{smcl} {* documented: June 12, 2007}{...} {* revised: December 16, 2011}{...} {cmd:help fmm} {right:also see: {helpb fmm postestimation}} {hline} {title:Title} {cmd :fmm} {hline 2} Finite mixture models {title:Syntax} {phang} Finite mixture models {p 8 14 2} {cmd:fmm} {depvar} [{indepvars}] {ifin} {weight}{cmd:,} {opt comp:onents(#)} {opth mix:tureof(fmm##density:density)} [{it:{help fmm##fmm_options:fmm_options}}] {synoptset 28 tabbed}{...} {marker fmm_options}{...} {synopthdr :fmm_options} {synoptline} {syntab :Model} {synopt :{opt comp:onents(#)}}specifies the number of mixture components. It is required.{p_end} {synopt :{opth mix:tureof(fmm##density:density)}}specifies the component density. It is required.{p_end} {syntab :Model 2} {synopt :{opth prob:ability(varlist)}}specifies the variables used to model the component probabilities.{p_end} {synopt :{opt df(#)}}specifies the degrees of freedom of the Student-t density. The default is 5.{p_end} {synopt :{opt nocons:tant}}suppress constant term{p_end} {synopt :{opth exp:osure(varname)}}include ln({it:varname}) in model with coefficient constrained to 1.{p_end} {synopt :{opth off:set(varname)}}include {it:varname} in model with coefficient constrained to 1.{p_end} {synopt :{opth cons:traint(constraint)}}apply specified linear constraints.{p_end} {syntab :SE/Robust} {synopt :{opth vce(vcetype)}}{it:vcetype} may be {opt oim}, {opt r:obust}, {opt opg}, {opt boot:strap}, or {opt jack:knife}{p_end} {synopt :{opt r:obust}}synonym for {cmd:vce(robust)}{p_end} {synopt :{opth cl:uster(varname)}}adjust standard errors for intragroup correlation{p_end} {syntab :Max options} {synopt :{it:{help fmm##fmm_maximize:maximize_options}}}control the maximization process; some options may be useful{p_end} {synoptline} {p2colreset}{...} {p 4 6 2} {it:depvar}, {it:indepvars}, {it:varname_e}, and {it:varname_o} may contain time-series operators; see {help tsvarlist}.{p_end} {p 4 6 2} {cmd:fweight}s, {cmd:pweight}s, {cmd:iweight}s, and {cmd:aweight}s are allowed; see {help weight}.{p_end} {p 4 6 2} See {help postestimation commands} for features available after estimation. {marker density}{...} {synoptset 23}{...} {synopthdr :density} {synoptline} {synopt :{opt gamma}}Gamma{p_end} {synopt :{opt lognormal}}Lognormal{p_end} {synopt :{opt negbin1}}Negative Binomial-1 (constant dispersion){p_end} {synopt :{opt negbin2}}Negative Binomial-2 (mean dispersion){p_end} {synopt :{opt normal}}Normal or Gaussian{p_end} {synopt :{opt poisson}}Poisson{p_end} {synopt :{opt studentt}}Student-t with {opt df} degrees of freedom{p_end} {synoptline} {p2colreset}{...} {title:Description} {pstd} {cmd:fmm} fits a finite mixture regression model of {it:depvar} on {it:indepvars} using maximum likelihood estimation. The model is a {it:J}-component finite mixture of densities, with the density within a component (j) allowed to vary in location and scale. Optionally, the mixing probabilities may be specified with covariates. {title:Options for fmm} {dlgtab:Model} {phang} {opt comp:onents(#)} specifies the number of mixing components. It is an integral part of specifying the finite mixture model and is not optional. {it:#} should be an integer between 2 and 9. {phang} {opt mix:tureof(density)} specifies the component density in the mixture model. It is not optional. For more on the available choices of component densities and associated specifications of conditional means, see {opt Remarks} below. {dlgtab:Model 2} {phang} {opt prob:ability(varlist)} specifies the variables used to model the component probabilities. The probabilities are specified using a multinomial logit parameterization. {phang} {opt df(#)} specifies the degrees of freedom if a Student-t component density is specified. The default value is 5. {phang} {opt nocons:tant}, {opth exp:osure(varname)}, {opt off:set(varname)}, {opt cons:traints(constraints)}; see {help estimation options}. {dlgtab:SE/Robust} {phang} {opt vce(vcetype)}; see {it:{help vce_option}}. {phang} {opt r:obust}, {opt cl:uster(varname)}; see {help estimation options}. {opt cl:uster()} can be used with {help pweight}s to produce estimates for unstratified cluster-sampled data. {dlgtab:Reporting} {phang} {opt level(#)}; see {help estimation options}. {marker fmm_maximize}{...} {dlgtab:Max options} {phang} {it:maximize_options}: {opt dif:ficult}, {opt tech:nique(algorithm_spec)}, {opt iter:ate(#)}, [{cmdab:no:}]{opt lo:g}, {opt tr:ace}, {opt grad:ient}, {opt showstep}, {opt hess:ian}, {opt shownr:tolerance}, {opt tol:erance(#)}, {opt ltol:erance(#)}, {opt gtol:erance(#)}, {opt nrtol:erance(#)}, {opt nonrtol:erance}, {opt fr:om(init_specs)}; see {help maximize} are standard {help ml} options.{p_end} {phang} {opt sh:ift(#)} generates alternative starting values by systematically shifting some values from the default algorithm by the proportion {opt #}.{p_end} {phang} {opt se:arch(spec)} {it:spec} may be {opt on} or {opt off} and specifies whether {help ml}'s initial search algorithm is used. The default is {opt off}.{p_end} {phang} Because finite mixture models have complicated likelihood functions, {opt shift(#)}, {opt search(spec)}, {opt dif:ficult} and {opt from(init_specs)} may be useful choices if the default setup fails. The other options are seldom used.{p_end} {title:Remarks} {pstd} If {opt components(2)} is specified, default starting values are specified using the parameters from the associate degenerate mixture model. In order to take advantage of the built-in algorithms for specifying starting values for models with {it #} components, ({it #}>2), the user must estimate models sequentially {it #}=2. This is the preferred estimation approach. But {cmd:fmm} will not check for reasonableness of the prior {cmd:fmm} estimates, so proceed carefully. Otherwise, {cmd:fmm} expects the user to specify starting values using the {opt from(init_specs)} option.{p_end} {pstd} The available component densities and the associated conditional means are {tab}Density {col 30} {cmd:fmm} option {col 50} cond. mean {tab}{hline 70} {tab}Gamma {col 30} {cmd:density(gamma)} {col 50} alpha_j exp(xb_j) {tab}Lognormal {col 30} {cmd:density(lognormal)} {col 50} exp(xb_j + 0.5 sigma_j^2) {tab}Negative Binomial-1 {col 30} {cmd:density(negbin1)} {col 50} exp(xb_j) {tab}Negative Binomial-2 {col 30} {cmd:density(negbin2)} {col 50} exp(xb_j) {tab}Normal(Gaussian) {col 30} {cmd:density(normal)} {col 50} xb_j {tab}Poisson {col 30} {cmd:density(poisson)} {col 50} exp(xb_j) {tab}Student-t {col 30} {cmd:density(studentt)} {col 50} xb_j {pstd} Note that {cmd:fmm} has not been updated to accommodate factor variables. {title:Saved results} {pstd}In addition to standard results saved by maximum likelihood procedures in {opt e()}, {cmd:fmm} saves the following scalars: {tab}{opt e(parname_est)} parameter estimate {tab}{opt e(parname_se)} standard error of estimate {pstd}where {it:parname} denotes either a scale parameter or a mixing probability parameter. {title:Examples} {pstd}Mixture of normals {phang}{stata "webuse womenwk, clear" : . webuse womenwk, clear} {phang}{stata "fmm wagefull educ age married, mix(normal) comp(2)" : . fmm wagefull educ age married, mix(normal) comp(2)} {pstd}Mixture of Negative Binomials (Type 2) {phang}{stata "webuse medpar, clear" : . webuse medpar, clear} {phang}{stata "gen los0 = los - 1" : . gen los0 = los - 1} {phang}{stata "fmm los0 died hmo type2-type3, mix(negbin2) comp(2)" : . fmm exlos died hmo type2-type3, mix(negbin2) comp(2) comp(2)} {title:References} {p 4 8 2}Conway, K. and P. Deb, (2005), Is Prenatal Care Really Ineffective? Or, is the 'Devil' in the Distribution?, {it:Journal of Health Economics}, 24, 489-513. {p 4 8 2}Deb, P. and P. K. Trivedi (1997), Demand for Medical Care by the Elderly: A Finite Mixture Approach, {it:Journal of Applied Econometrics}, 12, 313-326. {p 4 8 2}McLachlan, G.J., and D. Peel (2000), {it:Finite Mixture Models}, New York: John Wiley. {p 4 8 2}Titterington, D.M., A.F.M. Smith and U.E. Makow (1985), {it:Statistical Analysis of Finite Mixture Distributions}, New York: John Wiley, 1985. {title:Author} {phang}Partha Deb, Hunter College and the Graduate Center, City University of New York, USA{p_end} {phang}partha.deb@hunter.cuny.edu{p_end} {title:Also see} {psee} Online: {help fmm postestimation}{p_end}