# Log likelihood of a hidden Markov model Calculate the log likelihood of a hidden Markov model with discrete non-parametric observation distributions. ```r logLikHmm(y, model=NULL, tpm=NULL, ispd=NULL, Rho=NULL, X=NULL, addIntercept=NULL, warn=TRUE) ``` ## Arguments - `y`: A vector, or list of vectors, or a one or two column matrix or a list of such matrics, whose entries consist of observations from a hidden Markov model with discrete non-parametric observation distributions. - `model`: An object specifying a hidden Markov model, usually returned by `hmm()`. - `tpm`: The transition probability matrix of the Markov chain. Ignored (and extracted from `model`) if `model` is non-`NULL`. - `ispd`: The vector of probabilities specifying the initial state probability distribution, or a matrix each of whose columns is a trivial (delta function ) vector specifying the most probable initial state for each observation sequence. If `ispd` is missing then `ispd` is calculated as the stationary distribution determined by `tpm`. Ignored (and extracted from `model`) if `model` is non-`NULL`. - `Rho`: An object specifying the emission probabilities of the observations. (See the Details in the help for `hmm()`.) Ignored (and extracted from `model`) if `model` is non-`NULL`. - `X`: An optional **numeric** matrix, or a list of such matrices, of **predictors**. The use of such predictors is (currently, at least) applicable only in the univariate emissions setting. If `X` is a list it must be of the same length as `y` and all entries of this list must have the same number of columns. The number of rows of each entry must be equal to the length of the corresponding entry of `y`. If `X` is a matrix then `y` should be a vector or one-column matrix (or a list with a single entry equal to such). - `addIntercept`: Logical scalar. See the documentation of `hmm()`. If this argument is not specified, and if `model` is `NULL` then an error is thrown. - `warn`: Logical scalar; should a warning be issued if `Rho` hasn't got relevant dimension names? (Note that if this is so, then the corresponding dimension names are formed from the sorted unique values of `y` or of the appropriate column(s) of `y`. And if **this** is so, then the user should be sure that the ordering of the entries of `Rho` corresponds properly to the the sorted unique values of `y`.) This argument is passed to the utility function `check.yval()` which actually issues the warning if `warn=TRUE`. ## Details If `y` is not provided the function simply returns the `log.like` component of `model` (which could be `NULL` if `model` was not produced by `hmm()`. The observation values (the entries of the vector or matrix `y`, or of the vectors or matrices which constitute the entries of `y` if `y` is a list) must be consistent with the appropriate dimension names of `Rho` or of its entries when `Rho` is a list. More specifically, if `Rho` has dimension names (or its entries have dimension names) then the observation values must all be found as entries of the appropriate dimension name vector. If a vector of dimension names is `NULL` then the corresponding dimension must be equal to the number of unique observations of the appropriate variate. integers between `1` and `nrow(Rho)`. ## Returns The loglikehood of `y` given the parameter values specified in `par`. ## References See `hmm()` for references. ## Author(s) Rolf Turner r.turner@auckland.ac.nz ## See Also `hmm()`, `pr()`, `sp()` ## Examples ```r # TO DO: One or more bivariate examples. P <- matrix(c(0.7,0.3,0.1,0.9),2,2,byrow=TRUE) R <- matrix(c(0.5,0,0.1,0.1,0.3, 0.1,0.1,0,0.3,0.5),5,2) set.seed(42) lll <- sample(250:350,20,TRUE) set.seed(909) y.num <- rhmm(ylengths=lll,nsim=1,tpm=P,Rho=R,drop=TRUE) set.seed(909) y.let <- rhmm(ylengths=lll,nsim=1,tpm=P,Rho=R,yval=letters[1:5],drop=TRUE) row.names(R) <- 1:5 ll1 <- logLikHmm(y.num,tpm=P,Rho=R) row.names(R) <- letters[1:5] ll2 <- logLikHmm(y.let,tpm=P,Rho=R) ll3 <- logLikHmm(y.let,tpm=P,Rho=R,ispd=c(0.5,0.5)) fit <- hmm(y.num,K=2,itmax=10) ll4 <- logLikHmm(y.num,fit) # Use the fitted rather than the "true" parameters. ```

logLikHmm function