logisticp-valueregressionstata
This picture is from page 1290 in the Stata manual:
The model can be made with the following code in Stata:
use https://www.stata-press.com/data/r16/auto
keep make mpg weight foreign
logit foreign weight mpg
As I understand the overall fit for the model is calculated with a chi2 test (Prob > chi2 = 0.0000), but how are the individual P-values (P>|z|) calculated?
As pointed out in comments, the more complicated model has too many predictors to be taken seriously. I focus here on models with 6 predictors.
I have used MATLAB very occasionally in the past but not for any related purpose and am emphatically no expert. But on the face of it your MATLAB call does not feed a fractional response (outcome, dependent variable) to the function either directly or indirectly and it is amazing that it produces any output at all. If you are using the same naming conventions across different software, then FC is a count, not a binary response, and not a fit present for a logit function.
Here is the result of a calculation in Stata 14 of a logit model in which the response is treated as a continuous proportion:
. fracreg logit fcperhab ddp schabs train exp_hab exp_ratio sch_tot
Iteration 0: log pseudolikelihood = -19.110279
Iteration 1: log pseudolikelihood = -18.06008
Iteration 2: log pseudolikelihood = -17.979059
Iteration 3: log pseudolikelihood = -17.976617
Iteration 4: log pseudolikelihood = -17.976616
Fractional logistic regression Number of obs = 30
Wald chi2(6) = 21.06
Prob > chi2 = 0.0018
Log pseudolikelihood = -17.976616 Pseudo R2 = 0.0865
------------------------------------------------------------------------------
| Robust
fcperhab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ddp | .0033372 .0044366 0.75 0.452 -.0053583 .0120327
schabs | .0195366 .0162846 1.20 0.230 -.0123806 .0514538
train | .0000243 8.40e-06 2.90 0.004 7.85e-06 .0000408
exp_hab | -4.832934 10.20002 -0.47 0.636 -24.8246 15.15873
exp_ratio | -.0016535 .904611 -0.00 0.999 -1.774658 1.771351
sch_tot | 1.15e-06 9.91e-07 1.16 0.248 -7.98e-07 3.09e-06
_cons | -.1102337 .3944965 -0.28 0.780 -.8834326 .6629653
------------------------------------------------------------------------------
For all that the results may seem disappointing, there is nothing pathological about the output. Non-Stata users can probably guess that _cons means the intercept. As context here are some summary statistics:
. su fcperhab ddp schabs train exp_hab exp_ratio sch_tot
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
fcperhab | 30 .6355612 .2472515 .2056616 .9978048
ddp | 30 7.766667 19.39016 0 85
schabs | 30 8.83 10.14478 0 40.2
train | 30 18741.83 26769.19 0 108643
exp_hab | 30 .0152065 .0195379 0 .1046035
-------------+---------------------------------------------------------
exp_ratio | 30 .3794279 .2442145 0 .7318189
sch_tot | 30 203229.1 410059.5 251 2198181
Stata users who have not yet upgraded to 14 [released 7 April 2015] may note that glm fcperhab ddp schabs train exp_hab exp_ratio sch_tot, link(logit) f(binomial) vce(robust) gives the same calculation. But it is important here to spell out to Stata, in whatever version is used, that binomial is at best a convenient fiction here. In fracreg that is automatic; otherwise, vce(robust) is that signal and if we omit it results are quite different, but still free of pathological very high or very low P-values:
. glm fcperhab ddp schabs train exp_hab exp_ratio sch_tot, link(logit) f(binomial)
note: fcperhab has noninteger values
Iteration 0: log likelihood = -13.058365
Iteration 1: log likelihood = -12.952102
Iteration 2: log likelihood = -12.950226
Iteration 3: log likelihood = -12.950225
Iteration 4: log likelihood = -12.950225
Generalized linear models No. of obs = 30
Optimization : ML Residual df = 23
Scale parameter = 1
Deviance = 5.476451096 (1/df) Deviance = .2381066
Pearson = 4.86766495 (1/df) Pearson = .2116376
Variance function: V(u) = u*(1-u/1) [Binomial]
Link function : g(u) = ln(u/(1-u)) [Logit]
AIC = 1.330015
Log likelihood = -12.95022455 BIC = -72.75109
------------------------------------------------------------------------------
| OIM
fcperhab | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ddp | .0033372 .023125 0.14 0.885 -.0419869 .0486613
schabs | .0195366 .0430982 0.45 0.650 -.0649343 .1040075
train | .0000243 .0000275 0.88 0.377 -.0000297 .0000783
exp_hab | -4.832937 27.53167 -0.18 0.861 -58.79402 49.12815
exp_ratio | -.0016538 1.961583 -0.00 0.999 -3.846287 3.842979
sch_tot | 1.15e-06 2.69e-06 0.43 0.671 -4.13e-06 6.43e-06
_cons | -.1102337 .785408 -0.14 0.888 -1.649605 1.429138
------------------------------------------------------------------------------
There are many other scientific and statistical issues not clear without further discussion and analysis, and I will raise just two:
Some predictors appear to be absolute counts or amounts, and it's not all clear why absolute values are natural here.
Some of the predictors may need or benefit from transformation.
Whether or not you want to omit a variable (or do something else) when the correlation is very high but not perfect is a choice. Stata treats its users as adults and lets you make your own choices. With perfect collinearity there is no choice: there is no information present in the data that allows Stata to separate the two effects. It could return an error message and not estimate the model, or Stata can chose one of the offending variables to omit. StataCorp chose the latter.
Best Answer
The tests shown by Stata for the individual coefficients are Wald tests whose test statistics have the form $$ W_j = \frac{\hat{\beta}_j}{\widehat{\operatorname{SE}}(\hat{\beta}_j)}\sim N(0,1) $$
Under the hypothesis than an individual coefficient is zero, these statistics will asymptotically follow the standard normal distribution. Hence, they are $z$-values. The corresponding $p$-values are calculated from the standard normal cdf $\Phi(x)$. Specifically, for two-sided $p$-values: $p=2\cdot\Phi(-|z|)$. For example in Stata for the coefficient for
mpg:Reference
Hosmer DW, Lemeshow S, Sturdivant RX (2013): Applied Logistic Regression. 3rd ed. Wiley.