Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="3">Model</td><td class="align_center" colspan="4">LPML</td></tr><tr class="thead"><td class="align_center" colspan="2">  BAY I  </td><td class="align_center" colspan="2"> BAY II </td></tr><tr class="thead"><td class="align_center"> Mean </td><td class="align_center"> SD </td><td class="align_center"> Mean </td><td class="align_center"> SD </td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left"><span style="width: 18.6024ptpx;"><svg height="10.0062pt" id="M390" style="vertical-align:-0.04980946pt" version="1.1" viewbox="-0.0498162 -9.95639 18.6024 10.0062" width="18.6024pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="985" vert-adv-y="985"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.807,-5.741)"><path d="M546 97L529 123C499 91 459 65 450 65C443 65 439 73 445 106C468 226 496 341 523 451H513L436 424C423 357 412 311 403 276C356 195 245 59 190 59C165 59 158 99 166 135L236 445L227 451L152 428L60 18C43 -58 24 -145 24 -183C24 -237 43 -257 66 -257C96 -257 123 -236 130 -224L129 -216C115 -205 96 -156 96 -102C96 -57 105 -7 113 26H115C127 -1 137 -12 158 -12S198 -5 230 19C284 60 332 117 385 186H387C381 154 378 142 370 107C347 1 367 -12 388 -12C422 -12 492 32 546 97Z" id="g50-234"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="564" vert-adv-y="564"></glyph.data></g></svg></span></td><td class="align_center"> −253.0577 </td><td class="align_center"> 60.7693 </td><td class="align_center"> −274.9704 </td><td class="align_center"> 14.7176 </td></tr><tr><td class="align_left"><span style="width: 17.3693ptpx;"><svg height="10.0062pt" id="M391" style="vertical-align:-0.04980946pt" version="1.1" viewbox="-0.0498162 -9.95639 17.3693 10.0062" width="17.3693pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="985" vert-adv-y="985"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.807,-5.741)"><path d="M405 401C405 425 369 451 305 451C246 451 170 419 123 380C63 330 24 254 24 171C24 46 87 -12 184 -12C256 -12 327 30 380 85L362 111C308 67 260 48 213 48C148 48 112 99 112 190V211L316 205L325 257L116 251C135 342 192 405 254 405C291 405 324 389 347 357C355 346 365 344 379 355C396 368 405 387 405 401Z" id="g50-227"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="429" vert-adv-y="429"></glyph.data></g></svg></span></td><td class="align_center"> −176.5289 </td><td class="align_center"> 110.0227 </td><td class="align_center"> −188.8361 </td><td class="align_center"> 175.3741 </td></tr><tr><td class="align_left"><span style="width: 22.5209ptpx;"><svg height="10.0062pt" id="M392" style="vertical-align:-0.04980946pt" version="1.1" viewbox="-0.0498162 -9.95639 22.5209 10.0062" width="22.5209pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="985" vert-adv-y="985"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.807,-5.741)"><path d="M546 97L529 123C499 91 459 65 450 65C443 65 439 73 445 106C468 226 496 341 523 451H513L436 424C423 357 412 311 403 276C356 195 245 59 190 59C165 59 158 99 166 135L236 445L227 451L152 428L60 18C43 -58 24 -145 24 -183C24 -237 43 -257 66 -257C96 -257 123 -236 130 -224L129 -216C115 -205 96 -156 96 -102C96 -57 105 -7 113 26H115C127 -1 137 -12 158 -12S198 -5 230 19C284 60 332 117 385 186H387C381 154 378 142 370 107C347 1 367 -12 388 -12C422 -12 492 32 546 97Z" id="g50-234"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="564" vert-adv-y="564"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.94,-5.741)"><path d="M405 401C405 425 369 451 305 451C246 451 170 419 123 380C63 330 24 254 24 171C24 46 87 -12 184 -12C256 -12 327 30 380 85L362 111C308 67 260 48 213 48C148 48 112 99 112 190V211L316 205L325 257L116 251C135 342 192 405 254 405C291 405 324 389 347 357C355 346 365 344 379 355C396 368 405 387 405 401Z" id="g50-227"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="429" vert-adv-y="429"></glyph.data></g></svg></span></td><td class="align_center"> −193.2270 </td><td class="align_center"> 81.3209 </td><td class="align_center"> −209.0063 </td><td class="align_center"> 77.0664 </td></tr><tr><td class="align_left"><span style="width: 23.8636ptpx;"><svg height="12.0797pt" id="M393" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -12.0298 23.8636 12.0797" width="23.8636pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="985" vert-adv-y="985"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.807,-5.741)"><path d="M546 97L529 123C499 91 459 65 450 65C443 65 439 73 445 106C468 226 496 341 523 451H513L436 424C423 357 412 311 403 276C356 195 245 59 190 59C165 59 158 99 166 135L236 445L227 451L152 428L60 18C43 -58 24 -145 24 -183C24 -237 43 -257 66 -257C96 -257 123 -236 130 -224L129 -216C115 -205 96 -156 96 -102C96 -57 105 -7 113 26H115C127 -1 137 -12 158 -12S198 -5 230 19C284 60 332 117 385 186H387C381 154 378 142 370 107C347 1 367 -12 388 -12C422 -12 492 32 546 97Z" id="g50-234"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="564" vert-adv-y="564"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.94,-5.741)"><path d="M552 243C552 372 474 431 385 468C378 471 378 492 382 510L419 675L401 683L345 637L224 54C173 71 118 128 118 218C118 323 174 382 270 423L255 458C130 420 24 339 24 204C24 97 93 14 213 -8L188 -131C170 -220 197 -250 217 -257L224 -254L278 -7C427 -3 552 98 552 243ZM478 228C478 124 408 37 287 40L363 405C401 395 478 336 478 228Z" id="g50-243"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="576" vert-adv-y="576"></glyph.data></g></svg></span></td><td class="align_center"> −235.7465 </td><td class="align_center"> 15.3588 </td><td class="align_center"> −235.7465 </td><td class="align_center"> 11.6911 </td></tr><tr><td class="align_left"><span style="width: 22.6305ptpx;"><svg height="12.0797pt" id="M394" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -12.0298 22.6305 12.0797" width="22.6305pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="985" vert-adv-y="985"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.807,-5.741)"><path d="M405 401C405 425 369 451 305 451C246 451 170 419 123 380C63 330 24 254 24 171C24 46 87 -12 184 -12C256 -12 327 30 380 85L362 111C308 67 260 48 213 48C148 48 112 99 112 190V211L316 205L325 257L116 251C135 342 192 405 254 405C291 405 324 389 347 357C355 346 365 344 379 355C396 368 405 387 405 401Z" id="g50-227"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="429" vert-adv-y="429"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,16.712,-5.741)"><path d="M552 243C552 372 474 431 385 468C378 471 378 492 382 510L419 675L401 683L345 637L224 54C173 71 118 128 118 218C118 323 174 382 270 423L255 458C130 420 24 339 24 204C24 97 93 14 213 -8L188 -131C170 -220 197 -250 217 -257L224 -254L278 -7C427 -3 552 98 552 243ZM478 228C478 124 408 37 287 40L363 405C401 395 478 336 478 228Z" id="g50-243"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="576" vert-adv-y="576"></glyph.data></g></svg></span></td><td class="align_center"> −267.4536 </td><td class="align_center"> 10.2084 </td><td class="align_center"> −271.2875 </td><td class="align_center"> 10.4206 </td></tr><tr><td class="align_left"><span style="width: 27.7821ptpx;"><svg height="12.0797pt" id="M395" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -12.0298 27.7821 12.0797" width="27.7821pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="985" vert-adv-y="985"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.807,-5.741)"><path d="M546 97L529 123C499 91 459 65 450 65C443 65 439 73 445 106C468 226 496 341 523 451H513L436 424C423 357 412 311 403 276C356 195 245 59 190 59C165 59 158 99 166 135L236 445L227 451L152 428L60 18C43 -58 24 -145 24 -183C24 -237 43 -257 66 -257C96 -257 123 -236 130 -224L129 -216C115 -205 96 -156 96 -102C96 -57 105 -7 113 26H115C127 -1 137 -12 158 -12S198 -5 230 19C284 60 332 117 385 186H387C381 154 378 142 370 107C347 1 367 -12 388 -12C422 -12 492 32 546 97Z" id="g50-234"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="564" vert-adv-y="564"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.94,-5.741)"><path d="M405 401C405 425 369 451 305 451C246 451 170 419 123 380C63 330 24 254 24 171C24 46 87 -12 184 -12C256 -12 327 30 380 85L362 111C308 67 260 48 213 48C148 48 112 99 112 190V211L316 205L325 257L116 251C135 342 192 405 254 405C291 405 324 389 347 357C355 346 365 344 379 355C396 368 405 387 405 401Z" id="g50-227"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="429" vert-adv-y="429"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,21.845,-5.741)"><path d="M552 243C552 372 474 431 385 468C378 471 378 492 382 510L419 675L401 683L345 637L224 54C173 71 118 128 118 218C118 323 174 382 270 423L255 458C130 420 24 339 24 204C24 97 93 14 213 -8L188 -131C170 -220 197 -250 217 -257L224 -254L278 -7C427 -3 552 98 552 243ZM478 228C478 124 408 37 287 40L363 405C401 395 478 336 478 228Z" id="g50-243"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="576" vert-adv-y="576"></glyph.data></g></svg></span></td><td class="align_center"> −255.2335 </td><td class="align_center"> 27.2208 </td><td class="align_center"> −258.7124 </td><td class="align_center"> 15.8416 </td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mean and standard deviation (SD) of LPML in the political and economic risk data.

Journal of Applied Mathematics

tab3

Table 3

Table 3: Assessing Heterogeneity for Factor Analysis Model with Continuous and Ordinal Outcomes 