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Table 2 A 5-interval projection in a hypothetical three-state (path) membership model with states unaffiliated (U), joined (J), and active (A)

From: Rates, intrinsic linkages, and multistate population dynamics

  Fraction in state (f) z2t Rates of transfer (Eqs. (20)–(21))
Time U J A   m UJ m JU m JA m AJ
A. Interval by interval calculations (Eq. (1))
 0 .85 .10 .05
 1 .82925 .10985 .06090 .70 .01317 .06586 .08474 .12106
 2 .81243 .11769 .06988 .71 .01335 .06674 .08291 .11678
 3 .79876 .12391 .07733 .72 .01357 .06785 .08026 .11147
 4 .78759 .12885 .08356 .73 .01384 .06921 .07698 .10545
 5 .77844 .13275 .08881 .74 .01419 .07093 .07318 .09890
B. Stable population values (τj5) implied by time 5 rates
 5 .74184 .14837 .10979      
C. Time 5 values calculated directly from time 0 populations and z values (Eq. (2))  
 5 .77844 .13275 .08881      
  1. Notes: Fixed values are w = 0.8, n = 5, and z 1 = m UJ/m JU = 0.20. Rate ratio z 2t = m JAt/m AJt increases as shown above. Stable population proportions are τ2t = z 1/(1 + z 1 + z 1 z 2t), τ3t = z 1 z 2t/(1 + z 1 + z 1 z 2t)