# Attachment as two dimensions, not four boxes. Simulated questionnaire data in the style of the
# ECR (Brennan, Clark & Shaver 1998): each person has true anxiety and avoidance scores; the
# questionnaire measures them with error (reliability about 0.90 per scale). "Styles" are then made
# by cutting each scale at its midpoint (secure = low/low, preoccupied = high anxiety only,
# dismissing = high avoidance only, fearful = high/high). How often does the label change when the
# same people answer again a few weeks later, although nothing about them has changed?
import math, random
rng = random.Random(1)
N, REL = 2000, 0.90
err_sd = math.sqrt((1 - REL) / REL)            # error SD relative to true-score SD 1

def label(anx, avo):
    return {(0, 0): "secure", (1, 0): "preoccupied", (0, 1): "dismissing", (1, 1): "fearful"}[(anx > 0, avo > 0)]

people = [(rng.gauss(0, 1), rng.gauss(0, 1)) for _ in range(N)]
flips, near, near_flips = 0, 0, 0
counts, a1s, a2s = {}, [], []
for anx, avo in people:
    a1, a2 = anx + rng.gauss(0, err_sd), anx + rng.gauss(0, err_sd)
    a1s.append(a1); a2s.append(a2)
    t1 = label(a1, avo + rng.gauss(0, err_sd))
    t2 = label(a2, avo + rng.gauss(0, err_sd))
    counts[t1] = counts.get(t1, 0) + 1
    if t1 != t2: flips += 1
    if min(abs(anx), abs(avo)) < 0.5:
        near += 1; near_flips += t1 != t2
print("labels at time 1:", ", ".join(f"{k} {v / N:.0%}" for k, v in sorted(counts.items())))
print(f"same people, same true scores, re-tested: label changes for {flips / N:.0%}")
print(f"among people within 0.5 SD of a cut-off on either scale ({near / N:.0%} of all): {near_flips / near:.0%} change")
def corr(x, y):
    mx, my = sum(x) / len(x), sum(y) / len(y)
    sxy = sum((a - mx) * (b - my) for a, b in zip(x, y))
    return sxy / math.sqrt(sum((a - mx) ** 2 for a in x) * sum((b - my) ** 2 for b in y))
print(f"yet the continuous anxiety score correlates r = {corr(a1s, a2s):.2f} between the two occasions")
# labels at time 1: dismissing 25%, fearful 25%, preoccupied 26%, secure 25%
# same people, same true scores, re-tested: label changes for 26%
# among people within 0.5 SD of a cut-off on either scale (62% of all): 41% change
# yet the continuous anxiety score correlates r = 0.90 between the two occasions

# Internal working model as a prior belief about a partner's availability. theta = probability that
# the partner responds when one reaches out ("makes a bid"). Belief = Beta(a, b); each bid that is
# answered adds 1 to a, each one that is missed adds w_neg to b. A toy version of the idea, worked
# out far more fully with active inference by Cittern et al. (2018); all parameters illustrative.
#   secure-leaning : expects availability (prior mean 0.8), counts misses at face value, bids often
#   anxiety-leaning: unsure prior (mean 0.5), a missed bid weighs twice as much (w_neg = 2)
#   avoidance-leaning: expects unavailability (prior mean 0.25), and rarely bids, so learns little
# The partner is the same for all three: answers 80 % of bids.
import random
PROFILES = {"secure-leaning": (8, 2, 1.0, 1.0), "anxiety-leaning": (2, 2, 2.0, 1.0),
            "avoidance-leaning": (2, 6, 1.0, 0.25)}          # a0, b0, weight of a miss, P(bid)
TRUE_P = 0.8

def run(a, b, w_neg, p_bid, n_occasions, rng):
    for _ in range(n_occasions):
        if rng.random() < p_bid:
            if rng.random() < TRUE_P: a += 1
            else: b += w_neg
    return a / (a + b)

rng = random.Random(3)
print("belief that the partner will respond (true value 0.80), mean over 2,000 simulated histories")
print("profile            | start | after 10 occasions | after 50 | after 200")
for name, (a0, b0, w, pb) in PROFILES.items():
    row = [sum(run(a0, b0, w, pb, n, rng) for _ in range(2000)) / 2000 for n in (10, 50, 200)]
    print(f"{name:18s} | {a0 / (a0 + b0):5.2f} | {row[0]:18.2f} | {row[1]:8.2f} | {row[2]:9.2f}")
# The asymmetric weight does not wash out: with w_neg = 2 the belief settles near
# p / (p + 2(1 - p)) = 0.8 / 1.2 = 0.67, however long the relationship lasts.
print(f"long-run belief with misses counted double: {TRUE_P / (TRUE_P + 2 * (1 - TRUE_P)):.2f}")
# Avoidance learns slowly because it collects little evidence, not because evidence is ignored.
# belief that the partner will respond (true value 0.80), mean over 2,000 simulated histories
# profile            | start | after 10 occasions | after 50 | after 200
# secure-leaning     |  0.80 |               0.80 |     0.80 |      0.80
# anxiety-leaning    |  0.50 |               0.63 |     0.66 |      0.67
# avoidance-leaning  |  0.25 |               0.37 |     0.58 |      0.73
# long-run belief with misses counted double: 0.67