p7]c@sdZddlZddlZddlZddljjZddl j Z ddl Z ddl mZddlmZddlmZddlmZddlZdefdYZd efd YZd Zd ejfd YZdejfdYZdS(se This module implements maximum likelihood-based estimation (MLE) of Gaussian models for finite-dimensional observations made on infinite-dimensional processes. The ProcessMLE class supports regression analyses on grouped data, where the observations within a group are dependent (they are made on the same underlying process). The main application is repeated measures regression for temporal (longitudinal) data, in which the repeated measures occur at arbitrary real-valued time points. The mean structure is specified as a linear model. The covariance parameters depend on covariates via a link function. iN(t string_types(tminimize(tsummary2(t approx_fprimetProcessCovariancecBs eZdZdZdZRS(s A covariance model for a process indexed by a real parameter. An implementation of this class is based on a positive definite correlation function h that maps real numbers to the interval [0, 1], such as the Gaussian (squared exponential) correlation function :math:`\exp(-x^2)`. It also depends on a positive scaling function `s` and a positive smoothness function `u`. cCs tdS(s Returns the covariance matrix for given time values. Parameters ---------- time : array-like The time points for the observations. If len(time) = p, a pxp covariance matrix is returned. sc : array-like The scaling parameters for the observations. sm : array-like The smoothness parameters for the observation. See class docstring for details. N(tNotImplementedError(tselfttimetsctsm((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pytget_cov)scCs tdS(s The Jacobian of the covariance respect to the parameters. See get_cov for parameters. Returns ------- jsc : list-like jsc[i] is the derivative of the covariance matrix with respect to the i^th scaling parameter. jsm : list-like jsm[i] is the derivative of the covariance matrix with respect to the i^th smoothness parameter. N(R(RRRR ((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pytjac:s(t__name__t __module__t__doc__R R (((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyRs  tGaussianCovariancecBs eZdZdZdZRS(s An implementation of ProcessCovariance using the Gaussian kernel. This class represents a parametric covariance model for a Gaussian process as described in the work of Paciorek et al. cited below. Following Paciorek et al [1]_, the covariance between observations with index `i` and `j` is given by: .. math:: s[i] \cdot s[j] \cdot h(|time[i] - time[j]| / \sqrt{(u[i] + u[j]) / 2}) \cdot \frac{u[i]^{1/4}u[j]^{1/4}}{\sqrt{(u[i] + u[j])/2}} The ProcessMLE class allows linear models with this covariance structure to be fit using maximum likelihood (ML), which is equivalent to generalized least squares (GLS) in this setting. The mean and covariance parameters of the model are fit jointly. The mean, scaling, and smoothing parameters can be linked to covariates. The mean parameters are linked linearly, and the scaling and smoothing parameters use an exponential link to preserve positivity. The reference of Paciorek et al. below provides more details. Note that here we only implement the 1-dimensional version of their approach. References ---------- .. [1] Paciorek, C. J. and Schervish, M. J. (2006). Spatial modeling using a new class of nonstationary covariance functions. Environmetrics, 17:483–506. https://papers.nips.cc/paper/2350-nonstationary-covariance-functions-for-gaussian-process-regression.pdf cCstjj||}tjj||d}|||}tj| dtj|}|tj||d9}|tj||9}|S(Nig?(tnptsubtracttoutertaddtexptsqrt(RRRR tdatdstqmattcm((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyR qs!cCstjj||}tjj||d}tj|}||}||}t|} tj| d} tj||d} | | |} | |d} tj| | f}tj| | f}tj||}g}x1t|D]#\}}|d9}||ddfcd7<|dd|fcd7$t(tsuperR>t__init__thasattrtlistR?RR2tdatat param_namestNoneRtcovR=t collectionst defaultdictRRt _groups_ixtFalsetverboseR7tk_exogR8tk_scaleR9tk_smoothR:tk_noise(RR6R7R8R9R:RR;RItkwargstxnamestjt groups_ixR*tg((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyRCsJ *...       cCs|jj}d}||||j!}||j7}||||j!}||j7}||||j!}||j7}||||j!}||||fS(Ni(RFRGRORPRQRR(RRTtqt mean_namest scale_namest smooth_namest noise_names((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyt_split_param_names1s    cOsYd|kr|d}n tdd|kr>|d}n tdd|krc|d} n tdd|kr|d} n tdd |kr|d } n td |dk rtjd n|dk rtjd nt| trtj|| } nt| tr;tj|| } ntj ||} | j } | j }tj| } tj ||}|j }|j }tj|}tj | |}|j }|j }tj|}t t |j|d |ddd| d|d|d| d | }| |j_||j_||j_|j||||j_|S(Nt scale_formulas$scale_formula is a required argumenttsmooth_formulas%smooth_formula is a required argumentt noise_formulas$noise_formula is a required argumentRstime is a required argumentR;sgroups is a required arguments'subset' is ignoreds'drop_cols' is ignoredRFtsubsetR8R9R:(R5RHtwarningstwarnt isinstanceRRtasarraytpatsytdmatrixt design_infot column_namesRBR>t from_formulaRFtscale_design_infotsmooth_design_infotnoise_design_infot exog_namesRG(tclstformulaRFRat drop_colstargsRSR^R_R`RR;R8RkRZR9RlR[R:RmR\tmod((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyRj=sb                           c Cs|jjd}|d|!}|jjd}||||!}|jjd}||||||!}||||}||||fS(s@ Split the packed parameter vector into blocks. ii(R7R2R8R9( Rtztpmtmnpartpvtscpartpstsmpartnopar((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pytunpacks cCsutj|j|j}|j}|jjd|jjd}||jjd7}t j |j t j |fS(Ni( R tOLSR6R7tfitR8R2R9R:Rt concatenatetparamsR(Rtmodeltresulttm((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyt _get_starts  cCsy|j|\}}}}|jtj|j|}tjtj|j|}tjtj|j|}tjtj|j|} d} x|j j D]\} } |j j |j | || || } | jdd| jddc| | d7<|| }| dtjj| d8} | dtj|tjj| |8} qW|jrud| fGHn| S(s Calculate the log-likelihood function for the model. Parameters ---------- params : array-like The packed parameters for the model. Returns ------- The log-likelihood value at the given parameter point. Notes ----- The mean, scaling, and smoothing parameters are packed into a vector. Use `unpack` to access the component vectors. gNiiig?sL=(R|R6RtdotR7RR8R9R:RLtitemsRIR RtflatR2tlinalgtslogdettsolveRN(RRRvRxRzR{tresidRR tnotllR+tixRtre((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pytloglikes'/ - c& Cs|j|\}}}}t|t|t|}}}|jtj|j|} tjtj|j|} tjtj|j|} tjtj|j |} tj t|t|t|t|} x|j j D]\}}| |}| |}| |}| |}|j |}|j|ddf}|j|ddf}|j|ddf}|j |ddf}|jj|||}|jdd|jddc| |d7s1 9 J  2 X U 2RcBsMeZdZdZdedZdZdZdddddZ RS(s? Results class for Gaussian process regression models. cCstt|j|||j|j}|d|_|d|_|d|_|d|_|j j dt |j|_ |j jj d|_|j jj d|_|j jj d|_|j jj d|_dS(Niiii(RBRRCR|Rt mean_paramsRRt no_paramsR6R2Rtdf_residRR7ROR8RPR9RQR:RR(RRtmlefittpa((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyRCs      cOs`|stjdnt|dks:t|dkrJtjdn|jj|j|S(Ns''transform=False' is ignored in predictis$extra arguments ignored in 'predict'(RbRcRRRR(RR7t transformRrRS((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyRs $cCs"|jj||j|j||S(s Returns a fitted covariance matrix. Parameters ---------- time : array-like The time points at which the fitted covariance matrix is calculated. scale : array-like The data used to determine the scale parameter, must have len(time) rows. smooth: array-like The data used to determine the smoothness parameter, must have len(time) rows. Returns ------- A covariance matrix. Notes ----- If the model was fit using formulas, `scale` and `smooth` should be Dataframes, containing all variables that were present in the respective scaling and smoothing formulas used to fit the model. Otherwise, `scale` and `smooth` should be data arrays whose columns align with the fitted scaling and smoothing parameters. (RRRR(RRRtsmooth((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyRsc Cs|jj|}t|dkrAdt|}t|n|jj|ddf}|jj|ddf}|jj\}}}}tj |d|}tj |d|}|jj |} |jj | |j |j ||S(NisGroup '%s' does not existR?(RRLRRR5R8R9R]tpdt DataFrameRRRR( RtgroupRR<RRR+RZR[R((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pytcovariance_groups g?c Cstj}dg|jdg|jdg|jdg|j|d<|j|d|t|is[%.3fs%.3f]s#Gaussian process regression results(RRRORPRQRRRRRtdiagRRtnantscipy.stats.distributionsRRtsftabsRtppfRRFRGtindexRtSummaryRHt add_titletadd_df( RtynametxnamettitletalphatdfRRtsumm((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pytsummary7s( > & #!%     N( R R RRCRHtTrueRRRR(((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyRs   (RtnumpyRtpandasRRftstatsmodels.base.modeltbaseRtstatsmodels.apitapiR RJtstatsmodels.compat.pythonRtscipy.optimizeRtstatsmodels.iolibRtstatsmodels.tools.numdiffRRbtobjectRRR=tLikelihoodModelR>tGenericLikelihoodModelResultsR(((sHlib/python2.7/site-packages/statsmodels/regression/process_regression.pyts$     ._ "