Estadística

Análisis de la regresión

La función logit es una parte importante de la regresión logística: para más información, por favor ver ese artículo.

En matemáticas, especialmente aquellas aplicadas en estadística, el logit de un número p entre 0 y 1 es

(La base de la función logaritmo usada aquí es de poca importancia en el presente artículo, puesto que es mayor que 1, aunque ellogaritmo natural con base e es usado a menudo.) La función logit es la inversa del "sigmoide", o función "logística".

Si p es una probabilidad entonces p/(1 − p) es el correspondiente odds, y el logit de la probabilidad es el logaritmo de los odds; similarmente la diferencia entre los logits de dos probabilidades es el logaritmo del odds ratio (OR), obteniéndose así un mecanismo aditivo para combinar odds-ratios:

Gráfica de la función logit de 0 a 1 usando ecomo base

El modelo logit fue introducido por Joseph Berkson en 1944, quien sugirió el nombre. El nombre fue traído como una analogía al muy similar modelo probitdesarrollado por Chester Ittner Bliss in 1934. G. A. Barnard en 1949 trajo el término comúnmente usado log-odds; los log-odds de un evento es el logit de la probabilidad de un evento.

    [R] logit -- Logistic regression, reporting coefficients





Syntax



        logit depvar [indepvars] [if] [in] [weight] [, options]



    options                       Description
    -------------------------------------------------------------------------
    Model
      noconstant                  suppress constant term
      offset(varname)             include varname in model with coefficient
                                    constrained to 1
      asis                        retain perfect predictor variables
      constraints(constraints)    apply specified linear constraints
      collinear                   keep collinear variables



    SE/Robust
      vce(vcetype)                vcetype may be oim, robust, cluster
                                    clustvar, bootstrap, or jackknife



    Reporting
      level(#)                    set confidence level; default is level(95)
      or                          report odds ratios
      nocnsreport                 do not display constraints
      display_options             control columns and column formats, row
                                    spacing, line width, display of omitted
                                    variables and base and empty cells, and
                                    factor-variable labeling



    Maximization
      maximize_options            control the maximization process; seldom
                                    used



      nocoef                      do not display coefficient table; seldom
                                    used
      coeflegend                  display legend instead of statistics
    -------------------------------------------------------------------------
    indepvars may contain factor variables; see fvvarlist.
    depvar and indepvars may contain time-series operators; see tsvarlist.
    bootstrap, by, fp, jackknife, mfp, mi estimate, nestreg, rolling,
      statsby, stepwise, and svy are allowed; see prefix.
    vce(bootstrap) and vce(jackknife) are not allowed with the mi estimate
      prefix.
    Weights are not allowed with the bootstrap prefix.
    vce(), nocoef, and weights are not allowed with the svy prefix.
    fweights, iweights, and pweights are allowed; see weight.
    nocoef and coeflegend do not appear in the dialog box.
    See [R] logit postestimation for features available after estimation.





Menu



    Statistics > Binary outcomes > Logistic regression, reporting
        coefficients





Description



    logit fits a logit model for a binary response by maximum likelihood; it
    models the probability of a positive outcome given a set of regressors.
    depvar equal to nonzero and nonmissing (typically depvar equal to one)
    indicates a positive outcome, whereas depvar equal to zero indicates a
    negative outcome.



    Also see [R] logistic; logistic displays estimates as odds ratios.  Many
    users prefer the logistic command to logit.  Results are the same
    regardless of which you use -- both are the maximum-likelihood estimator.
    Several auxiliary commands that can be run after logit, probit, or
    logistic estimation are described in [R] logistic postestimation.  A list
    of related estimation commands is given in logistic estimation commands.





Options



        +-------+
    ----+ Model +------------------------------------------------------------



    noconstant, offset(varname), constraints(constraints), collinear; see [R]
        estimation options.



    asis forces retention of perfect predictor variables and their associated
        perfectly predicted observations and may produce instabilities in
        maximization; see [R] probit.



        +-----------+
    ----+ SE/Robust +--------------------------------------------------------



    vce(vcetype) specifies the type of standard error reported, which
        includes types that are derived from asymptotic theory (oim), that
        are robust to some kinds of misspecification (robust), that allow for
        intragroup correlation (cluster clustvar), and that use bootstrap or
        jackknife methods (bootstrap, jackknife); see [R] vce_option.





        +-----------+
    ----+ Reporting +--------------------------------------------------------



    level(#); see [R] estimation options.



    or reports the estimated coefficients transformed to odds ratios, that
        is, exp(b) rather than b.  Standard errors and confidence intervals
        are similarly transformed.  This option affects how results are
        displayed, not how they are estimated.  or may be specified at
        estimation or when replaying previously estimated results.



    nocnsreport; see [R] estimation options.



    display_options:  noci, nopvalues, noomitted, vsquish, noemptycells,
        baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style),
        cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R]
        estimation options.



        +--------------+
    ----+ Maximization +-----------------------------------------------------



    maximize_options:  difficult, technique(algorithm_spec), iterate(#),
        [no]log, trace, gradient, showstep, hessian, showtolerance,
        tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance, and
        from(init_specs); see [R] maximize.  These options are seldom used.



    The following options are available with logit but are not shown in the
    dialog box:



    nocoef specifies that the coefficient table not be displayed.  This
        option is sometimes used by program writers but is of no use
        interactively.



    coeflegend; see [R] estimation options.





Examples



    ---------------------------------------------------------------------------
    Setup
        . webuse lbw



    Logistic regression
        . logit low age lwt i.race smoke ptl ht ui
        . logit, level(99)



    ---------------------------------------------------------------------------
    Setup
        . webuse nhanes2d
        . svyset



    Logistic regression using survey data
        . svy: logit highbp height weight age female
    ---------------------------------------------------------------------------





Stored results



    logit stores the following in e():



    Scalars        
      e(N)                number of observations
      e(N_cds)            number of completely determined successes
      e(N_cdf)            number of completely determined failures
      e(k)                number of parameters
      e(k_eq)             number of equations in e(b)
      e(k_eq_model)       number of equations in overall model test
      e(k_dv)             number of dependent variables
      e(df_m)             model degrees of freedom
      e(r2_p)             pseudo-R-squared
      e(ll)               log likelihood
      e(ll_0)             log likelihood, constant-only model
      e(N_clust)          number of clusters
      e(chi2)             chi-squared
      e(p)                significance of model test
      e(rank)             rank of e(V)
      e(ic)               number of iterations
      e(rc)               return code
      e(converged)        1 if converged, 0 otherwise



    Macros         
      e(cmd)              logit
      e(cmdline)          command as typed
      e(depvar)           name of dependent variable
      e(wtype)            weight type
      e(wexp)             weight expression
      e(title)            title in estimation output
      e(clustvar)         name of cluster variable
      e(offset)           linear offset variable
      e(chi2type)         Wald or LR; type of model chi-squared test
      e(vce)              vcetype specified in vce()
      e(vcetype)          title used to label Std. Err.
      e(opt)              type of optimization
      e(which)            max or min; whether optimizer is to perform
                            maximization or minimization
      e(ml_method)        type of ml method
      e(user)             name of likelihood-evaluator program
      e(technique)        maximization technique
      e(properties)       b V
      e(estat_cmd)        program used to implement estat
      e(predict)          program used to implement predict
      e(marginsnotok)     predictions disallowed by margins
      e(asbalanced)       factor variables fvset as asbalanced
      e(asobserved)       factor variables fvset as asobserved



    Matrices       
      e(b)                coefficient vector
      e(Cns)              constraints matrix
      e(ilog)             iteration log (up to 20 iterations)
      e(gradient)         gradient vector
      e(mns)              vector of means of the independent variables
      e(rules)            information about perfect predictors
      e(V)                variance-covariance matrix of the estimators
      e(V_modelbased)     model-based variance



    Functions      
      e(sample)           marks estimation sample