summary(mod <- rma(yi = g, vi = gvar, method = "REML", test= 't', data = dat, slab = id))
##
## Random-Effects Model (k = 100; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## 71.5281 -143.0562 -139.0562 -133.8659 -138.9312
##
## tau^2 (estimated amount of total heterogeneity): 0.0091 (SE = 0.0020)
## tau (square root of estimated tau^2 value): 0.0956
## I^2 (total heterogeneity / total variability): 69.76%
## H^2 (total variability / sampling variability): 3.31
##
## Test for Heterogeneity:
## Q(df = 99) = 339.2855, p-val < .0001
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## 0.2333 0.0120 19.4898 99 <.0001 0.2096 0.2571 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
predict(mod)
##
## pred se ci.lb ci.ub pi.lb pi.ub
## 0.2333 0.0120 0.2096 0.2571 0.0422 0.4245
influence(mod)
##
## rstudent dffits cook.d cov.r tau2.del QE.del hat weight dfbs inf
## 1 -0.3028 -0.0336 0.0011 1.0232 0.0093 338.7833 0.0126 1.2570 -0.0336
## 2 -0.2222 -0.0247 0.0006 1.0242 0.0093 338.9832 0.0128 1.2821 -0.0247
## 3 -1.5977 -0.1630 0.0262 0.9959 0.0089 331.9820 0.0102 1.0229 -0.1631
## 4 0.2875 0.0189 0.0004 1.0078 0.0092 339.1775 0.0042 0.4199 0.0189
## 5 -0.3061 -0.0311 0.0010 1.0193 0.0093 338.9825 0.0105 1.0493 -0.0311
## 6 0.8269 0.0937 0.0088 1.0165 0.0092 335.8346 0.0126 1.2632 0.0937
## 7 -0.3097 -0.0333 0.0011 1.0217 0.0093 338.8677 0.0118 1.1800 -0.0333
## 8 0.2467 0.0238 0.0006 1.0168 0.0092 339.1541 0.0089 0.8914 0.0238
## 9 -1.8186 -0.1999 0.0389 0.9875 0.0088 326.3470 0.0117 1.1737 -0.1997
## 10 -1.3520 -0.1429 0.0202 1.0027 0.0090 333.1681 0.0110 1.0978 -0.1429
## 11 1.4460 0.1532 0.0232 1.0004 0.0090 332.2210 0.0112 1.1164 0.1531
## 12 -0.4163 -0.0269 0.0007 1.0074 0.0092 339.0422 0.0042 0.4199 -0.0269
## 13 1.1221 0.1252 0.0156 1.0096 0.0091 333.5334 0.0123 1.2319 0.1252
## 14 0.1729 0.0176 0.0003 1.0186 0.0093 339.2146 0.0097 0.9736 0.0176
## 15 0.4308 0.0392 0.0015 1.0143 0.0092 338.9178 0.0081 0.8073 0.0392
## 16 1.3255 0.1194 0.0142 1.0028 0.0091 335.7243 0.0081 0.8106 0.1195
## 17 -1.1765 -0.1260 0.0158 1.0073 0.0091 334.2733 0.0113 1.1303 -0.1260
## 18 -0.9104 -0.0938 0.0088 1.0122 0.0092 336.7148 0.0105 1.0524 -0.0938
## 19 -0.1102 -0.0096 0.0001 1.0156 0.0092 339.2563 0.0081 0.8106 -0.0096
## 20 -0.0834 -0.0089 0.0001 1.0245 0.0093 339.2380 0.0127 1.2711 -0.0089
## 21 0.5705 0.0635 0.0041 1.0198 0.0092 337.8843 0.0121 1.2138 0.0636
## 22 1.7491 0.1690 0.0282 0.9924 0.0089 331.8838 0.0094 0.9387 0.1692
## 23 -1.0558 -0.1174 0.0138 1.0109 0.0091 334.1854 0.0122 1.2189 -0.1174
## 24 2.3599 0.2590 0.0635 0.9646 0.0085 317.0976 0.0120 1.1985 0.2582
## 25 -0.2323 -0.0164 0.0003 1.0095 0.0092 339.2013 0.0051 0.5053 -0.0164
## 26 0.3762 0.0229 0.0005 1.0066 0.0092 339.1071 0.0036 0.3634 0.0229
## 27 -1.0101 -0.1143 0.0131 1.0124 0.0091 333.9155 0.0126 1.2632 -0.1143
## 28 -0.5435 -0.0526 0.0028 1.0155 0.0092 338.5237 0.0094 0.9387 -0.0526
## 29 0.9897 0.1057 0.0112 1.0117 0.0091 335.8706 0.0113 1.1281 0.1057
## 30 -1.9761 -0.2073 0.0418 0.9830 0.0088 327.1644 0.0107 1.0733 -0.2073
## 31 0.1991 0.0230 0.0005 1.0239 0.0093 339.1019 0.0126 1.2599 0.0230
## 32 -0.1286 -0.0110 0.0001 1.0146 0.0092 339.2489 0.0076 0.7644 -0.0110
## 33 0.1000 0.0092 0.0001 1.0149 0.0092 339.2688 0.0078 0.7756 0.0092
## 34 0.9564 0.0748 0.0056 1.0067 0.0091 337.8215 0.0061 0.6066 0.0748
## 35 -0.5613 -0.0620 0.0039 1.0200 0.0092 337.7916 0.0122 1.2217 -0.0620
## 36 1.6362 0.1823 0.0325 0.9941 0.0089 327.2250 0.0123 1.2313 0.1820
## 37 0.8477 0.0936 0.0088 1.0153 0.0092 336.2746 0.0120 1.2016 0.0936
## 38 0.3679 0.0365 0.0013 1.0172 0.0092 338.9570 0.0095 0.9523 0.0365
## 39 0.9555 0.0707 0.0050 1.0060 0.0091 337.9130 0.0054 0.5434 0.0707
## 40 -0.2806 -0.0259 0.0007 1.0161 0.0092 339.0979 0.0087 0.8665 -0.0259
## 41 -0.4386 -0.0466 0.0022 1.0199 0.0092 338.5461 0.0114 1.1380 -0.0466
## 42 -0.6528 -0.0729 0.0054 1.0190 0.0092 337.1367 0.0124 1.2441 -0.0729
## 43 0.5242 0.0596 0.0036 1.0212 0.0092 337.9144 0.0126 1.2626 0.0596
## 44 -0.4244 -0.0463 0.0022 1.0211 0.0093 338.4721 0.0120 1.2001 -0.0463
## 45 -0.9094 -0.0635 0.0040 1.0056 0.0091 338.0740 0.0049 0.4852 -0.0635
## 46 2.4977 0.2815 0.0740 0.9560 0.0084 310.3010 0.0125 1.2548 0.2800
## 47 -0.8032 -0.0909 0.0083 1.0169 0.0092 335.7420 0.0127 1.2727 -0.0910
## 48 -0.0241 -0.0021 0.0000 1.0228 0.0093 339.2806 0.0118 1.1826 -0.0021
## 49 -0.3364 -0.0323 0.0011 1.0170 0.0092 338.9895 0.0093 0.9340 -0.0323
## 50 -1.5033 -0.1654 0.0269 0.9984 0.0090 330.1090 0.0118 1.1826 -0.1653
## 51 0.6379 0.0722 0.0052 1.0196 0.0092 337.2960 0.0125 1.2548 0.0722
## 52 1.0777 0.1131 0.0128 1.0095 0.0091 335.5506 0.0109 1.0912 0.1131
## 53 0.1942 0.0199 0.0004 1.0190 0.0093 339.1910 0.0100 0.9993 0.0199
## 54 -0.4993 -0.0519 0.0027 1.0184 0.0092 338.4456 0.0108 1.0818 -0.0519
## 55 -0.1996 -0.0212 0.0005 1.0221 0.0093 339.1124 0.0117 1.1654 -0.0212
## 56 -1.1990 -0.1028 0.0105 1.0044 0.0091 336.5791 0.0073 0.7290 -0.1028
## 57 0.4634 0.0404 0.0016 1.0129 0.0092 338.8926 0.0074 0.7412 0.0403
## 58 -0.4714 -0.0410 0.0017 1.0130 0.0092 338.8410 0.0076 0.7568 -0.0409
## 59 0.0230 0.0023 0.0000 1.0136 0.0092 339.2851 0.0070 0.7036 0.0023
## 60 -0.4356 -0.0423 0.0018 1.0166 0.0092 338.7842 0.0095 0.9478 -0.0423
## 61 1.1420 0.1187 0.0141 1.0080 0.0091 335.2572 0.0107 1.0719 0.1187
## 62 0.4178 0.0468 0.0022 1.0216 0.0093 338.5352 0.0122 1.2174 0.0468
## 63 2.2901 0.2530 0.0608 0.9675 0.0085 317.4737 0.0121 1.2131 0.2523
## 64 0.1037 0.0107 0.0001 1.0187 0.0093 339.2619 0.0097 0.9736 0.0107
## 65 -0.1956 -0.0208 0.0004 1.0222 0.0093 339.1173 0.0117 1.1691 -0.0208
## 66 -0.6196 -0.0666 0.0045 1.0181 0.0092 337.7801 0.0115 1.1526 -0.0666
## 67 0.4754 0.0545 0.0030 1.0221 0.0093 338.0843 0.0128 1.2821 0.0546
## 68 -0.4721 -0.0364 0.0013 1.0102 0.0092 338.9154 0.0060 0.5957 -0.0364
## 69 0.3026 0.0347 0.0012 1.0234 0.0093 338.8366 0.0127 1.2659 0.0347
## 70 -0.9094 -0.0820 0.0067 1.0094 0.0092 337.5547 0.0081 0.8073 -0.0820
## 71 0.6685 0.0736 0.0054 1.0181 0.0092 337.4839 0.0119 1.1886 0.0736
## 72 -0.0447 -0.0042 0.0000 1.0210 0.0093 339.2757 0.0109 1.0899 -0.0042
## 73 -1.0165 -0.0672 0.0045 1.0042 0.0091 337.8421 0.0044 0.4351 -0.0672
## 74 0.8166 0.0774 0.0060 1.0117 0.0092 337.7881 0.0089 0.8860 0.0774
## 75 0.2928 0.0270 0.0007 1.0152 0.0092 339.1158 0.0082 0.8205 0.0270
## 76 -1.2271 -0.1319 0.0173 1.0061 0.0091 333.7591 0.0114 1.1369 -0.1319
## 77 -0.3497 -0.0365 0.0013 1.0201 0.0093 338.8440 0.0111 1.1054 -0.0365
## 78 -1.1951 -0.1364 0.0185 1.0078 0.0091 331.4288 0.0128 1.2787 -0.1363
## 79 -0.6197 -0.0553 0.0031 1.0125 0.0092 338.4876 0.0079 0.7935 -0.0552
## 80 0.3204 0.0359 0.0013 1.0223 0.0093 338.8606 0.0121 1.2093 0.0359
## 81 0.7850 0.0604 0.0036 1.0080 0.0092 338.3233 0.0058 0.5846 0.0603
## 82 0.5357 0.0538 0.0029 1.0165 0.0092 338.5379 0.0099 0.9858 0.0538
## 83 0.3739 0.0401 0.0016 1.0201 0.0093 338.8274 0.0111 1.1116 0.0401
## 84 -0.2384 -0.0244 0.0006 1.0201 0.0093 339.0901 0.0107 1.0704 -0.0244
## 85 -2.9570 -0.3390 0.1043 0.9316 0.0081 301.9409 0.0123 1.2319 -0.3368 *
## 86 0.8130 0.0890 0.0080 1.0157 0.0092 336.6725 0.0118 1.1800 0.0890
## 87 0.7190 0.0539 0.0029 1.0081 0.0092 338.5022 0.0056 0.5555 0.0539
## 88 0.3583 0.0210 0.0004 1.0061 0.0092 339.1271 0.0034 0.3375 0.0210
## 89 -0.7509 -0.0483 0.0023 1.0058 0.0092 338.5099 0.0041 0.4122 -0.0483
## 90 0.1142 0.0101 0.0001 1.0140 0.0092 339.2644 0.0073 0.7290 0.0101
## 91 1.1744 0.1314 0.0172 1.0083 0.0091 332.8763 0.0124 1.2378 0.1313
## 92 -1.1172 -0.1188 0.0141 1.0086 0.0091 334.9070 0.0112 1.1152 -0.1188
## 93 0.3632 0.0413 0.0017 1.0227 0.0093 338.6570 0.0125 1.2536 0.0414
## 94 2.5864 0.2816 0.0743 0.9543 0.0084 314.0590 0.0118 1.1818 0.2807
## 95 -1.2490 -0.1353 0.0182 1.0057 0.0091 333.3324 0.0115 1.1537 -0.1353
## 96 0.7834 0.0707 0.0050 1.0111 0.0092 338.0558 0.0080 0.8039 0.0707
## 97 -0.4675 -0.0522 0.0028 1.0217 0.0093 338.1161 0.0126 1.2576 -0.0523
## 98 -0.9850 -0.0697 0.0049 1.0051 0.0091 337.8482 0.0050 0.4987 -0.0697
## 99 -1.1453 -0.1310 0.0171 1.0092 0.0091 331.8642 0.0129 1.2859 -0.1310
## 100 -0.2611 -0.0279 0.0008 1.0218 0.0093 338.9954 0.0117 1.1663 -0.0279
dat %>%
mutate(g_excl = case_when(id == 85~ NA_real_,
TRUE~ g)) -> dat
summary(mod2<-rma(yi = g_excl, vi = gvar, mod=~college_deg_perc, method = "REML", test = 't', data = dat, slab = id))
## Warning: 1 study with NAs omitted from model fitting.
##
## Mixed-Effects Model (k = 99; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## 73.8086 -147.6172 -141.6172 -133.8931 -141.3592
##
## tau^2 (estimated amount of residual heterogeneity): 0.0080 (SE = 0.0018)
## tau (square root of estimated tau^2 value): 0.0896
## I^2 (residual heterogeneity / unaccounted variability): 66.75%
## H^2 (unaccounted variability / sampling variability): 3.01
## R^2 (amount of heterogeneity accounted for): 0.51%
##
## Test for Residual Heterogeneity:
## QE(df = 97) = 297.9967, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 97) = 1.4054, p-val = 0.2387
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.2637 0.0251 10.4933 97 <.0001 0.2138 0.3135 ***
## college_deg_perc -0.0005 0.0004 -1.1855 97 0.2387 -0.0014 0.0003
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
predict(mod2, 81)
##
## pred se ci.lb ci.ub pi.lb pi.ub
## 0.2221 0.0172 0.1880 0.2562 0.0411 0.4031
summary(mod<-rma(yi = g_excl, vi = gvar, mod=~us_dc, method = "REML",test = 't',data = dat, slab = id))
## Warning: 1 study with NAs omitted from model fitting.
##
## Mixed-Effects Model (k = 99; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## 77.6641 -155.3282 -149.3282 -141.6040 -149.0701
##
## tau^2 (estimated amount of residual heterogeneity): 0.0071 (SE = 0.0017)
## tau (square root of estimated tau^2 value): 0.0842
## I^2 (residual heterogeneity / unaccounted variability): 63.96%
## H^2 (unaccounted variability / sampling variability): 2.77
## R^2 (amount of heterogeneity accounted for): 12.08%
##
## Test for Residual Heterogeneity:
## QE(df = 97) = 271.3003, p-val < .0001
##
## Test of Moderators (coefficient 2):
## F(df1 = 1, df2 = 97) = 9.5415, p-val = 0.0026
##
## Model Results:
##
## estimate se tval df pval ci.lb ci.ub
## intrcpt 0.2037 0.0155 13.1193 97 <.0001 0.1729 0.2345 ***
## us_dc 0.0685 0.0222 3.0889 97 0.0026 0.0245 0.1125 **
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1