% Variation power simulation -- Monte-Carlo power for the paper's stim x day
% interaction, using THIS folder's data as the ground truth, for BOTH metrics:
%   metric = count : behavior = # successes         -> power_result.txt
%   metric = rate  : behavior = success / attempts  -> power_result_rate.txt
%
% Ground truth: fitlme(behavior ~ stim + day + stim:day + (1|rat)) on data.csv
% (day within-window). Its fixed effects, per-rat intercept SD, and residual SD
% generate NREP synthetic datasets at each rats-per-group N and each true-effect
% multiplier (1 = observed, 0.5 = half). Each is scored at alpha=0.05 by:
%   per-animal : Welch t on per-rat behavior~day slopes (cluster-honest power)
%   LME        : the fitlme stim:day p (observation-level DF -- optimistic)
% Writes power_result[_rate].txt. Run:  matlab -batch "powersim"
% (Copy of analysis/matlab/variation_power.m; see make_variation_power.m.)

here = fileparts(mfilename('fullpath'));
if isempty(here); here = pwd; end
vname = regexprep(here, '.*[/\\]', '');
D = readtable(fullfile(here, 'data.csv'), 'TextType', 'string');

localPower(D, 'count', here, vname);
localPower(D, 'rate', here, vname);

% ---------------------------------------------------------------- per metric
function localPower(D, metric, here, vname)
NS = [3 5 8 12 16 24]; EFFMULS = [1 0.5]; NREP = 120;
FORMULA = 'behavior ~ stim + day + stim:day + (1|rat)';
if strcmp(metric, 'rate')
    D = D(D.total > 0, :); beh = D.success ./ D.total; mlabel = 'success RATE'; suffix = '_rate';
else
    beh = D.success; mlabel = '# successes (count)'; suffix = '';
end
warnState = warning('off', 'all'); rng(1);
day0 = min(D.day);
tbl0 = table(beh, D.day - day0, double(D.stim), categorical(D.subject), ...
    'VariableNames', {'behavior', 'day', 'stim', 'rat'});
nStim = numel(unique(D.subject(D.stim == 1)));
nCtrl = numel(unique(D.subject(D.stim == 0)));

bar = repmat('=', 1, 78);
s = sprintf('%s\nPOWER SIMULATION -- %s   [metric: %s]\n%s\n', bar, vname, mlabel, bar);
s = [s sprintf('model: %s   (behavior = %s; day within-window)\n', FORMULA, mlabel)];
s = [s sprintf('observed groups: stim n=%d, control n=%d   nrep=%d, alpha=0.05\n', nStim, nCtrl, NREP)];

if nStim < 2 || nCtrl < 2 || numel(unique(tbl0.day)) < 2
    s = [s sprintf('\nInsufficient data for a power simulation.\n')];
    localFinish(s, here, suffix); warning(warnState); return
end

lme = fitlme(tbl0, FORMULA);
cn = lme.CoefficientNames; be = lme.fixedEffects;
b0 = be(strcmp(cn, '(Intercept)')); bStim = be(strcmp(cn, 'stim'));
bDay = be(strcmp(cn, 'day')); bInt = be(strcmp(cn, 'day:stim'));
psi = covarianceParameters(lme); sRat = sqrt(psi{1}); sRes = sqrt(lme.MSE);
days = (0:max(tbl0.day))';

s = [s sprintf('ground truth: stim:day=%+.4g/day, rat SD=%.4g, residual SD=%.4g, days=%d\n', ...
    bInt, sRat, sRes, numel(days))];

for eMul = EFFMULS
    bI = bInt * eMul;
    s = [s sprintf('\n true stim:day interaction = %+.4g (%.0f%% of observed)\n', bI, eMul * 100)];
    s = [s sprintf('  %-8s | per-animal power | LME power\n  %s\n', 'N/group', repmat('-', 1, 42))];
    for N = NS
        sigPA = 0; sigL = 0;
        for r = 1:NREP
            tb = localSim(N, days, b0, bStim, bDay, bI, sRat, sRes);
            sigPA = sigPA + (localPAp(tb) < 0.05);
            try
                m = fitlme(tb, FORMULA); Cm = m.Coefficients;
                sigL = sigL + (Cm.pValue(strcmp(Cm.Name, 'day:stim')) < 0.05);
            catch
            end
        end
        star = '';
        if N == nStim || N == nCtrl; star = '  <- observed'; end
        s = [s sprintf('  %-8d | %5.2f            | %5.2f%s\n', N, sigPA / NREP, sigL / NREP, star)];
    end
end
s = [s sprintf('\nRead the per-animal column as the honest power; LME is optimistic (obs-level DF).\n')];
localFinish(s, here, suffix);
warning(warnState);
end

% ---------------------------------------------------------------- helpers
function localFinish(s, here, suffix)
fprintf('%s', s);
fid = fopen(fullfile(here, ['power_result' suffix '.txt']), 'w');
fprintf(fid, '%s', s); fclose(fid);
end

function tbl = localSim(N, days, b0, bStim, bDay, bI, sRat, sRes)
nd = numel(days); rows = 2 * N * nd;
rat = strings(rows, 1); day = zeros(rows, 1); stim = zeros(rows, 1); behavior = zeros(rows, 1);
k = 0;
for g = 0:1
    for sIdx = 1:N
        re = sRat * randn;
        rid = sprintf('g%d_r%d', g, sIdx);
        for d = 1:nd
            k = k + 1;
            rat(k) = rid; day(k) = days(d); stim(k) = g;
            behavior(k) = b0 + bStim * g + bDay * days(d) + bI * days(d) * g + re + sRes * randn;
        end
    end
end
tbl = table(categorical(rat), day, stim, behavior, ...
    'VariableNames', {'rat', 'day', 'stim', 'behavior'});
end

function p = localPAp(tbl)
rats = unique(tbl.rat); sl = zeros(numel(rats), 1); gr = zeros(numel(rats), 1);
for i = 1:numel(rats)
    r = tbl.rat == rats(i);
    c = polyfit(tbl.day(r), tbl.behavior(r), 1); sl(i) = c(1);
    gr(i) = tbl.stim(find(r, 1));
end
[~, p] = ttest2(sl(gr == 1), sl(gr == 0), 'Vartype', 'unequal');
end