# Multivariate Count Conditional Transformation Models A proof-of-concept implementation of multivariate conditional transformation models for count data. ```r mcotram(..., formula = ~ 1, data, conditional = FALSE, theta = NULL, fixed = NULL, scale = FALSE, optim = mltoptim(hessian = TRUE), M = 1000, dofit = TRUE, domargins = TRUE) ``` ## Arguments - ``...``: marginal count transformation models, one for each response - `formula`: a model formula describing a model for the dependency structure via the lambda parameters. The default is set to `~ 1` for constant lambdas. - `data`: a data.frame. - `conditional`: logical; parameters are defined conditionally (only possible when all models are probit models). This is the default as described by Klein et al. (2022). If `FALSE`, parameters can be directly interpreted marginally, this is explained in Section 2.6 by Klein et al. (2022). Using `conditional = FALSE` with probit-only models gives the same likelihood but different parameter estimates. - `theta`: an optional vector of starting values. - `fixed`: an optional named numeric vector of predefined parameter values. - `scale`: a logical indicating if (internal) scaling shall be applied to the model coefficients. - `optim`: a list of optimisers as returned by `mltoptim` - `M`: number of Halton sequences used to approximate the log-likelihood in `lpmvnorm`. - `dofit`: logical; parameters are fitted by default, otherwise a list with log-likelihood and score function is returned. - `domargins`: logical; all model parameters are fitted by default, including the parameters of marginal models. ## Details The function implements multivariate count conditional transformation models. The response is assumed to be a vector of counts. ## Returns An object of class `mmlt` with `coef` and `predict` methods. ## References Luisa Barbani, Roland Brandl, Torsten Hothorn (2022), Multi-species Count Transformation Models, tools:::Rd_expr_doi("10.48550/arXiv.2201.13095") . Nadja Klein, Torsten Hothorn, Luisa Barbanti, Thomas Kneib (2020), Multivariate Conditional Transformation Models. **Scandinavian Journal of Statistics**, tools:::Rd_expr_doi("10.1111/sjos.12501") . ## Examples ```r library("cotram") data("spiders", package = "cotram") ### for illustration only OR <- 1 ### order of transformation function ### OR = 1 means log-linear, use OR ~ 6 M <- 100 ### number of Halton sequences, seem sufficient here fastopt <- mltoptim(abstol = 1e-3, reltol = 1e-3) ### faster convergence ## fit conditional marginal count transformation models ## one for each species m_PF <- cotram(Pardosa_ferruginea ~ Elevation + Canopy_openess, data = spiders, method = "probit", order = OR) m_HL <- cotram(Harpactea_lepida ~ Elevation + Canopy_openess, data = spiders, method = "probit", order = OR) m_CC <- cotram(Callobius_claustrarius ~ Elevation + Canopy_openess, data = spiders, method = "probit", order = OR) m_CT <- cotram(Coelotes_terrestris ~ Elevation + Canopy_openess, data = spiders, method = "probit", order = OR) m_PL <- cotram(Pardosa_lugubris ~ Elevation + Canopy_openess, data = spiders, method = "probit", order = OR) m_PR <- cotram(Pardosa_riparia ~ Elevation + Canopy_openess, data = spiders, method = "probit", order = OR) ### fit dependence parameters mm <- mcotram(m_PF, m_HL, m_CC, m_CT, m_PL, m_PR, data = spiders, M = M, scale = TRUE, optim = fastopt) logLik(mm) ### Kendall's tau: Dependence of species after accounting ### for elevation and canopy openess in marginal models coef(mm, type = "Kendall") ### regress dependencies on elevation and canopy openess mmc <- mcotram(m_PF, m_HL, m_CC, m_CT, m_PL, m_PR, data = spiders, formula = ~ Elevation + Canopy_openess, M = M, scale = TRUE, optim = fastopt) logLik(mmc) ### weak evidence for such effects pchisq(2 * (logLik(mmc) - logLik(mm)), df = 30, lower.tail = FALSE) ### plot Kendall's tau for different elevations / openess levels nd <- expand.grid(Elevation = 80:120 * 10, Canopy_openess = 1:10 * 10) KD <- Lower_tri(coef(mmc, newdata = nd, type = "Kendall")) f <- factor(rownames(KD)) nd <- cbind(f = rep(f, nrow(nd)), nd[rep(1:nrow(nd), each = nlevels(f)),]) nd$KD <- c(KD) if (require("lattice")) contourplot(KD ~ Elevation + Canopy_openess | f, data = nd, cuts = 18, xlab = "Elevation", ylab = "Canopy openess") ### for example: ### => constant negative dependence of Pardosa_lugubris and Coelotes_terrestris ### => weak dependence of Harpactea_lepida and Pardosa_ferruginea ### for low elevations, negative dependence increasing with elevation ```

mcotram function