Simulated household survey data for the rural area of Ipixuna (Para state, Brazil), used to illustrate spatial item factor analysis. Ten binary items, a household-level `wealth` covariate, and spatial coordinates are simulated for each household so that they reproduce the spatial multidimensional item response structure described in the SPIFA paper (Chacón-Montalván, E. A., Giorgi, E. and Taylor, B.). The data is provided as an `sf` object, already in the format [spifa()] requires.
Format
An `sf` tibble with one row per household (100 rows) and columns:
- id
Household identifier.
- wealth
A simulated household-level covariate.
- items
A 100x10 binary (0/1) matrix of responses to the food insecurity items.
- geometry
An `sfc_POINT` geometry column with the household's spatial coordinates (longitude/latitude), concentrated towards the town centre.
It has an attribute `"parameters"` holding the true generating parameters used in the simulation (`easiness`, `discrimination`, `abilities` (the true latent factor scores, useful for checking recovery), `effect`, `resid_params` (list with `sd` and `corr`, the residual covariance of the latent factors), `mgp_params` (list with `sd` and `phi`, the spatial Gaussian process hyperparameters)), which is convenient for specifying sensible restrictions and checking recovery of the model in examples and tests.
Source
Simulated; see `data-raw/ipixuna.R` for the generating code and `attr(ipixuna, "parameters")` for the generating values.
Examples
data(ipixuna)
head(dplyr::select(ipixuna, -geometry, -items))
#> Simple feature collection with 6 features and 2 fields
#> Geometry type: POINT
#> Dimension: XY
#> Bounding box: xmin: -71.69689 ymin: -7.053396 xmax: -71.68464 ymax: -7.039144
#> Geodetic CRS: WGS 84
#> id wealth geometry
#> 1 1 -0.57212306 POINT (-71.69689 -7.052244)
#> 2 2 -0.92003870 POINT (-71.68695 -7.039144)
#> 3 3 1.23197630 POINT (-71.68732 -7.047609)
#> 4 4 0.30801774 POINT (-71.69005 -7.047915)
#> 5 5 -0.06247617 POINT (-71.68464 -7.053396)
#> 6 6 2.05414943 POINT (-71.69039 -7.042424)
attr(ipixuna, "parameters")
#> $easiness
#> [1] -0.68 -0.51 -0.34 -0.17 0.00 0.17 0.34 0.51 0.68 0.85
#>
#> $discrimination
#> [,1] [,2] [,3]
#> [1,] 0.7710143 1.4157676 -0.6627994
#> [2,] 0.6514647 0.8364208 -0.9059919
#> [3,] 0.5964618 0.8002601 -0.7571054
#> [4,] 0.0000000 0.0000000 -0.7796418
#> [5,] 1.2853150 0.0000000 0.0000000
#> [6,] 1.2939590 0.0000000 0.0000000
#> [7,] 0.8592413 0.0000000 -0.8146235
#> [8,] 0.0000000 0.0000000 -1.2927663
#> [9,] 0.8178851 0.5583285 -1.0271718
#> [10,] 1.0611414 0.0000000 -1.0957406
#>
#> $abilities
#> [,1] [,2] [,3]
#> [1,] 1.413937686 -0.58630664 -0.099680412
#> [2,] 0.825838022 -0.21059611 0.137576011
#> [3,] -1.613061355 2.14781644 -1.243780538
#> [4,] -0.909450634 -0.77918567 1.625438500
#> [5,] 0.844097357 0.59970303 -0.323414313
#> [6,] -2.173470537 2.57771735 1.994219323
#> [7,] -0.988924572 2.45060279 1.987676155
#> [8,] -0.494843192 0.59132100 -0.320485344
#> [9,] -1.902606808 -0.30671683 3.176979588
#> [10,] -0.360730328 -0.26273279 -0.466240900
#> [11,] 1.967469500 0.38917856 -0.118396784
#> [12,] 0.421618650 -1.76187566 1.971123718
#> [13,] 0.332748862 -0.07098196 -0.062163121
#> [14,] -2.283288977 0.57391384 0.715845686
#> [15,] 0.043860268 -2.51772905 -0.190498289
#> [16,] -1.228577498 0.90843476 0.692119242
#> [17,] -0.771693279 0.21622179 -1.141685834
#> [18,] 1.616756579 -0.26885817 -0.312126825
#> [19,] -0.174411654 1.91846090 1.561171689
#> [20,] -0.091206637 -0.17156453 -0.008979438
#> [21,] -1.984407478 2.05220590 1.369499102
#> [22,] -2.034301799 0.32382785 -0.015490794
#> [23,] -0.957084021 0.45090802 0.485592007
#> [24,] -0.836882975 0.62433677 1.403573107
#> [25,] -0.235888098 -0.30238993 1.249903906
#> [26,] 0.044055223 0.84153054 0.614536665
#> [27,] -0.072975283 -0.67719460 -0.989601582
#> [28,] 2.420591416 0.33460738 0.680392412
#> [29,] 0.779507146 -0.01234442 -2.227501501
#> [30,] -2.558946613 0.93491846 0.308082274
#> [31,] -1.191976792 0.77346318 1.050358462
#> [32,] 0.505425850 -0.13646312 0.167258074
#> [33,] 0.947986823 -0.76638061 -0.605123260
#> [34,] -1.563727823 2.26745363 0.036681509
#> [35,] 0.338358346 -1.41609014 -0.793270495
#> [36,] 0.801990550 -0.44738631 1.106656379
#> [37,] -0.985468744 0.99900889 0.396691336
#> [38,] 1.102751075 -0.64574353 -0.961350233
#> [39,] 0.702186217 -0.30465745 0.095445680
#> [40,] 0.663920882 0.27600212 0.407843523
#> [41,] 0.627803093 0.02411670 -0.622977623
#> [42,] -0.331617656 -0.34851372 -0.198818159
#> [43,] 0.729089158 0.83461336 0.940577091
#> [44,] 0.388600873 -0.73525184 -1.678718792
#> [45,] -1.017943927 0.23195958 0.564862600
#> [46,] -0.516638907 0.87213290 1.159091282
#> [47,] -1.154145062 2.22516373 1.860037779
#> [48,] -0.234474259 1.14827578 -0.318132649
#> [49,] -0.186013414 2.34935103 -0.392492801
#> [50,] -0.562896081 1.79438231 -0.808784683
#> [51,] -0.368482133 -0.11881173 -0.184340598
#> [52,] 1.489123975 -2.33735910 0.699117379
#> [53,] -0.052130778 0.25588417 0.071721244
#> [54,] -0.019499361 -0.40603183 1.174548212
#> [55,] -0.393761128 0.20454726 0.289681210
#> [56,] 0.614305694 -0.74571834 0.410975107
#> [57,] 2.250432473 -0.02550603 -0.729580515
#> [58,] 0.035283471 -0.84799443 -0.819100036
#> [59,] -1.339325999 1.45521555 1.233771607
#> [60,] -0.518471854 2.33241486 0.083248958
#> [61,] 0.750815158 -0.79875157 0.205978616
#> [62,] -0.267665676 0.50603271 1.095057859
#> [63,] 1.356065817 -0.87680234 -0.885404723
#> [64,] -0.791093903 -0.98957530 0.740405441
#> [65,] 0.812668704 -0.80362833 0.943549050
#> [66,] 0.440684694 -0.42080421 0.113016472
#> [67,] 0.420529536 -2.01342919 0.534553278
#> [68,] -0.508242237 -0.62049188 0.329240871
#> [69,] -0.286478751 0.03845402 0.537745189
#> [70,] 0.673381143 -1.22438103 -0.764710970
#> [71,] -0.525773296 0.39415276 0.580757280
#> [72,] -1.294128605 -0.28837051 -1.397742986
#> [73,] 0.905226220 -0.61760218 -0.775381535
#> [74,] -0.414610645 0.68992586 -0.831918592
#> [75,] -0.585447124 1.03238136 -0.916838740
#> [76,] 1.633428370 -0.31050016 -0.019800554
#> [77,] -1.050774756 0.82522834 -0.400192576
#> [78,] -1.245920491 0.35229530 -0.732854980
#> [79,] -0.524879112 -0.71255004 0.529651366
#> [80,] -2.028793501 0.70602706 0.322998774
#> [81,] 0.331070884 0.65218734 -0.467477392
#> [82,] -0.452619756 0.20333906 0.028217576
#> [83,] 1.276824051 -1.17938702 -0.142587786
#> [84,] 0.184666441 -0.04542801 -0.996224834
#> [85,] -0.355574342 0.75164560 1.432361951
#> [86,] -0.626201884 0.80568678 1.131327334
#> [87,] 0.465730561 1.21604730 0.134522036
#> [88,] -0.200864854 1.24956891 1.684438318
#> [89,] -0.831041095 1.13483275 -0.292074609
#> [90,] 0.665478458 0.17036962 0.230913983
#> [91,] 0.693940960 -0.98713137 -0.283678233
#> [92,] -0.427737470 0.62573016 0.245238010
#> [93,] -0.083122268 -0.21320860 0.316618448
#> [94,] -0.622176708 0.96391516 -0.214383194
#> [95,] 2.135480495 -1.91108928 -1.470825524
#> [96,] 0.594385094 0.96408760 -0.048860640
#> [97,] -0.004708989 0.13547504 -0.073482387
#> [98,] 0.745414286 -1.03483989 0.025587836
#> [99,] 1.050802462 -1.22459103 0.199521938
#> [100,] -1.009598273 0.36162423 0.630423289
#>
#> $effect
#> [1] -0.7 0.7 0.3
#>
#> $resid_params
#> $resid_params$sd
#> [1] 0.4472136 0.5477226 0.4472136
#>
#> $resid_params$corr
#> [1] -0.7 0.1 -0.1
#>
#>
#> $mgp_params
#> $mgp_params$sd
#> [1] 0.6324555 0.5477226 0.7071068
#>
#> $mgp_params$phi
#> [1] 100 150 250
#>
#>