def fitNull(self, verbose=False, cache=False, out_dir='./cache', fname=None, rewrite=False, seed=None, n_times=10, factr=1e3, init_method=None):
        """
        Fit null model
        """
        if seed is not None:    sp.random.seed(seed)

        read_from_file = False
        if cache:
            assert fname is not None, 'MultiTraitSetTest:: specify fname'
            if not os.path.exists(out_dir):
                os.makedirs(out_dir)
            out_file = os.path.join(out_dir,fname)
            read_from_file = os.path.exists(out_file) and not rewrite

        RV = {}
        if read_from_file:
            f = h5py.File(out_file,'r')
            for key in list(f.keys()):
                RV[key] = f[key][:]
            f.close()
            self.setNull(RV)
        else:
            start = TIME.time()
            if self.bgRE:
                self._gpNull = GP2KronSum(Y=self.Y, F=None, A=None, Cg=self.Cg, Cn=self.Cn, R=None, S_R=self.S_R, U_R=self.U_R)
            else:
                self._gpNull = GP2KronSumLR(self.Y, self.Cn, G=sp.ones((self.N,1)), F=self.F, A=self.A)
                # freezes Cg to 0
                n_params = self._gpNull.covar.Cr.getNumberParams()
                self._gpNull.covar.Cr.setParams(1e-9 * sp.ones(n_params))
                self._gpNull.covar.act_Cr = False
            for i in range(n_times):
                params0 = self._initParams(init_method=init_method)
                self._gpNull.setParams(params0)
                conv, info = self._gpNull.optimize(verbose=verbose, factr=factr)
                if conv: break
            if not conv:    warnings.warn("not converged")
            LMLgrad = (self._gpNull.LML_grad()['covar']**2).mean()
            LML = self._gpNull.LML()
            if self._gpNull.mean.n_terms==1:
                RV['B'] = self._gpNull.mean.B[0]
            elif self._gpNull.mean.n_terms>1:
                warning.warn('generalize to more than 1 fixed effect term')
            if self.bgRE:
                RV['params0_g'] = self.Cg.getParams()
            else:
                RV['params0_g'] = sp.zeros_like(self.Cn.getParams())
            RV['params0_n'] = self.Cn.getParams()
            if self.bgRE:
                RV['Cg'] = self.Cg.K()
            else:
                RV['Cg'] = sp.zeros_like(self.Cn.K())
            RV['Cn'] = self.Cn.K()
            RV['conv'] = sp.array([conv])
            RV['time'] = sp.array([TIME.time()-start])
            RV['NLL0'] = sp.array([LML])
            RV['LMLgrad'] = sp.array([LMLgrad])
            RV['nit'] = sp.array([info['nit']])
            RV['funcalls'] = sp.array([info['funcalls']])
            self.null = RV
            if cache:
                f = h5py.File(out_file,'w')
                smartDumpDictHdf5(RV,f)
                f.close()
        return RV