# How much does early attachment fix adult attachment? Pinquart, Feussner & Ahnert (2013) pooled
# 127 studies: overall stability r = .39, higher over short intervals, and no significant stability
# over intervals longer than 15 years. Three ways to read such numbers.
import math
r = 0.39
print(f"1. r = {r:.2f} means the earlier measure accounts for r^2 = {r * r:.0%} of the variance of the later one")
# 2. If 'secure' vs 'insecure' is a median split of an underlying continuous variable, the chance
#    that a person falls on the same side twice is 1/2 + arcsin(r)/pi (bivariate normal, Sheppard).
same = 0.5 + math.asin(r) / math.pi
print(f"2. same side of a median split both times: {same:.0%} (50 % by chance alone; kappa = {2 * same - 1:.2f})")
# 3. Two simple models of change (compared by Fraley 2002). Yearly correlation of the changing part
#    0.80 in both; the 'prototype' model adds a stable component carrying 25 % of the variance.
print("3. correlation between age 1 and later ages under two models")
print("   years later |  1   |  2   |  5   |  10  |  15  |  20")
rev = [0.8 ** k for k in (1, 2, 5, 10, 15, 20)]
pro = [0.25 + 0.75 * 0.8 ** k for k in (1, 2, 5, 10, 15, 20)]
print("   revisionist | " + " | ".join(f"{v:.2f}" for v in rev))
print("   prototype   | " + " | ".join(f"{v:.2f}" for v in pro))
print("   the revisionist model decays toward 0; the prototype model levels off at the stable share (0.25)")
# 1. r = 0.39 means the earlier measure accounts for r^2 = 15% of the variance of the later one
# 2. same side of a median split both times: 63% (50 % by chance alone; kappa = 0.26)
# 3. correlation between age 1 and later ages under two models
#    years later |  1   |  2   |  5   |  10  |  15  |  20
#    revisionist | 0.80 | 0.64 | 0.33 | 0.11 | 0.04 | 0.01
#    prototype   | 0.85 | 0.73 | 0.50 | 0.33 | 0.28 | 0.26
#    the revisionist model decays toward 0; the prototype model levels off at the stable share (0.25)

# Can a relationship revise an early working model? A three-state Markov chain, one step per month,
# for felt security within a relationship: 0 = insecure, 1 = mixed, 2 = secure. With a responsive
# partner, a month moves a person up one state with probability 0.08 and down with 0.03; with an
# unresponsive partner the numbers are swapped. The probabilities are illustrative assumptions, not
# estimates; the chain only shows how small monthly tilts add up (cf. Arriaga et al. 2018).
def step(dist, up, down):
    new = [0.0, 0.0, 0.0]
    for s, p in enumerate(dist):
        u = up if s < 2 else 0.0; d = down if s > 0 else 0.0
        new[s] += p * (1 - u - d)
        if s < 2: new[s + 1] += p * u
        if s > 0: new[s - 1] += p * d
    return new

def after(months, up, down, start=(1.0, 0.0, 0.0)):
    dist = list(start)
    for _ in range(months): dist = step(dist, up, down)
    return dist

def stationary(up, down):
    q = up / down                     # birth-death chain: pi_s proportional to q^s
    w = [1, q, q * q]; return [v / sum(w) for v in w]

def mean_months_to_secure(up, down):
    # expected months to first reach state 2 from state 0, from the first-step equations
    #   T0 = 1 + up*T1 + (1-up)*T0        T1 = 1 + down*T0 + (1-up-down)*T1
    a11, a12, b1 = up, -up, 1.0                     # up*T0 - up*T1 = 1
    a21, a22, b2 = -down, up + down, 1.0            # -down*T0 + (up+down)*T1 = 1
    det = a11 * a22 - a12 * a21
    return (b1 * a22 - a12 * b2) / det

print("starting insecure; share in each state (insecure / mixed / secure)")
for label, up, down in (("responsive partner", 0.08, 0.03), ("unresponsive partner", 0.03, 0.08)):
    rows = [after(m, up, down) for m in (12, 36, 60)]
    print(f"{label:21s}: 1 yr " + " / ".join(f"{v:.0%}" for v in rows[0]) + "; 3 yr " + " / ".join(f"{v:.0%}" for v in rows[1])
          + "; 5 yr " + " / ".join(f"{v:.0%}" for v in rows[2]))
    print(f"{'':21s}  long run " + " / ".join(f"{v:.0%}" for v in stationary(up, down))
          + f"; mean time from insecure to secure {mean_months_to_secure(up, down) / 12:.1f} years")
# starting insecure; share in each state (insecure / mixed / secure)
# responsive partner   : 1 yr 43% / 36% / 21%; 3 yr 16% / 29% / 55%; 5 yr 11% / 26% / 64%
#                        long run 9% / 25% / 66%; mean time from insecure to secure 2.5 years
# unresponsive partner : 1 yr 79% / 18% / 3%; 3 yr 69% / 24% / 8%; 5 yr 67% / 25% / 9%
#                        long run 66% / 25% / 9%; mean time from insecure to secure 13.0 years