/** Test the goodness-of-fit between two \ref apop_pmf models.
If you send two histograms, I assume that the histograms are synced: for PMFs,
you've used \ref apop_data_to_bins to generate two histograms using the same binspec,
or you've used \ref apop_data_pmf_compress to guarantee that each observation value
appears exactly once in each data set.
In any case, you are confident that all values in the \c observed set appear in the \c
expected set with nonzero weight; otherwise this will return a \f$\chi^2\f$ statistic
of \c GSL_POSINF, indicating that it is impossible for the \c observed data to have
been drawn from the \c expected distribution.
\li If an observation row has weight zero, I skip it. if <tt>apop_opts.verbose >=1 </tt> I will show a warning.
\ingroup histograms
*/
apop_data *apop_histograms_test_goodness_of_fit(apop_model *observed, apop_model *expected){
int df = observed->data->weights->size;
double diff = 0;
for (int i=0; i< observed->data->weights->size; i++){
Apop_data_row(observed->data, i, one_obs);
double obs_val = gsl_vector_get(observed->data->weights, i);
double exp_val = apop_p(one_obs, expected);
if (exp_val == 0){
diff = GSL_POSINF;
break;
}
if (obs_val==0){
Apop_notify(1, "element %i of the observed data has weight zero. Skipping it.", i);
df --;
} else
diff += gsl_pow_2(obs_val - exp_val)/exp_val;
}
//Data gathered. Now output
apop_data *out = apop_data_alloc();
double toptail = gsl_cdf_chisq_Q(diff, df-1);
sprintf(out->names->title, "Goodness-of-fit test via Chi-squared statistic");
apop_data_add_named_elmt(out, "Chi squared statistic", diff);
apop_data_add_named_elmt(out, "df", df-1);
apop_data_add_named_elmt(out, "p value", toptail);
apop_data_add_named_elmt(out, "confidence", 1 - toptail);
return out;
}
/** Run the Kolmogorov-Smirnov test to determine whether two distributions are identical.
\param m1, m2 Two models, most likely of \ref apop_pmf type. I will ue the cdf method, so if your function doesn't have one, expect this to run the slow default. I run it for each row of each data set, so if your model has a \c NULL at the data, I won't know what to do.
\return An \ref apop_data set including the \f$p\f$-value from the Kolmogorov test that the two distributions are equal.
\li I assume that the data sets are sorted.
\include ks_tests.c
\ingroup histograms
*/
apop_data *apop_test_kolmogorov(apop_model *m1, apop_model *m2){
//version for not a pair of histograms
Apop_assert(m1->data, "I will test the CDF at each point in the data set, but the first model has a NULL data set. "
"Maybe generate, then apop_data_sort, a few thousand random draws?");
Apop_assert(m2->data, "I will test the CDF at each point in the data set, but the second model has a NULL data set. "
"Maybe generate, then apop_data_sort, a few thousand random draws?");
int maxsize1, maxsize2;
{Get_vmsizes(m1->data); maxsize1 = maxsize;}//copy one of the macro's variables
{Get_vmsizes(m2->data); maxsize2 = maxsize;}// to the full function's scope.
double largest_diff=GSL_NEGINF;
for (size_t i=0; i< maxsize1; i++){
Apop_data_row(m1->data, i, arow);
largest_diff = GSL_MAX(largest_diff, fabs(apop_cdf(arow, m1)-apop_cdf(arow, m2)));
}
for (size_t i=0; i< maxsize2; i++){ //There should be matched data rows, so there is redundancy.
Apop_data_row(m2->data, i, arow); // Feel free to submit a smarter version.
largest_diff = GSL_MAX(largest_diff, fabs(apop_cdf(arow, m1)-apop_cdf(arow, m2)));
}
apop_data *out = apop_data_alloc();
sprintf(out->names->title, "Kolmogorov-Smirnov test");
apop_data_add_named_elmt(out, "max distance", largest_diff);
double ps = psmirnov2x(largest_diff, maxsize1, maxsize2);
apop_data_add_named_elmt(out, "p value, 2 tail", 1-ps);
apop_data_add_named_elmt(out, "confidence, 2 tail", ps);
return out;
}
apop_model* apop_chi_estimate(apop_data *d, apop_model *m){
Apop_assert(d, "No data with which to count df. (the default estimation method)");
Get_vmsizes(d); //vsize, msize1, msize2
apop_model *out = apop_model_copy(*m);
apop_data_add_named_elmt(out->parameters, "df", tsize - 1);
apop_data_add_named_elmt(out->info, "log likelihood", out->log_likelihood(d, out));
return out;
}
apop_model* apop_fdist_estimate(apop_data *d, apop_model *m){
Apop_assert(d, "No data with which to count df. (the default estimation method)");
apop_name_add(m->parameters->names, "df", 'r');
apop_name_add(m->parameters->names, "df2", 'r');
apop_data_set(m->parameters, 0, -1, d->vector->size -1);
apop_data_set(m->parameters, 1, -1, d->matrix->size1 * d->matrix->size2 -1);
apop_data_add_named_elmt(m->info, "log likelihood", apop_f_distribution.log_likelihood(d, m));
return m;
}
apop_data *kappa_and_pi(apop_data const *tab_in){
apop_data *out = apop_data_alloc();
Apop_stopif(!tab_in, out->error='n'; return out, 0, "NULL input. Returning output with 'n' error code.");
Apop_stopif(!tab_in->matrix, out->error='m'; return out, 0, "NULL input matrix. Returning output with 'm' error code.");
Apop_stopif(tab_in->matrix->size1 != tab_in->matrix->size2, out->error='s'; return out, 0, "Input rows=%zu; input cols=%zu; "
"these need to be equal. Returning output with error code 's'.", tab_in->matrix->size1, tab_in->matrix->size2);
apop_data *tab = apop_data_copy(tab_in);
double total = apop_matrix_sum(tab->matrix);
gsl_matrix_scale(tab->matrix, 1./total);
double p_o = 0, p_e = 0, scott_pe = 0, ia = 0, row_ent = 0, col_ent = 0;
for (int c=0; c< tab->matrix->size1; c++){
double this_obs = apop_data_get(tab, c, c);
p_o += this_obs;
Apop_row_v(tab, c, row);
Apop_col_v(tab, c, col);
double rsum = apop_sum(row);
double csum = apop_sum(col);
p_e += rsum * csum;
scott_pe += pow((rsum+csum)/2, 2);
ia += this_obs * log2(this_obs/(rsum * csum));
row_ent -= rsum * log2(rsum);
col_ent -= csum * log2(csum);
}
apop_data_free(tab);
asprintf(&out->names->title, "Scott's π and Cohen's κ");
apop_data_add_named_elmt(out, "total count", total);
apop_data_add_named_elmt(out, "percent agreement", p_o);
apop_data_add_named_elmt(out, "κ", ((p_e==1)? 0: (p_o - p_e) / (1-p_e) ));
apop_data_add_named_elmt(out, "π", ((p_e==1)? 0: (p_o - scott_pe) / (1-scott_pe)));
apop_data_add_named_elmt(out, "P_I", ia/((row_ent+col_ent)/2));
apop_data_add_named_elmt(out, "Cohen's p_e", p_e);
apop_data_add_named_elmt(out, "Scott's p_e", scott_pe);
apop_data_add_named_elmt(out, "information in agreement", ia);
apop_data_add_named_elmt(out, "row entropy", row_ent);
apop_data_add_named_elmt(out, "column entropy", col_ent);
return out;
}
apop_model* apop_t_estimate(apop_data *d, apop_model *m){
Apop_assert(d, "No data with which to count df. (the default estimation method)");
Get_vmsizes(d); //vsize, msize1, msize2, tsize
apop_model *out = apop_model_copy(*m);
double vmu = vsize ? apop_mean(d->vector) : 0;
double v_sum_sq = vsize ? apop_var(d->vector)*(vsize-1) : 0;
double m_sum_sq = 0;
double mmu = 0;
if (msize1) {
apop_matrix_mean_and_var(d->matrix, &mmu, &m_sum_sq);
m_sum_sq *= msize1*msize2-1;
}
apop_data_add_names(out->parameters, 'r', "mean", "standard deviation", "df");
apop_data_set(out->parameters, 0, -1, (vmu *vsize + mmu * msize1*msize2)/tsize);
apop_data_set(out->parameters, 1, -1, sqrt((v_sum_sq*vsize + m_sum_sq * msize1*msize2)/(tsize-1)));
apop_data_set(out->parameters, 2, -1, tsize-1);
apop_data_add_named_elmt(out->info, "log likelihood", out->log_likelihood(d, out));
return out;
}
