.000213 0.00690 1.0000 23
## transmanual(m5) 0.00933 -0.000418 0.00728 0.0000 38
## classpickup 0.00700 0.000378 0.00817 1.0000 28
## manufacturerlincoln 0.00467 0.000280 0.01592 1.0000 8
## transauto(l6) 0.00000 0.000000 0.00000 NA 34
##
## Mean no. regressors Draws Burnins Time
## "10.7270" "3000" "1000" "0.1537 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "625" "5.5e+11" "1.1e-07" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "0.8248" "234" "random / 19.5" "UIP"
## Shrinkage-Stats
## "Av=0.9957"
##
## Time difference of 0.154 secs#print
BMS_fit2## PIP Post Mean Post SD Cond.Pos.Sign Idx
## manufacturerchevrolet 1.00000 0.483059 0.10120 1.0000 1
## cyl 1.00000 0.558532 0.02499 1.0000 16
## drvr 1.00000 0.439126 0.10019 1.0000 18
## classcompact 1.00000 -0.593211 0.10848 0.0000 25
## classmidsize 1.00000 -0.480104 0.12170 0.0000 26
## classsubcompact 1.00000 -0.603914 0.10511 0.0000 29
## manufacturerland rover 0.87867 -0.570335 0.27114 0.0000 7
## manufacturerpontiac 0.79633 0.452436 0.27684 1.0000 11
## drvf 0.67967 -0.160791 0.12689 0.0000 17
## fle 0.35700 -0.117626 0.17739 0.0000 22
## transauto(s4) 0.26100 0.134249 0.25414 1.0000 35
## manufacturerhonda 0.23367 -0.069989 0.14498 0.0000 4
## transauto(s5) 0.23067 0.106832 0.21835 1.0000 36
## manufacturersubaru 0.19633 0.037026 0.09493 1.0000 12
## classminivan 0.18367 -0.055012 0.12873 0.0000 27
## year 0.15067 0.001852 0.00485 1.0000 15
## manufacturernissan 0.09333 0.019610 0.06883 1.0000 10
## transauto(l4) 0.09067 -0.007028 0.02803 0.0000 32
## manufacturerdodge 0.06233 0.004570 0.02755 1.0000 2
## cty 0.05467 -0.000581 0.00401 0.0915 19
## flr 0.05267 -0.000820 0.01444 0.3734 24
## manufacturertoyota 0.05000 0.002604 0.01995 1.0000 13
## transauto(l5) 0.04700 -0.001754 0.01709 0.1489 33
## classsuv 0.04633 -0.001889 0.01734 0.0144 30
## hwy 0.03967 -0.000441 0.00332 0.0420 20
## manufacturervolkswagen 0.03867 -0.002978 0.02284 0.0000 14
## transauto(s6) 0.02500 0.001813 0.01947 1.0000 37
## manufacturermercury 0.02467 0.000897 0.02880 1.0000 9
## transmanual(m6) 0.02333 0.002655 0.02165 1.0000 39
## manufacturerford 0.01967 0.002586 0.02244 1.0000 3
## transauto(l3) 0.01800 -0.001685 0.03621 0.0000 31
## manufacturerhyundai 0.01600 -0.000732 0.01482 0.0000 5
## fld 0.01267 0.000657 0.01890 1.0000 21
## manufacturerjeep 0.01233 0.001253 0.01878 1.0000 6
## flp 0.01133 0.000213 0.00690 1.0000 23
## transmanual(m5) 0.00933 -0.000418 0.00728 0.0000 38
## classpickup 0.00700 0.000378 0.00817 1.0000 28
## manufacturerlincoln 0.00467 0.000280 0.01592 1.0000 8
## transauto(l6) 0.00000 0.000000 0.00000 NA 34
##
## Mean no. regressors Draws Burnins Time
## "10.7270" "3000" "1000" "0.1537 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "625" "5.5e+11" "1.1e-07" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "0.8248" "234" "random / 19.5" "UIP"
## Shrinkage-Stats
## "Av=0.9957"#summary
BMS_fit2 %>% summary()## Mean no. regressors Draws Burnins Time
## "10.7270" "3000" "1000" "0.1537 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "625" "5.5e+11" "1.1e-07" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "0.8248" "234" "random / 19.5" "UIP"
## Shrinkage-Stats
## "Av=0.9957"#default plots
BMS_fit2 %>% plot()
#coefs
BMS_fit2 %>% coef()## PIP Post Mean Post SD Cond.Pos.Sign Idx
## manufacturerchevrolet 1.00000 0.483059 0.10120 1.0000 1
## cyl 1.00000 0.558532 0.02499 1.0000 16
## drvr 1.00000 0.439126 0.10019 1.0000 18
## classcompact 1.00000 -0.593211 0.10848 0.0000 25
## classmidsize 1.00000 -0.480104 0.12170 0.0000 26
## classsubcompact 1.00000 -0.603914 0.10511 0.0000 29
## manufacturerland rover 0.87867 -0.570335 0.27114 0.0000 7
## manufacturerpontiac 0.79633 0.452436 0.27684 1.0000 11
## drvf 0.67967 -0.160791 0.12689 0.0000 17
## fle 0.35700 -0.117626 0.17739 0.0000 22
## transauto(s4) 0.26100 0.134249 0.25414 1.0000 35
## manufacturerhonda 0.23367 -0.069989 0.14498 0.0000 4
## transauto(s5) 0.23067 0.106832 0.21835 1.0000 36
## manufacturersubaru 0.19633 0.037026 0.09493 1.0000 12
## classminivan 0.18367 -0.055012 0.12873 0.0000 27
## year 0.15067 0.001852 0.00485 1.0000 15
## manufacturernissan 0.09333 0.019610 0.06883 1.0000 10
## transauto(l4) 0.09067 -0.007028 0.02803 0.0000 32
## manufacturerdodge 0.06233 0.004570 0.02755 1.0000 2
## cty 0.05467 -0.000581 0.00401 0.0915 19
## flr 0.05267 -0.000820 0.01444 0.3734 24
## manufacturertoyota 0.05000 0.002604 0.01995 1.0000 13
## transauto(l5) 0.04700 -0.001754 0.01709 0.1489 33
## classsuv 0.04633 -0.001889 0.01734 0.0144 30
## hwy 0.03967 -0.000441 0.00332 0.0420 20
## manufacturervolkswagen 0.03867 -0.002978 0.02284 0.0000 14
## transauto(s6) 0.02500 0.001813 0.01947 1.0000 37
## manufacturermercury 0.02467 0.000897 0.02880 1.0000 9
## transmanual(m6) 0.02333 0.002655 0.02165 1.0000 39
## manufacturerford 0.01967 0.002586 0.02244 1.0000 3
## transauto(l3) 0.01800 -0.001685 0.03621 0.0000 31
## manufacturerhyundai 0.01600 -0.000732 0.01482 0.0000 5
## fld 0.01267 0.000657 0.01890 1.0000 21
## manufacturerjeep 0.01233 0.001253 0.01878 1.0000 6
## flp 0.01133 0.000213 0.00690 1.0000 23
## transmanual(m5) 0.00933 -0.000418 0.00728 0.0000 38
## classpickup 0.00700 0.000378 0.00817 1.0000 28
## manufacturerlincoln 0.00467 0.000280 0.01592 1.0000 8
## transauto(l6) 0.00000 0.000000 0.00000 NA 34BAS
#fit
BAS_fit = BAS::bas.lm(model_form, data = mpg)
#print
BAS_fit##
## Call:
## BAS::bas.lm(formula = model_form, data = mpg)
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept manufacturerchevrolet manufacturerdodge
## 1.0000 0.9991 0.0318
## manufacturerford manufacturerhonda manufacturerhyundai
## 0.0319 0.1631 0.0260
## manufacturerjeep manufacturerland rover manufacturerlincoln
## 0.0231 0.9265 0.0209
## manufacturermercury manufacturernissan manufacturerpontiac
## 0.0204 0.1149 0.7963
## manufacturersubaru manufacturertoyota manufacturervolkswagen
## 0.0507 0.0238 0.0308
## year cyl drvf
## 0.2018 1.0000 0.7243
## drvr cty hwy
## 0.9967 0.0437 0.0387
## fld fle flp
## 0.0232 0.3303 0.0257
## flr classcompact classmidsize
## 0.0245 1.0000 0.9983
## classminivan classpickup classsubcompact
## 0.1808 0.0242 1.0000
## classsuv transauto(l3) transauto(l4)
## 0.0283 0.0222 0.0491
## transauto(l5) transauto(l6) transauto(s4)
## 0.0243 0.0214 0.2517
## transauto(s5) transauto(s6) transmanual(m5)
## 0.2187 0.0287 0.0313
## transmanual(m6)
## 0.0399#summary
BAS_fit %>% summary()## P(B != 0 | Y) model 1 model 2 model 3 model 4
## Intercept 1.0000 1.0000 1.0000 1.0000 1.0000
## manufacturerchevrolet 0.9991 1.0000 1.0000 1.0000 1.0000
## manufacturerdodge 0.0318 0.0000 0.0000 0.0000 0.0000
## manufacturerford 0.0319 0.0000 0.0000 0.0000 0.0000
## manufacturerhonda 0.1631 0.0000 0.0000 0.0000 0.0000
## manufacturerhyundai 0.0260 0.0000 0.0000 0.0000 0.0000
## manufacturerjeep 0.0231 0.0000 0.0000 0.0000 0.0000
## manufacturerland rover 0.9265 1.0000 1.0000 1.0000 1.0000
## manufacturerlincoln 0.0209 0.0000 0.0000 0.0000 0.0000
## manufacturermercury 0.0204 0.0000 0.0000 0.0000 0.0000
## manufacturernissan 0.1149 0.0000 0.0000 0.0000 0.0000
## manufacturerpontiac 0.7963 1.0000 1.0000 1.0000 1.0000
## manufacturersubaru 0.0507 0.0000 0.0000 0.0000 0.0000
## manufacturertoyota 0.0238 0.0000 0.0000 0.0000 0.0000
## manufacturervolkswagen 0.0308 0.0000 0.0000 0.0000 0.0000
## year 0.2018 0.0000 0.0000 0.0000 1.0000
## cyl 1.0000 1.0000 1.0000 1.0000 1.0000
## drvf 0.7243 1.0000 1.0000 1.0000 1.0000
## drvr 0.9967 1.0000 1.0000 1.0000 1.0000
## cty 0.0437 0.0000 0.0000 0.0000 0.0000
## hwy 0.0387 0.0000 0.0000 0.0000 0.0000
## fld 0.0232 0.0000 0.0000 0.0000 0.0000
## fle 0.3303 0.0000 0.0000 1.0000 1.0000
## flp 0.0257 0.0000 0.0000 0.0000 0.0000
## flr 0.0245 0.0000 0.0000 0.0000 0.0000
## classcompact 1.0000 1.0000 1.0000 1.0000 1.0000
## classmidsize 0.9983 1.0000 1.0000 1.0000 1.0000
## classminivan 0.1808 0.0000 0.0000 0.0000 0.0000
## classpickup 0.0242 0.0000 0.0000 0.0000 0.0000
## classsubcompact 1.0000 1.0000 1.0000 1.0000 1.0000
## classsuv 0.0283 0.0000 0.0000 0.0000 0.0000
## transauto(l3) 0.0222 0.0000 0.0000 0.0000 0.0000
## transauto(l4) 0.0491 0.0000 0.0000 0.0000 0.0000
## transauto(l5) 0.0243 0.0000 0.0000 0.0000 0.0000
## transauto(l6) 0.0214 0.0000 0.0000 0.0000 0.0000
## transauto(s4) 0.2517 0.0000 0.0000 0.0000 0.0000
## transauto(s5) 0.2187 0.0000 1.0000 0.0000 0.0000
## transauto(s6) 0.0287 0.0000 0.0000 0.0000 0.0000
## transmanual(m5) 0.0313 0.0000 0.0000 0.0000 0.0000
## transmanual(m6) 0.0399 0.0000 0.0000 0.0000 0.0000
## BF NA 0.6936 0.6563 0.6395 1.0000
## PostProbs NA 0.0907 0.0286 0.0279 0.0165
## R2 NA 0.9323 0.9340 0.9340 0.9359
## dim NA 10.0000 11.0000 11.0000 12.0000
## logmarg NA 281.2686 281.2134 281.1873 281.6344
## model 5
## Intercept 1.0000
## manufacturerchevrolet 1.0000
## manufacturerdodge 0.0000
## manufacturerford 0.0000
## manufacturerhonda 0.0000
## manufacturerhyundai 0.0000
## manufacturerjeep 0.0000
## manufacturerland rover 1.0000
## manufacturerlincoln 0.0000
## manufacturermercury 0.0000
## manufacturernissan 0.0000
## manufacturerpontiac 1.0000
## manufacturersubaru 0.0000
## manufacturertoyota 0.0000
## manufacturervolkswagen 0.0000
## year 1.0000
## cyl 1.0000
## drvf 1.0000
## drvr 1.0000
## cty 0.0000
## hwy 0.0000
## fld 0.0000
## fle 0.0000
## flp 0.0000
## flr 0.0000
## classcompact 1.0000
## classmidsize 1.0000
## classminivan 0.0000
## classpickup 0.0000
## classsubcompact 1.0000
## classsuv 0.0000
## transauto(l3) 0.0000
## transauto(l4) 0.0000
## transauto(l5) 0.0000
## transauto(l6) 0.0000
## transauto(s4) 0.0000
## transauto(s5) 0.0000
## transauto(s6) 0.0000
## transmanual(m5) 0.0000
## transmanual(m6) 0.0000
## BF 0.3528
## PostProbs 0.0154
## R2 0.9336
## dim 11.0000
## logmarg 280.5926#default plots
BAS_fit %>% plot()
#coefs
BAS_fit %>% coef()##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 524288 models
## post mean post SD post p(B != 0)
## Intercept 3.471795 0.022403 1.000000
## manufacturerchevrolet 0.480615 0.100959 0.999117
## manufacturerdodge 0.002324 0.020977 0.031846
## manufacturerford 0.002740 0.022423 0.031863
## manufacturerhonda -0.048674 0.124861 0.163073
## manufacturerhyundai -0.001701 0.022057 0.026037
## manufacturerjeep 0.001505 0.022050 0.023064
## manufacturerland rover -0.601233 0.241350 0.926543
## manufacturerlincoln 0.000669 0.033285 0.020947
## manufacturermercury 0.000268 0.025317 0.020372
## manufacturernissan 0.022457 0.071530 0.114919
## manufacturerpontiac 0.455230 0.277301 0.796308
## manufacturersubaru 0.008221 0.046696 0.050725
## manufacturertoyota 0.000834 0.012177 0.023765
## manufacturervolkswagen -0.002075 0.019748 0.030761
## year 0.002386 0.005333 0.201832
## cyl 0.556705 0.023859 1.000000
## drvf -0.174740 0.124634 0.724319
## drvr 0.436080 0.103187 0.996738
## cty -0.000662 0.004280 0.043691
## hwy -0.000408 0.003236 0.038680
## fld 0.001761 0.029961 0.023196
## fle -0.110006 0.175106 0.330327
## flp 0.001042 0.014124 0.025651
## flr 0.000393 0.012094 0.024467
## classcompact -0.588832 0.109251 0.999993
## classmidsize -0.475386 0.120403 0.998326
## classminivan -0.054624 0.130719 0.180804
## classpickup 0.000600 0.018764 0.024160
## classsubcompact -0.604796 0.107325 0.999983
## classsuv -0.001766 0.019723 0.028289
## transauto(l3) -0.002265 0.040481 0.022186
## transauto(l4) -0.003506 0.019951 0.049053
## transauto(l5) -0.000811 0.012120 0.024271
## transauto(l6) -0.000596 0.023202 0.021391
## transauto(s4) 0.133088 0.257093 0.251730
## transauto(s5) 0.099927 0.211357 0.218744
## transauto(s6) 0.002164 0.021304 0.028654
## transmanual(m5) -0.001708 0.014458 0.031325
## transmanual(m6) 0.003844 0.025464 0.039860