Multiplicative component description of origin-destination migration flow tables
Source:R/multi_comp.R
multi_comp.RdMultiplicative component descriptions of n-dimension flow tables based on total reference coding system.
Value
matrix or array of multiplicative components of m. When output is an array the total for each table of origin-destination flows is used.
References
Rogers, A., Willekens, F., Little, J., & Raymer, J. (2002). Describing migration spatial structure. Papers in Regional Science, 81(1), 29–48. https://doi.org/10.1007/s101100100090
Raymer, J., Bonaguidi, A., & Valentini, A. (2006). Describing and projecting the age and spatial structures of interregional migration in Italy. Population, Space and Place, 12(5), 371–388. https://doi.org/10.1002/psp.414
Examples
r <- LETTERS[1:4]
m0 <- matrix(data = c(0, 100, 30, 70, 50, 0, 45, 5, 60, 35, 0, 40, 20, 25, 20, 0),
nrow = 4, ncol = 4, byrow = TRUE, dimnames = list(orig = r, dest = r))
addmargins(m0)
#> dest
#> orig A B C D Sum
#> A 0 100 30 70 200
#> B 50 0 45 5 100
#> C 60 35 0 40 135
#> D 20 25 20 0 65
#> Sum 130 160 95 115 500
multi_comp(m = m0)
#> dest
#> orig A B C D Sum
#> A 0.0000000 1.5625000 0.7894737 1.5217391 0.4000000
#> B 1.9230769 0.0000000 2.3684211 0.2173913 0.2000000
#> C 1.7094017 0.8101852 0.0000000 1.2882448 0.2700000
#> D 1.1834320 1.2019231 1.6194332 0.0000000 0.1300000
#> Sum 0.2600000 0.3200000 0.1900000 0.2300000 500.0000000
# data frame
library(dplyr)
italy_area %>%
filter(year == 2000) %>%
multi_comp() %>%
round(digits = 3)
#> , , age_grp = 0-4
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.401 0.859 0.909 2.370 0.010
#> Islands 0.970 0.000 1.181 1.513 0.681 0.012
#> North-East 1.053 1.916 0.000 1.179 2.501 0.010
#> North-West 0.877 2.490 0.887 0.000 2.023 0.014
#> South 1.409 0.531 1.184 1.102 0.000 0.025
#> Sum 0.016 0.007 0.017 0.018 0.014 0.072
#>
#> , , age_grp = 5-9
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.589 0.779 0.762 2.243 0.007
#> Islands 1.166 0.000 1.393 1.707 0.562 0.010
#> North-East 0.840 1.932 0.000 0.936 2.085 0.006
#> North-West 0.877 2.714 0.844 0.000 1.963 0.010
#> South 1.387 0.507 1.283 1.151 0.000 0.018
#> Sum 0.011 0.005 0.012 0.012 0.009 0.050
#>
#> , , age_grp = 10-14
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.570 0.738 0.667 1.978 0.005
#> Islands 1.333 0.000 1.572 1.791 0.463 0.008
#> North-East 0.861 1.834 0.000 0.840 1.805 0.004
#> North-West 0.793 2.694 0.826 0.000 1.959 0.007
#> South 1.424 0.411 1.332 1.226 0.000 0.014
#> Sum 0.009 0.004 0.010 0.009 0.006 0.037
#>
#> , , age_grp = 15-19
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.358 0.732 0.668 1.673 0.005
#> Islands 1.261 0.000 1.617 2.109 0.417 0.009
#> North-East 0.677 1.769 0.000 0.847 1.697 0.004
#> North-West 0.629 2.606 0.818 0.000 1.803 0.007
#> South 1.449 0.347 1.449 1.340 0.000 0.016
#> Sum 0.009 0.004 0.011 0.011 0.006 0.041
#>
#> , , age_grp = 20-24
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.044 0.852 0.759 1.552 0.014
#> Islands 0.983 0.000 1.490 1.948 0.436 0.025
#> North-East 0.593 1.530 0.000 0.852 1.808 0.012
#> North-West 0.533 1.880 0.726 0.000 1.449 0.018
#> South 1.419 0.425 1.788 1.624 0.000 0.055
#> Sum 0.025 0.009 0.036 0.037 0.017 0.124
#>
#> , , age_grp = 25-29
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.092 0.992 0.939 2.093 0.027
#> Islands 0.915 0.000 1.221 1.599 0.544 0.034
#> North-East 0.910 1.420 0.000 1.161 1.829 0.023
#> North-West 0.795 1.652 0.947 0.000 1.719 0.034
#> South 1.473 0.482 1.457 1.373 0.000 0.079
#> Sum 0.044 0.014 0.053 0.054 0.032 0.197
#>
#> , , age_grp = 30-34
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.211 1.088 1.159 2.136 0.025
#> Islands 0.915 0.000 1.053 1.390 0.526 0.025
#> North-East 1.143 1.384 0.000 1.362 1.837 0.021
#> North-West 0.945 1.857 1.091 0.000 1.756 0.031
#> South 1.544 0.445 1.205 1.244 0.000 0.059
#> Sum 0.039 0.012 0.040 0.043 0.027 0.160
#>
#> , , age_grp = 35-39
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.439 1.175 1.245 2.126 0.016
#> Islands 0.956 0.000 1.073 1.372 0.407 0.015
#> North-East 1.278 1.396 0.000 1.484 1.719 0.013
#> North-West 1.158 2.026 1.229 0.000 1.753 0.020
#> South 1.465 0.424 1.089 1.085 0.000 0.032
#> Sum 0.024 0.008 0.024 0.025 0.015 0.096
#>
#> , , age_grp = 40-44
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.547 1.283 1.266 2.200 0.009
#> Islands 1.001 0.000 1.090 1.445 0.367 0.008
#> North-East 1.322 1.563 0.000 1.417 1.626 0.007
#> North-West 1.234 2.353 1.261 0.000 1.885 0.012
#> South 1.317 0.354 1.044 1.001 0.000 0.017
#> Sum 0.013 0.005 0.014 0.014 0.009 0.054
#>
#> , , age_grp = 45-49
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.638 1.130 1.204 2.331 0.005
#> Islands 1.076 0.000 1.100 1.372 0.400 0.005
#> North-East 1.406 1.701 0.000 1.501 1.607 0.005
#> North-West 1.320 2.600 1.354 0.000 2.007 0.008
#> South 1.286 0.408 0.919 0.912 0.000 0.010
#> Sum 0.008 0.003 0.008 0.008 0.006 0.033
#>
#> , , age_grp = 50-54
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.887 1.064 1.110 2.579 0.005
#> Islands 0.997 0.000 0.861 1.226 0.361 0.004
#> North-East 1.449 1.709 0.000 1.505 1.541 0.004
#> North-West 1.519 3.174 1.595 0.000 2.391 0.008
#> South 1.267 0.366 0.738 0.831 0.000 0.007
#> Sum 0.007 0.003 0.006 0.006 0.005 0.028
#>
#> , , age_grp = 55-59
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 2.263 1.084 1.029 2.894 0.004
#> Islands 0.845 0.000 0.643 1.027 0.343 0.003
#> North-East 1.448 1.641 0.000 1.455 1.391 0.003
#> North-West 1.724 3.929 1.892 0.000 2.921 0.008
#> South 1.160 0.398 0.544 0.722 0.000 0.005
#> Sum 0.006 0.003 0.005 0.005 0.005 0.023
#>
#> , , age_grp = 60-64
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 2.271 1.067 1.084 3.282 0.004
#> Islands 0.767 0.000 0.397 0.933 0.414 0.002
#> North-East 1.331 1.473 0.000 1.578 1.500 0.003
#> North-West 1.633 4.038 1.938 0.000 3.047 0.008
#> South 1.245 0.395 0.444 0.734 0.000 0.005
#> Sum 0.005 0.003 0.004 0.004 0.005 0.022
#>
#> , , age_grp = 65-69
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 2.383 1.159 1.030 3.451 0.003
#> Islands 0.827 0.000 0.435 0.876 0.385 0.002
#> North-East 1.222 1.237 0.000 1.629 1.439 0.002
#> North-West 1.518 3.324 1.891 0.000 2.933 0.005
#> South 1.340 0.479 0.419 0.874 0.000 0.004
#> Sum 0.004 0.002 0.003 0.004 0.004 0.017
#>
#> , , age_grp = 70-74
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 2.409 0.999 1.353 3.269 0.003
#> Islands 0.723 0.000 0.381 1.253 0.385 0.002
#> North-East 1.301 1.200 0.000 1.765 1.113 0.002
#> North-West 1.421 2.608 1.719 0.000 2.445 0.004
#> South 1.451 0.432 0.460 1.065 0.000 0.004
#> Sum 0.004 0.001 0.003 0.004 0.003 0.014
#>
#> , , age_grp = 75-79
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.926 1.174 1.311 2.957 0.003
#> Islands 0.819 0.000 0.352 1.352 0.431 0.002
#> North-East 1.395 0.840 0.000 2.114 0.929 0.002
#> North-West 1.327 2.463 1.810 0.000 1.963 0.003
#> South 1.450 0.437 0.488 1.173 0.000 0.004
#> Sum 0.003 0.001 0.003 0.004 0.002 0.013
#>
#> , , age_grp = 80-84
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.846 1.070 1.503 2.636 0.002
#> Islands 0.804 0.000 0.428 1.295 0.519 0.001
#> North-East 1.466 0.631 0.000 2.117 0.986 0.001
#> North-West 1.232 2.001 1.825 0.000 1.826 0.002
#> South 1.571 0.408 0.493 1.258 0.000 0.003
#> Sum 0.002 0.001 0.002 0.002 0.001 0.008
#>
#> , , age_grp = 85-89
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.545 1.509 1.606 2.575 0.001
#> Islands 0.739 0.000 0.383 1.345 0.414 0.001
#> North-East 1.766 1.254 0.000 2.809 0.913 0.001
#> North-West 1.090 1.667 1.944 0.000 1.395 0.002
#> South 1.410 0.301 0.415 1.240 0.000 0.002
#> Sum 0.002 0.000 0.001 0.002 0.001 0.007
#>
#> , , age_grp = 90-94
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 1.319 1.211 1.906 2.277 0.001
#> Islands 0.809 0.000 0.418 1.033 0.359 0.000
#> North-East 1.469 1.083 0.000 2.835 0.660 0.000
#> North-West 1.494 1.635 2.216 0.000 1.778 0.001
#> South 1.452 0.250 0.387 1.142 0.000 0.001
#> Sum 0.001 0.000 0.001 0.001 0.000 0.003
#>
#> , , age_grp = 95+
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 0.886 1.076 1.504 2.207 0.000
#> Islands 0.847 0.000 0.521 0.835 0.523 0.000
#> North-East 1.383 1.750 0.000 2.340 0.698 0.000
#> North-West 1.707 2.593 2.149 0.000 2.263 0.000
#> South 1.394 0.485 0.523 0.965 0.000 0.000
#> Sum 0.000 0.000 0.000 0.000 0.000 0.001
#>
#> , , age_grp = Sum
#>
#> dest
#> orig Center Islands North-East North-West South Sum
#> Center 0.000 0.017 0.037 0.039 0.054 0.148
#> Islands 0.038 0.000 0.048 0.067 0.013 0.166
#> North-East 0.030 0.016 0.000 0.041 0.037 0.125
#> North-West 0.045 0.037 0.056 0.000 0.063 0.202
#> South 0.120 0.013 0.111 0.115 0.000 0.360
#> Sum 0.233 0.084 0.253 0.263 0.168 277436.000
#>