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Microsimulation model projecting small area populations using contextual variables: An application to the Montreal metropolitan area, 2006–2031

  1. Guillaume Marois  Is a corresponding author
  2. Alain Bélanger  Is a corresponding author
  1. INRS – Centre Urbanisation Culture Société, Canada
Research article
Volume 7(1) Spring 2014
Cite this article as: G. Marois, A. Bélanger; 2014; Microsimulation model projecting small area populations using contextual variables: An application to the Montreal metropolitan area, 2006–2031; International Journal of Microsimulation; 7(1); 158-193. doi: 10.34196/ijm.00097
3 figures and 10 tables

Figures

Figure 1
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The central municipality of the MMC and municipalities included in the suburb.
Figure 2
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Projected population growth rates by municipality, MMC, 2006 to 2031.
Figure 3
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Projected growth of the population aged 65 and over by municipality, MMC, 2006 to 2031.

Tables

Table 1
Summary of events.
Events Population at risk Outcome Independent variables
Age Sex Place of birth Number of years since arrival Age at immigra-tion RCM Munici-pality Type of municipality Language spoken at home
Death Everyone If the event occurs, the individual is removed from the simulation. Otherwise, time variables (age, duration of residence for immigrants) are incremented by one x x x x
Fertility Women aged between 15 and 49 years old A new individual is added to the simulation. Child characteristics are determined in the birth module x x x x x
International emigration Everyone, except births of the year The individual is removed from the simulation x x
Interprovincial out-migration Everyone, except births of the year The individual is removed from the simulation x x x x x
Intraprovincial out-migration Everyone, except births of the year The individual is removed from the simulation x x x x
Migration from the central municipality to the suburb People living in the central municipality, except births of the year The individual is identified as a migrant from the central municipality to the suburb. The municipality of residence is determined in the residential location module x x
Migration from the suburb to the central municipality People living in the suburb, except births of the year The municipality of residence becomes the central municipality (Montreal) x x x
Migration within the suburb People living in the suburb, except births of the year The individual is identified as a migrant within the suburb. The municipality of residence is determined in the residential location module x x x x
Language shift toward French Allophones The language spoken at home is changed to French x x x x
Language shift toward English Allophones The language spoken at home is changed to English x x x x
Table 2
Estimated emigration rates of immigrants by years since arrival.
Number of years since arrival Emigration rate
1 4.40%
2 4.40%
3 2.95%
4 1.50%
5 1.50%
6 1.50%
7 1.50%
8 1.40%
9 1.30%
10 1.30%
11 1.30%
12 1.30%
13 0.65%

  1. Source: Termote, Payeur et al. 2011. Annualized by authors.

Table 3
Parameters of interprovincial and intraprovincial outmigration, Montreal metropolitan community, 2001 and 2006 census.
Interprovincial out-migration (n=1,292,224) Intraprovincial out-migration (n=1,292,224)
Intercept −5.796*** −3.652***
Age groups (ref=30–34)
0–4 −0.063 −0.173***
5–9 −0.268*** −0.632***
10–14 −0.718*** −0.955***
15–19 −0.696*** −0.707***
20–24 0.322*** 0.263***
25–29 0.419*** 0.305***
35–39 −0.338*** −0.387***
40–44 −0.619*** −0.688***
45–49 −0.812*** −0.789***
50–54 −0.956*** −0.651***
55–59 −0.993*** −0.534***
60–64 −0.874*** −0.638***
65–69 −1.285*** −0.896***
70–74 −1.461*** −1.357***
75+ −1.024*** −1.381***
Language spoken at home (ref = French)
English 2.206*** −1.680***
Other(s) 1.421*** −1.856***
Place of birth (ref = born in Canada)
Foreign-born −0.883***
Number of years since arrival (ref = Born in Canada)
0–4 1.074***
5–9 0.602***
10–14 0.189**
15+ −0.291***
RCM of residence (ref = RCM66)
RCM55 and RCM57 −0.581*** 0.326***
RCM58 −0.420*** −0.067*
RCM59 −0.228 0.086
RCM60 −1.113*** 0.163***
RCM64 −0.817*** −0.009
RCM65 −0.870*** −0.252***
RCM67 and RCM70 −0.393*** 0.060
RCM71 −0.205** 0.388***
RCM72 −0.698*** −0.199**
RCM73 and RCM74 −0.546*** 0.236***
  1. *

    p<0.05.

  2. **

    p<0.01.

  3. ***

    p<0.0001.

Table 4
Parameters of logistic regressions modeling internal outmigration between municipalities of the Montreal metropolitan community, 2001 and 2006.
From the central municipality to the suburb (n=586,151) From the suburb to the central municipality (n=682,659) Within the suburb (n=682,659)
Intercept −3.024 *** −3.741 *** −3.004 ***
Age groups (ref=30–34)
0–4 −0.089 * −0.836 *** −0.199 ***
5–9 −0.501 *** −1.092 *** −0.558 ***
10–14 −0.753 *** −1.479 *** −0.935 ***
15–19 −1.065 *** −0.518 *** −0.892 ***
20–24 −0.490 *** 0.787 *** 0.064 *
25–29 0.058 0.711 *** 0.485 ***
35–39 −0.321 *** −0.502 *** −0.443 ***
40–44 −0.743 *** −0.804 *** −0.810 ***
45–49 −1.030 *** −0.871 *** −1.095 ***
50–54 −1.253 *** −0.976 *** −1.184 ***
55–59 −1.281 *** −1.263¨*** −1.264 ***
60–64 −1.397 *** −1.521 *** −1.412 ***
65–69 −1.517 *** −1.512 *** −1.518 ***
70–74 −1.748 *** −1.469 *** −1.529 ***
75+ −1.658 *** −1.226 *** −1.308 ***
Language spoken at home (ref = French)
English −0.353 *** −0.361 ***
Other(s) −0.631 *** −0.662 ***
Place of birth (ref = born in Canada)
Foreign-born 0.170 *** −0.200 ***
RCM of residence (ref = RCM66)
RCM55 and RCM57 −0.477 *** 0.386 ***
RCM58 −0.127 ** 0.126 **
RCM59 −0.456 *** 0.091
RCM60 0.120 * −0.278 ***
RCM64 −0.288 *** 0.083 *
RCM65 −0.133 ** −0.208 ***
RCM67 and RCM70 −0.295 *** 0.224 ***
RCM71 −0.277 *** 0.232 ***
RCM72 −0.429 *** 0.593 ***
RCM73 and RCM74 −0.556 *** 0.430 ***
  1. *

    p<0.05.

  2. **

    p<0.01.

  3. ***

    p<0.0001.

Table 5
Parameters of conditional logistic regressions modeling the municipality of destination for internal and external migrants, Montreal metropolitan community, 2001 and 2006 censuses.
Intraprovincial in-migrants (n=14528) Interprovincial in-migrants (n=4613) International immigrants (n=14993) Migrants from the central municipality (n=12565) Migrants from another suburb (n=18080)
Distance to downtown (km) −0.014 *** −0.007 **
Population size 1.894E-06 *** 2.301E-06 *** 2.444E-06 *** 8.848E-06 *** 7.864E-06 ***
Kind of municipality (ref = City)
Village −2.159 *** −1.966 *** −2.148 *** −2.220 *** −1.757 ***
Town −1.233 *** −0.997 *** −0.971 *** −1.155 *** −0.831 ***
New housings 5.230E-05 ** 2.900E-04 *** 2.097E-04 ***
Majority of Francophones 3.224 *** 0.937 *** 1.490 *** 0.544 *** 0.754 ***
* anglophone migrant −3.034 *** −1.412 *** −1.914 *** −2.550 *** −3.518 ***
* allophone migrant −2.258 *** −0.713 *** −0.815 *** −1.433 *** −2.740 ***
RCM of residence (ref = RCM65 and RCM66)
RCM55 and RCM57 −0.773 *** −1.438 *** −2.455 *** −0.007 1.527 ***
RCM58 −0.117 * −0.102 −0.170 ** 0.655 *** 1.525 ***
RCM59 −1.093 *** −1.554 *** −2.681 *** 0.007 1.199 ***
RCM60 −0.493*** −1.475 *** −2.459 *** 1.115 *** 1.315 ***
RCM64 −0.386 *** −0.927 *** −2.363 *** 1.057 *** 1.994 ***
RCM67 and RCM70 −0.988 *** −1.855 *** −2.995 *** 0.530 *** 1.324***
RCM 71 −0.893 *** −0.282 * −1.587 *** 0.966 *** 1.274 ***
RCM72 −0.988 *** −1.600 *** −2.257 *** 0.473 *** 1.777 ***
RCM73 and RCM74 −0.474 *** −0.967 *** −2.113 *** 0.325 *** 1.867 ***
  1. *

    p<0.05.

  2. **

    p<0.01.

  3. ***

    p<0.0001.

Table 6
Distribution of municipalities according to the absolute percent error.
[10%, ∞[ 4
[5%, 10%[ 15
[2.5%, 5%[ 21
[0, 2.5%[ 39
Table 7
Mean absolute percent error between population estimates in 2011 and the simulation by population size and growth rate of the municipality.
Total population Population by age groups (16)a
Overallb 3.4% 12.3%
Population size
[50,000, ∞[ 1.2% 5.6%
[15,000, 50,000[ 2.3% 9.3%
[5,000, 15,000[ 4.0% 12.5%
[0, 5,000[ 5.7% 21.4%
Population growth rate 2006–2011
[10%, ∞[ 4.3% 10.7%
[5%, 10%[ 2.9% 10.7%
[0%, 5%[ 3.0% 13.1%
]-∞, 0%[ 4.1% 15.1%
  1. a

    This is the arithmetic mean of the MAPE of 16 age groups.

  2. b

    This is the arithmetic mean of the MAPE of the 79 municipalities.

Table 8
Synthesis of population projection results, MMC, 2006–2031.
Distribution of municipalities by population growth between 2006–2031
[50%, ∞[ 10
[25%, 50%[ 23
[10%, 25%[ 28
[0%, 10%[ 13
]-∞, 0%[ 5
Mean relative growth by initial municipality’s population size
[50,000, ∞[ 33.4%
[15,000, 50,000[ 25.9%
[5,000, 15,000[ 23.5%
[0, 5,000[ 26.2%
Table 9
Distribution of municipalities according to the relative rate change in the proportion of francophones (percentage points), 2006 to 2031.
[0, ∞[ 14
[−5, 0[ 12
[−10, −5[ 11
[−15, −10[ 33
]-∞, −15[ 9
Table
Table Results from simulations and population estimates.
Population estimates Results from 2006–2011 pre-simulations
2006 2011 No adjustment Out-migration assumption adjusted Fertility assumption adjusted Results from 2011–2031 simulation
(1) (2) (3) (4) (5) (6)
Montréal 3,570,100 3,791,100 3,758,132 3,781,745 3,783,223 4,553,217
Baie-D’Urfé 3,900 3,930 3,828 3,620 3,850 4,151
Beaconsfield 19,255 20,330 19,557 20,269 20,332 24,016
Beauharnois 12,000 12,235 11,117 11,145 11,186 12,523
Beloeil 19,135 20,465 20,944 20,852 20,581 25,210
Blainville 47,025 53,165 52,059 51,757 51,568 63,538
Boisbriand 26,700 26,485 26,791 26,823 26,855 29,541
Bois-des-Filion 8,455 9,450 9,591 9,540 9,321 12,165
Boucherville 39,275 41,570 41,073 41,176 41,254 46,811
Brossard 71,765 80,235 79,763 80,580 79,432 95,579
Candiac 16,145 19,575 18,691 18,739 19,259 28,188
Carignan 7,545 8,020 7,989 7,637 8,009 9,414
Chambly 22,880 25,440 23,549 23,677 23,673 27,527
Charlemagne 5,670 5,775 5,621 5,697 5,965 6,480
Châteauguay 43,140 46,330 45,417 46,167 45,391 55,330
Contrecoeur 5,740 6,290 6,081 6,190 6,050 7,531
Côte-Saint-Luc 31,450 33,550 31,945 32,539 32,228 36,989
Delson 7,410 7,555 7,591 7,828 7,942 9,348
Deux-Montagnes 17,615 17,545 18,025 17,946 17,902 19,191
Dollard-Des Ormeaux 49,240 50,825 47,372 48,929 49,166 50,313
Dorval and L’Île-Dorval 18,185 19,250 19,197 19,253 18,999 23,112
Hampstead 6,995 7,500 7,382 7,179 7,531 8,585
Hudson 5,120 4,890 4,532 4,882 5,411 3,169
Kirkland 20,575 21,215 21,043 21,251 20,973 23,788
La Prairie 22,040 23,975 23,569 23,364 23,098 28,357
L’Assomption 16,940 19,755 19,531 20,132 19,993 29,545
Laval 372,415 404,110 403,016 400,079 401,717 521,664
Léry 2,420 2,325 2,622 2,456 2,793 3,265
Les Cèdres 5,810 5,960 5,959 6,009 5,546 6,765
L’Île-Perrot 10,105 10,595 10,774 10,460 10,708 13,003
Longueuil 231,585 236,755 236,858 235,889 235,395 249,684
Lorraine 9,685 9,420 9,437 9,461 9,439 9,780
Mascouche 34,305 40,960 41,288 40,776 41,969 59,383
McMasterville 5,290 5,520 5,459 5,784 5,429 6,656
Mercier 10,250 11,585 10,346 10,309 10,201 13,789
Mirabel 35,310 41,165 41,083 40,087 41,053 56,790
Montréal 1,638,870 1,723,940 1,704,182 1,734,634 1,733,374 2,070,328
Montréal-Est 3,865 4,010 3,963 3,910 3,903 4,088
Montréal-Ouest 5,225 5,395 5,095 5,171 5,250 6,143
Mont-Royal 18,995 20,225 20,156 20,462 19,720 21,950
Mont-Saint-Hilaire 15,865 17,410 18,671 18,438 18,194 23,341
Notre-Dame-de-l’Île-Perrot 10,030 10,430 9,826 10,153 10,099 10,910
Oka 3,310 3,700 3,373 3,510 3,252 4,031
Otterburn Park 8,580 8,470 8,613 8,502 8,260 9,527
Pincourt 11,375 13,690 12,928 12,456 12,793 13,812
Pointe-Calumet 6,645 6,455 7,148 6,425 6,754 7,386
Pointe-Claire 30,275 31,875 30,383 30,974 29,832 34,251
Pointe-des-Cascades 1,045 1,195 1,204 1,200 1,240 1,745
Repentigny 77,035 81,275 82,040 80,413 80,882 88,566
Richelieu 5,240 5,335 5,477 5,359 5,617 6,336
Rosemère 14,290 14,070 14,244 13,741 13,989 13,993
Saint-Amable 8,510 10,620 9,799 9,531 9,968 14,756
Saint-Basile-le-Grand 15,825 16,550 17,025 16,027 16,511 19,267
Saint-Bruno-de-Montarville 24,515 25,965 25,842 25,518 24,908 27,933
Saint-Constant 24,250 24,990 25,173 24,929 25,065 27,644
Sainte-Anne-de-Bellevue 5,235 5,425 5,415 5,743 5,408 7,110
Sainte-Anne-des-Plaines 13,165 13,730 12,769 12,909 12,888 13,204
Sainte-Catherine 16,405 16,885 17,435 17,620 17,383 22,110
Sainte-Julie 29,380 29,095 28,180 28,296 28,318 27,663
Sainte-Marthe-sur-le-Lac 11,485 14,840 13,341 12,841 13,595 12,816
Sainte-Thérèse 25,490 26,140 27,346 27,774 27,067 34,930
Saint-Eustache 42,610 43,525 44,060 42,886 43,773 48,375
Saint-Isidore 2,520 2,640 2,765 2,662 2,821 3,332
Saint-Jean-Baptiste 3,060 3,090 3,017 3,127 3,047 3,286
Saint-Joseph-du-Lac 5,035 6,245 6,437 6,730 6,490 9,209
Saint-Lambert 21,660 22,015 23,242 23,040 22,953 22,794
Saint-Lazare 17,260 18,980 19,040 19,279 19,452 24,881
Saint-Mathias-sur-Richelieu 4,570 4,465 4,376 4,579 4,523 4,691
Saint-Mathieu 1,890 1,990 1,929 1,823 1,827 2,173
Saint-Mathieu-de-Beloeil 2,315 2,545 2,398 2,524 2,763 3,327
Saint-Philippe 5,180 5,630 6,015 6,073 5,921 8,717
Saint-Sulpice 3,355 3,290 3,441 3,414 3,244 3,818
Senneville 980 985 897 1,107 974 967
Terrasse-Vaudreuil 2,000 1,925 2,034 1,895 1,958 2,031
Terrebonne 96,175 106,310 106,699 104,761 106,534 171,084
Varennes 21,175 20,680 22,028 21,518 21,476 23,841
Vaudreuil-Dorion 26,195 32,555 32,178 32,107 32,080 47,454
Vaudreuil-sur-le-Lac and L’Île-Cadieux 1,425 1,490 1,551 1,630 1,426 1,768
Verchères and Calixa-Lavallée 5,835 5,995 6,161 6,332 6,313 8,022
Westmount 20,580 21,280 21,136 21,240 21,159 18,427

  1. Source: Institut de la statistique du Québec (2006 and 2011 population estimates); Authors calculation (simulations).

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