diff --git a/docs/articles/a1_bayesdfa.html b/docs/articles/a1_bayesdfa.html index 45dcec4..e218d08 100644 --- a/docs/articles/a1_bayesdfa.html +++ b/docs/articles/a1_bayesdfa.html @@ -34,7 +34,7 @@
@@ -607,7 +607,7 @@lmer
or glmmTMB
, we allow
weights to be used in DFA models. Weights are currently only used for
Gaussian reponses and when data is in long format. Specifically, the
-weights are included by modifying each variance to be \[(sigma^2) / w_i\]. As a concrete example,
+weights are included by modifying each variance to be \[\sigma^2 / w_i\]. As a concrete example,
we’ll simulate a dataset, add some examples of standard errors on the
survey indices, and then perform the DFA.
Our simulated standard errors are the same for all surveys – except @@ -622,12 +622,18 @@
Next we can generate the weights (this is redundant, and “se” could -be used instead in the function call below)
+be used instead in the function call below). Because the weights are +used as an offset, \[\sigma^2 / w_i\], +we don’t want to use the SE alone as a weight but make them inversely +related to the SE. As a quick note, the scale of these may affect +estimation and some additional normalization may be needed (rather than +standard errors, it may be more helpful to think about the sample size +each data point represents).
-df$weights <- df$se
df$weights <- (1 / df$se)^2
And fit the model with the weights argument
f2 <- fit_dfa(
@@ -638,8 +644,8 @@ DFA model with weights##
## SAMPLING FOR MODEL 'dfa' NOW (CHAIN 1).
## Chain 1:
-## Chain 1: Gradient evaluation took 4.9e-05 seconds
-## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.49 seconds.
+## Chain 1: Gradient evaluation took 5e-05 seconds
+## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.5 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1:
## Chain 1:
@@ -656,9 +662,9 @@ DFA model with weights## Chain 1: Iteration: 450 / 500 [ 90%] (Sampling)
## Chain 1: Iteration: 500 / 500 [100%] (Sampling)
## Chain 1:
-## Chain 1: Elapsed Time: 12.3963 seconds (Warm-up)
-## Chain 1: 3.3721 seconds (Sampling)
-## Chain 1: 15.7684 seconds (Total)
+## Chain 1: Elapsed Time: 120.552 seconds (Warm-up)
+## Chain 1: 22.6953 seconds (Sampling)
+## Chain 1: 143.247 seconds (Total)
## Chain 1:
## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
@@ -668,139 +674,139 @@ DFA model with weights## https://mc-stan.org/misc/warnings.html#tail-ess
## Inference for the input samples (1 chains: each with iter = 250; warmup = 125):
##
-## Q5 Q50 Q95 Mean SD Rhat Bulk_ESS Tail_ESS
-## x[1,1] 0.1 0.4 0.6 0.3 0.2 1.00 99 73
-## x[2,1] 1.1 1.6 2.2 1.6 0.3 1.00 97 41
-## x[1,2] 0.6 1.1 1.5 1.1 0.3 1.01 92 61
-## x[2,2] 0.7 1.4 2.1 1.4 0.5 0.99 65 102
-## x[1,3] -0.9 -0.5 -0.1 -0.5 0.2 1.00 124 66
-## x[2,3] 0.6 1.1 1.9 1.2 0.4 1.00 119 108
-## x[1,4] -1.9 -1.3 -0.9 -1.4 0.3 1.04 43 30
-## x[2,4] 1.4 2.2 3.1 2.2 0.5 1.00 145 146
-## x[1,5] -0.5 0.0 0.3 0.0 0.2 1.05 110 97
-## x[2,5] 0.9 1.4 2.3 1.5 0.4 1.03 177 70
-## x[1,6] -1.9 -1.4 -0.9 -1.4 0.3 1.02 48 38
-## x[2,6] 0.1 0.8 1.5 0.8 0.4 1.00 71 77
-## x[1,7] -0.8 -0.4 -0.2 -0.4 0.2 1.00 138 81
-## x[2,7] -0.5 0.0 0.4 -0.1 0.3 1.00 138 86
-## x[1,8] -0.5 -0.2 0.0 -0.2 0.2 0.99 132 85
-## x[2,8] -1.0 -0.4 0.0 -0.5 0.3 0.99 151 121
-## x[1,9] 0.6 0.9 1.3 1.0 0.2 1.01 75 56
-## x[2,9] -2.1 -1.3 -0.6 -1.3 0.5 1.02 121 134
-## x[1,10] 0.3 0.6 1.0 0.6 0.2 1.03 87 34
-## x[2,10] -3.4 -2.6 -1.8 -2.6 0.5 1.00 86 78
-## x[1,11] 0.5 0.9 1.4 0.9 0.3 1.03 50 68
-## x[2,11] -3.8 -2.8 -1.9 -2.8 0.6 1.00 100 106
-## x[1,12] -0.5 -0.2 0.1 -0.2 0.2 1.00 189 103
-## x[2,12] -2.8 -1.8 -1.2 -1.9 0.5 1.01 118 95
-## x[1,13] -1.8 -1.2 -0.8 -1.2 0.3 1.02 42 81
-## x[2,13] -1.3 -0.6 0.1 -0.6 0.4 1.02 85 89
-## x[1,14] -2.1 -1.5 -1.1 -1.5 0.3 1.03 39 63
-## x[2,14] -1.4 -0.5 0.0 -0.6 0.4 0.99 67 86
-## x[1,15] -1.2 -0.8 -0.4 -0.8 0.2 1.00 62 68
-## x[2,15] -1.4 -0.8 -0.2 -0.8 0.4 1.00 63 52
-## x[1,16] 0.7 1.1 1.5 1.1 0.3 1.05 55 74
-## x[2,16] -0.3 0.2 0.7 0.2 0.3 1.00 95 61
-## x[1,17] 0.3 0.6 0.9 0.6 0.2 1.02 62 25
-## x[2,17] -0.6 -0.2 0.2 -0.2 0.3 1.01 132 138
-## x[1,18] 0.2 0.5 0.8 0.5 0.2 1.01 144 84
-## x[2,18] -0.2 0.2 0.8 0.3 0.3 1.01 104 104
-## x[1,19] 0.3 0.6 1.0 0.6 0.2 1.01 82 74
-## x[2,19] 0.6 1.1 1.7 1.1 0.3 1.00 86 100
-## x[1,20] 0.6 0.9 1.4 1.0 0.2 1.04 37 52
-## x[2,20] 0.9 1.5 2.2 1.5 0.4 1.01 70 86
-## Z[1,1] -1.5 -1.1 -0.7 -1.1 0.2 1.04 33 38
-## Z[2,1] -0.9 0.2 1.3 0.2 0.6 1.00 260 68
-## Z[3,1] -0.5 -0.2 0.1 -0.2 0.2 0.99 58 71
-## Z[4,1] 0.6 0.8 1.1 0.8 0.2 1.03 35 84
-## Z[1,2] 0.0 0.0 0.0 0.0 0.0 1.00 125 125
-## Z[2,2] 0.0 0.6 1.1 0.6 0.3 1.00 111 66
-## Z[3,2] 0.5 0.7 0.9 0.7 0.1 1.01 64 28
-## Z[4,2] -0.6 -0.4 -0.3 -0.4 0.1 1.02 65 81
-## log_lik[1] -0.5 0.5 0.9 0.4 0.7 1.01 42 38
-## log_lik[2] -1.9 -1.7 -1.4 -1.7 0.1 1.02 49 100
-## log_lik[3] -1.1 0.5 1.0 0.2 0.7 0.99 87 81
-## log_lik[4] -0.4 0.6 0.9 0.5 0.4 1.02 120 103
-## log_lik[5] -1.3 0.2 0.5 0.0 0.6 1.02 52 61
-## log_lik[6] -2.1 -1.7 -1.5 -1.7 0.2 1.01 56 105
-## log_lik[7] -1.0 0.4 0.7 0.2 0.5 1.02 53 101
-## log_lik[8] -1.4 0.3 0.6 0.1 0.6 1.00 93 133
-## log_lik[9] -3.7 -0.6 0.4 -1.0 1.3 1.00 128 60
-## log_lik[10] -1.9 -1.6 -1.5 -1.7 0.1 1.04 38 69
-## log_lik[11] -1.8 0.2 0.6 -0.1 0.8 1.00 185 108
-## log_lik[12] -4.8 -1.7 0.0 -1.9 1.6 1.01 64 134
-## log_lik[13] -1.6 0.3 0.8 0.0 0.8 1.00 128 85
-## log_lik[14] -2.5 -1.8 -1.5 -1.8 0.3 1.00 63 50
-## log_lik[15] -1.6 0.5 1.0 0.2 0.9 1.00 105 85
-## log_lik[16] -4.5 -0.9 0.6 -1.3 1.7 1.01 163 106
-## log_lik[17] -2.1 0.3 0.7 -0.1 1.0 1.01 100 82
-## log_lik[18] -1.9 -1.7 -1.5 -1.7 0.1 1.03 55 86
-## log_lik[19] -0.5 0.3 0.6 0.2 0.4 1.06 22 26
-## log_lik[20] -0.1 0.8 1.0 0.7 0.3 1.08 13 130
-## log_lik[21] -1.2 0.3 0.7 0.0 0.8 1.02 55 70
-## log_lik[22] -2.1 -1.7 -1.5 -1.7 0.2 1.02 28 69
-## log_lik[23] -0.7 0.5 0.9 0.4 0.5 1.02 54 44
-## log_lik[24] -0.6 0.7 0.9 0.5 0.5 1.03 55 62
-## log_lik[25] -0.9 0.4 0.8 0.2 0.6 1.01 71 45
-## log_lik[26] -1.9 -1.6 -1.5 -1.7 0.1 1.08 13 107
-## log_lik[27] -0.5 0.6 1.0 0.5 0.5 1.02 105 134
-## log_lik[28] -0.1 0.7 0.9 0.5 0.4 1.01 68 69
-## log_lik[29] -0.7 0.5 0.7 0.3 0.5 0.99 106 106
-## log_lik[30] -1.9 -1.7 -1.5 -1.7 0.1 1.08 17 70
-## log_lik[31] -0.6 0.2 0.5 0.1 0.4 1.03 58 48
-## log_lik[32] -0.9 0.5 1.0 0.4 0.5 1.01 106 82
-## log_lik[33] -3.3 0.3 0.9 -0.2 1.3 1.01 69 80
-## log_lik[34] -2.0 -1.7 -1.5 -1.7 0.2 1.01 38 69
-## log_lik[35] -2.5 -0.1 0.5 -0.4 1.1 1.08 201 104
-## log_lik[36] -4.0 -0.7 0.4 -1.1 1.4 0.99 223 134
-## log_lik[37] -1.4 0.5 0.8 0.2 0.7 1.00 106 141
-## log_lik[38] -2.1 -1.7 -1.5 -1.7 0.2 1.01 51 81
-## log_lik[39] -0.7 0.5 0.9 0.4 0.6 1.02 71 72
-## log_lik[40] -1.1 0.1 0.6 0.0 0.6 1.00 192 89
-## log_lik[41] -0.8 0.5 0.8 0.3 0.6 1.00 163 105
-## log_lik[42] -2.1 -1.7 -1.5 -1.8 0.2 1.01 47 85
-## log_lik[43] -0.9 0.7 1.0 0.4 0.6 1.05 38 104
-## log_lik[44] -1.7 0.1 0.6 -0.2 0.8 1.01 159 103
-## log_lik[45] -0.7 0.4 0.7 0.3 0.5 1.04 89 131
-## log_lik[46] -2.0 -1.7 -1.5 -1.7 0.2 1.03 58 83
-## log_lik[47] -1.1 0.2 0.6 0.0 0.6 1.02 123 62
-## log_lik[48] -0.5 0.6 0.9 0.4 0.5 1.00 91 69
-## log_lik[49] -1.2 0.4 0.8 0.2 0.7 1.01 58 60
-## log_lik[50] -2.0 -1.7 -1.5 -1.7 0.2 1.03 33 61
-## log_lik[51] -0.8 0.4 0.7 0.3 0.6 1.01 85 81
-## log_lik[52] -0.9 0.5 0.9 0.3 0.7 1.01 149 86
-## log_lik[53] -0.9 0.4 0.9 0.2 0.6 1.00 85 79
-## log_lik[54] -2.0 -1.7 -1.5 -1.7 0.2 1.01 33 76
-## log_lik[55] -0.6 0.6 1.0 0.4 0.6 1.02 83 108
-## log_lik[56] -0.6 0.5 0.8 0.4 0.5 1.01 91 85
-## log_lik[57] -1.4 0.1 0.5 -0.1 0.7 1.07 35 81
-## log_lik[58] -2.0 -1.7 -1.5 -1.7 0.1 1.02 44 134
-## log_lik[59] -0.8 0.4 0.8 0.3 0.5 1.03 80 78
-## log_lik[60] -0.5 0.3 0.6 0.2 0.3 1.02 54 83
-## log_lik[61] -5.7 -1.2 0.5 -1.8 1.9 0.99 195 90
-## log_lik[62] -2.1 -1.7 -1.5 -1.7 0.2 1.02 51 58
-## log_lik[63] -1.3 0.4 0.8 0.1 0.8 1.02 177 101
-## log_lik[64] -6.5 -2.3 -0.2 -2.5 1.9 1.00 89 103
-## log_lik[65] -0.7 0.4 0.7 0.2 0.4 1.03 73 108
-## log_lik[66] -1.9 -1.6 -1.4 -1.6 0.1 1.07 20 70
-## log_lik[67] -0.3 0.6 0.9 0.4 0.4 1.02 119 126
-## log_lik[68] -0.1 0.7 1.0 0.6 0.4 1.05 31 51
-## log_lik[69] -0.9 0.4 0.8 0.3 0.6 1.00 116 72
-## log_lik[70] -1.9 -1.7 -1.5 -1.7 0.1 1.07 19 81
-## log_lik[71] -0.4 0.5 0.8 0.4 0.4 1.08 60 104
-## log_lik[72] -0.9 0.4 0.7 0.2 0.5 1.01 70 71
-## log_lik[73] -0.8 0.4 0.8 0.2 0.5 1.07 17 43
-## log_lik[74] -1.9 -1.7 -1.5 -1.7 0.1 1.05 34 85
-## log_lik[75] -0.6 0.7 1.0 0.5 0.5 1.01 90 85
-## log_lik[76] -0.2 0.4 0.6 0.3 0.3 1.06 69 97
-## log_lik[77] -1.4 0.6 0.9 0.3 0.9 1.03 70 99
-## log_lik[78] -2.1 -1.7 -1.5 -1.7 0.2 1.01 66 137
-## log_lik[79] -1.5 0.5 1.0 0.2 1.0 1.01 99 83
-## log_lik[80] -2.3 -0.4 0.5 -0.6 0.9 1.00 164 108
-## xstar[1,1] -0.5 1.1 2.7 1.1 1.0 0.99 110 108
-## xstar[2,1] 0.1 1.6 3.4 1.6 1.1 1.01 125 135
-## sigma[1] 0.1 0.1 0.1 0.1 0.0 1.09 12 84
-## lp__ -41.0 -24.3 -13.7 -25.9 9.0 1.19 5 60
+## Q5 Q50 Q95 Mean SD Rhat Bulk_ESS Tail_ESS
+## x[1,1] -1.1 -0.4 0.2 -0.4 0.4 1.02 95 47
+## x[2,1] -2.5 -2.0 -1.3 -1.9 0.3 1.05 21 45
+## x[1,2] -1.7 -1.2 -0.8 -1.2 0.3 1.00 103 85
+## x[2,2] -2.9 -2.2 -1.3 -2.2 0.5 1.05 24 80
+## x[1,3] 0.2 0.6 0.9 0.6 0.2 1.00 226 145
+## x[2,3] -1.6 -1.1 -0.8 -1.1 0.3 1.05 22 67
+## x[1,4] 1.1 1.6 2.4 1.7 0.4 1.00 81 117
+## x[2,4] -2.1 -1.3 -0.6 -1.3 0.5 1.00 25 25
+## x[1,5] 0.0 0.4 0.9 0.4 0.3 1.00 103 103
+## x[2,5] -1.1 -0.8 -0.5 -0.8 0.2 1.01 27 39
+## x[1,6] 0.9 1.4 1.9 1.4 0.3 1.00 100 143
+## x[2,6] -1.6 -1.0 -0.3 -1.0 0.4 1.00 24 38
+## x[1,7] 0.2 0.7 1.1 0.7 0.3 1.00 186 39
+## x[2,7] 0.1 0.6 0.8 0.5 0.2 1.01 36 119
+## x[1,8] -0.1 0.4 0.9 0.4 0.3 1.00 157 81
+## x[2,8] 0.8 1.3 1.6 1.2 0.2 1.06 23 36
+## x[1,9] -1.2 -0.8 -0.2 -0.7 0.3 0.99 178 131
+## x[2,9] 1.2 1.6 2.3 1.7 0.4 1.06 19 81
+## x[1,10] -1.6 -0.9 -0.4 -1.0 0.4 1.00 74 108
+## x[2,10] 1.6 2.3 3.1 2.3 0.5 1.03 22 50
+## x[1,11] -1.7 -1.1 -0.7 -1.2 0.3 1.00 137 106
+## x[2,11] 1.8 2.6 3.5 2.6 0.5 1.05 20 40
+## x[1,12] -0.7 -0.2 0.3 -0.2 0.3 1.00 171 136
+## x[2,12] 0.8 1.2 1.6 1.2 0.2 1.04 28 37
+## x[1,13] 0.6 1.0 1.6 1.1 0.3 1.00 141 106
+## x[2,13] 0.1 0.6 1.0 0.5 0.3 1.00 27 104
+## x[1,14] 0.9 1.4 2.0 1.4 0.4 1.01 67 94
+## x[2,14] 0.0 0.7 1.3 0.7 0.4 1.00 26 53
+## x[1,15] 0.6 1.1 1.5 1.1 0.3 1.02 56 57
+## x[2,15] 1.1 1.8 2.3 1.7 0.4 1.03 23 32
+## x[1,16] -1.1 -0.7 -0.3 -0.7 0.3 1.01 95 108
+## x[2,16] 0.4 0.7 1.2 0.8 0.3 1.01 21 39
+## x[1,17] -1.1 -0.7 -0.2 -0.7 0.3 1.00 174 84
+## x[2,17] -0.3 0.0 0.4 0.1 0.2 0.99 32 59
+## x[1,18] -1.2 -0.8 -0.3 -0.8 0.3 1.00 127 96
+## x[2,18] -1.4 -1.0 -0.5 -1.0 0.3 1.02 26 63
+## x[1,19] -1.2 -0.7 -0.4 -0.8 0.3 1.02 110 78
+## x[2,19] -2.1 -1.6 -1.0 -1.6 0.4 1.02 26 69
+## x[1,20] -1.8 -1.2 -0.7 -1.2 0.4 1.00 83 131
+## x[2,20] -3.1 -2.3 -1.5 -2.3 0.5 1.03 24 69
+## Z[1,1] 0.6 0.9 1.2 0.9 0.2 1.00 48 80
+## Z[2,1] -0.4 -0.1 0.1 -0.1 0.2 1.00 25 36
+## Z[3,1] 0.1 0.3 0.6 0.3 0.2 1.00 51 85
+## Z[4,1] -1.1 -0.8 -0.6 -0.8 0.2 1.03 75 94
+## Z[1,2] 0.0 0.0 0.0 0.0 0.0 1.00 125 125
+## Z[2,2] -0.9 -0.6 -0.5 -0.7 0.1 1.06 20 36
+## Z[3,2] -0.8 -0.6 -0.4 -0.6 0.1 1.02 29 52
+## Z[4,2] 0.2 0.3 0.6 0.3 0.1 1.02 47 50
+## log_lik[1] -1.1 -0.2 0.0 -0.3 0.4 1.00 80 106
+## log_lik[2] 0.5 2.3 2.7 2.0 0.7 1.01 78 106
+## log_lik[3] -0.6 -0.3 -0.1 -0.3 0.2 1.00 107 138
+## log_lik[4] -1.3 -0.2 0.1 -0.3 0.5 0.99 90 132
+## log_lik[5] -0.9 0.2 0.4 0.0 0.4 0.99 108 104
+## log_lik[6] 0.2 2.2 2.7 1.9 1.0 0.99 80 82
+## log_lik[7] -0.5 0.0 0.3 0.0 0.3 1.00 116 108
+## log_lik[8] -0.8 0.1 0.4 0.0 0.4 1.01 77 96
+## log_lik[9] -3.1 -0.7 0.2 -1.0 1.1 1.00 149 108
+## log_lik[10] 0.9 2.3 2.7 2.1 0.6 1.00 64 74
+## log_lik[11] -0.3 0.0 0.2 0.0 0.2 1.02 94 85
+## log_lik[12] -2.7 -0.8 0.1 -1.0 1.0 1.00 146 60
+## log_lik[13] -1.4 -0.2 0.1 -0.4 0.6 1.00 134 108
+## log_lik[14] 0.5 2.3 2.7 2.0 0.8 1.00 106 62
+## log_lik[15] -0.8 -0.3 -0.1 -0.4 0.2 1.00 100 85
+## log_lik[16] -3.0 -0.9 -0.1 -1.2 1.1 0.99 101 108
+## log_lik[17] -3.0 -0.9 0.1 -1.1 0.9 1.00 95 127
+## log_lik[18] 0.6 2.2 2.7 2.0 0.7 1.02 88 85
+## log_lik[19] -1.5 -0.4 0.2 -0.5 0.5 0.99 88 144
+## log_lik[20] -0.6 -0.3 -0.1 -0.3 0.2 1.00 104 101
+## log_lik[21] -2.9 -0.6 0.1 -0.8 0.9 1.02 103 47
+## log_lik[22] 0.0 2.3 2.6 2.0 0.8 1.00 101 83
+## log_lik[23] -0.8 -0.3 0.0 -0.3 0.3 1.00 126 108
+## log_lik[24] -0.7 -0.3 0.0 -0.3 0.3 1.00 82 106
+## log_lik[25] -1.0 -0.2 0.1 -0.3 0.4 1.00 149 83
+## log_lik[26] 1.0 2.4 2.6 2.1 0.7 1.00 67 108
+## log_lik[27] -0.5 -0.2 -0.1 -0.3 0.1 0.99 103 71
+## log_lik[28] -0.7 -0.2 0.0 -0.3 0.3 1.00 110 99
+## log_lik[29] -1.1 -0.1 0.2 -0.2 0.6 1.00 126 85
+## log_lik[30] 1.0 2.3 2.6 2.0 0.6 1.00 77 64
+## log_lik[31] -1.1 -0.1 0.4 -0.2 0.5 0.99 111 83
+## log_lik[32] -0.9 -0.3 0.0 -0.3 0.3 1.00 79 78
+## log_lik[33] -2.4 -0.8 -0.2 -1.1 0.8 0.99 230 127
+## log_lik[34] 0.8 2.3 2.6 2.1 0.6 1.00 192 119
+## log_lik[35] -0.3 0.2 0.4 0.1 0.2 1.04 98 106
+## log_lik[36] -1.4 -0.1 0.2 -0.3 0.6 1.02 188 106
+## log_lik[37] -2.1 -0.3 0.0 -0.6 0.7 1.01 165 101
+## log_lik[38] 1.3 2.4 2.6 2.2 0.5 1.00 108 70
+## log_lik[39] -0.5 -0.1 0.1 -0.2 0.2 1.02 107 101
+## log_lik[40] -1.8 -0.1 0.3 -0.4 0.7 0.99 81 86
+## log_lik[41] -1.3 -0.2 0.1 -0.4 0.4 1.00 89 131
+## log_lik[42] 0.6 2.3 2.7 2.1 0.6 1.00 116 131
+## log_lik[43] -0.6 -0.3 0.0 -0.3 0.2 0.99 83 104
+## log_lik[44] -2.4 -0.4 0.3 -0.7 0.9 1.00 114 98
+## log_lik[45] -2.2 -0.5 0.1 -0.7 0.9 1.00 204 134
+## log_lik[46] 1.0 2.3 2.6 2.1 0.7 1.01 89 106
+## log_lik[47] -3.2 -1.6 -0.2 -1.6 0.9 1.00 133 108
+## log_lik[48] -0.7 -0.2 0.0 -0.3 0.2 0.99 114 108
+## log_lik[49] -1.4 -0.3 0.1 -0.4 0.5 1.00 119 96
+## log_lik[50] -0.2 2.3 2.6 1.9 1.0 0.99 107 70
+## log_lik[51] -1.3 -0.1 0.1 -0.3 0.5 1.00 112 105
+## log_lik[52] -0.9 -0.3 0.0 -0.4 0.3 1.00 169 106
+## log_lik[53] -1.9 -0.7 -0.1 -0.8 0.7 1.00 80 96
+## log_lik[54] 0.6 2.3 2.6 2.0 0.7 1.00 81 98
+## log_lik[55] -0.6 -0.3 -0.1 -0.3 0.2 1.00 125 102
+## log_lik[56] -1.1 -0.2 0.1 -0.3 0.4 1.01 89 119
+## log_lik[57] -0.6 0.2 0.4 0.1 0.4 1.01 132 101
+## log_lik[58] 0.8 2.3 2.7 2.0 0.7 1.00 76 51
+## log_lik[59] -0.6 -0.1 0.2 -0.1 0.2 1.01 89 106
+## log_lik[60] -0.6 0.2 0.4 0.1 0.3 1.01 82 127
+## log_lik[61] -6.5 -3.2 -0.9 -3.5 1.8 1.00 117 136
+## log_lik[62] 0.8 2.3 2.6 2.1 0.7 1.00 109 142
+## log_lik[63] -1.6 -0.7 -0.3 -0.8 0.5 1.02 96 112
+## log_lik[64] -2.5 -0.8 -0.1 -1.0 0.9 1.06 99 130
+## log_lik[65] -0.5 0.1 0.3 0.0 0.3 1.00 93 84
+## log_lik[66] 0.8 2.3 2.6 2.1 0.6 1.02 98 85
+## log_lik[67] -0.3 -0.1 0.1 -0.1 0.1 1.01 107 86
+## log_lik[68] -0.6 -0.2 0.0 -0.2 0.2 0.99 94 85
+## log_lik[69] -1.5 -0.3 0.0 -0.4 0.5 0.99 110 139
+## log_lik[70] 1.3 2.3 2.6 2.2 0.5 1.01 94 106
+## log_lik[71] -0.6 -0.1 0.1 -0.2 0.2 1.00 129 108
+## log_lik[72] -0.9 0.0 0.2 -0.2 0.4 0.99 89 102
+## log_lik[73] -0.6 -0.1 0.2 -0.1 0.3 1.01 107 106
+## log_lik[74] 0.9 2.3 2.6 2.1 0.6 0.99 59 81
+## log_lik[75] -0.5 -0.2 -0.1 -0.2 0.1 1.00 88 134
+## log_lik[76] -0.6 0.2 0.4 0.0 0.4 0.99 102 108
+## log_lik[77] -0.9 -0.2 0.0 -0.3 0.4 1.00 115 101
+## log_lik[78] 1.1 2.3 2.7 2.1 0.5 1.00 64 95
+## log_lik[79] -0.5 -0.3 -0.1 -0.3 0.2 0.99 122 102
+## log_lik[80] -1.1 -0.1 0.2 -0.2 0.5 1.02 122 101
+## xstar[1,1] -2.7 -1.3 0.5 -1.3 1.0 1.02 117 69
+## xstar[2,1] -3.9 -2.1 -0.4 -2.1 1.1 0.99 88 108
+## sigma[1] 0.7 0.8 0.9 0.8 0.1 0.99 107 108
+## lp__ 11.6 23.8 33.2 22.8 6.7 1.01 26 29
##
## For each parameter, Bulk_ESS and Tail_ESS are crude measures of
## effective sample size for bulk and tail quantities respectively (an ESS > 100
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