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Common VGAM Family Function Arguments

CommonVGAMffArguments.Rd

Here is a description of some common and typical arguments found in many VGAM family functions, e.g., zero, lsigma, isigma, gsigma, eq.mean, nsimEI and parallel.

Usage

TypicalVGAMfamilyFunction(lsigma = "loglink",
                          isigma = NULL,
                          zero = NULL, gsigma = exp(-5:5),
                          eq.mean = FALSE,
                          parallel = TRUE,
                          imethod = 1,
                          bhhh = FALSE, oim.bhhh = NULL,
                          vfl = FALSE, Form2 = NULL, 
                          type.fitted = c("mean", "quantiles", "Qlink",
                                          "pobs0", "pstr0", "onempstr0"),
                          percentiles = c(25, 50, 75),
                          probs.x = c(0.15, 0.85),
                          probs.y = c(0.25, 0.50, 0.75),
                          multiple.responses = FALSE, earg.link = FALSE,
                          ishrinkage = 0.95, nointercept = NULL,
                          whitespace = FALSE, bred = FALSE, lss = TRUE,
                          oim = FALSE, nsimEIM = 100, byrow.arg = FALSE,
                          link.list = list("(Default)" = "identitylink",
                                           x2          = "loglink",
                                           x3          = "logofflink",
                                           x4          = "multilogitlink",
                                           x5          = "multilogitlink"),
                          earg.list = list("(Default)" = list(),
                                           x2          = list(),
                                           x3          = list(offset = -1),
                                           x4          = list(),
                                           x5          = list()),
                          Thresh = NULL, nrfs = 1)

Arguments

lsigma

Character. Link function applied to a parameter and not necessarily a mean. See Links for a selection of choices. If there is only one parameter then this argument is often called link.

isigma

Optional initial values can often be inputted using an argument beginning with "i". For example, "isigma" and "ilocation", or just "init" if there is one parameter. A value of NULL means a value is computed internally, i.e., a self-starting VGAM family function. If a failure to converge occurs make use of these types of arguments.

zero

An important argument, either an integer vector, or a vector of character strings.

If an integer, then it specifies which linear/additive predictor is modelled as intercept-only. That is, the regression coefficients are set to zero for all covariates except for the intercept. If zero is specified then it may be a vector with values from the set \(\{1,2,\ldots,M\}\). The value zero = NULL means model all linear/additive predictors as functions of the explanatory variables. Here, \(M\) is the number of linear/additive predictors. Technically, if zero contains the value \(j\) then the \(j\)th row of every constraint matrix (except for the intercept) consists of all 0 values.

Some VGAM family functions allow the zero argument to accept negative values; if so then its absolute value is recycled over each (usual) response. For example, zero = -2 for the two-parameter negative binomial distribution would mean, for each response, the second linear/additive predictor is modelled as intercepts-only. That is, for all the \(k\) parameters in negbinomial (this VGAM family function can handle a matrix of responses).

Suppose zero = zerovec where zerovec is a vector of negative values. If \(G\) is the usual \(M\) value for a univariate response then the actual values for argument zero are all values in c(abs(zerovec), G + abs(zerovec), 2*G + abs(zerovec), ... ) lying in the integer range \(1\) to \(M\). For example, setting zero = -c(2, 3) for a matrix response of 4 columns with zinegbinomial (which usually has \(G = M = 3\) for a univariate response) would be equivalent to zero = c(2, 3, 5, 6, 8, 9, 11, 12). This example has \(M = 12\). Note that if zerovec contains negative values then their absolute values should be elements from the set 1:G.

Note: zero may have positive and negative values, for example, setting zero = c(-2, 3) in the above example would be equivalent to zero = c(2, 3, 5, 8, 11).

The argument zero also accepts a character vector (for VGAM 1.0-1 onwards). Each value is fed into grep with fixed = TRUE, meaning that wildcards "*" are not useful. See the example below—all the variants work; those with LOCAT issue a warning that that value is unmatched. Importantly, the parameter names are c("location1", "scale1", "location2", "scale2") because there are 2 responses. Yee (2015) described zero for only numerical input. Allowing character input is particularly important when the number of parameters cannot be determined without having the actual data first. For example, with time series data, an ARMA(\(p\),\(q\)) process might have parameters \(\theta_1,\ldots,\theta_p\) which should be intercept-only by default. Then specifying a numerical default value for zero would be too difficult (there are the drift and scale parameters too). However, it is possible with the character representation: zero = "theta" would achieve this. In the future, most VGAM family functions might be converted to the character representation—the advantage being that it is more readable. When programming a VGAM family function that allows character input, the variable predictors.names must be assigned correctly.

If the constraints argument is used then the family function's zero argument (if it exists) needs to be set to NULL. This avoids what could be a probable contradiction. Sometimes setting other arguments related to constraint matrices to FALSE is also a good idea, e.g., parallel = FALSE, exchangeable = FALSE.

gsigma

Grid-search initial values can be inputted using an argument beginning with "g", e.g., "gsigma", "gshape" and "gscale". If argument isigma is inputted then that has precedence over gsigma, etc. If the grid search is 2-dimensional then it is advisable not to make the vectors too long as a nested for loop may be used. Ditto for 3-dimensions etc. Sometimes a ".mux" is added as a suffix, e.g., gshape.mux; this means that the grid is created relatively and not absolutely, e.g., its values are multipled by some single initial estimate of the parameter in order to create the grid on an absolute scale.

Some family functions have an argument called gprobs.y. This is fed into the probs argument of quantile in order to obtain some values of central tendency of the response, i.e., some spread of values in the middle. when imethod = 1 to obtain an initial value for the mean Some family functions have an argument called iprobs.y, and if so, then these values can overwrite gprobs.y.

eq.mean

Logical. Constrain all the means to be equal? This type of argument is simpler than parallel because only a single TRUE or FALSE can be assigned and not a formula. Thus if TRUE then it will be enforced over all variables.

parallel

A logical, or a simple formula specifying which terms have equal/unequal coefficients. The formula must be simple, i.e., additive with simple main effects terms. Interactions and nesting etc. are not handled. To handle complex formulas use the constraints argument (of vglm etc.); however, there is a lot more setting up involved and things will not be as convenient.

Here are some examples. 1. parallel = TRUE ~ x2 + x5 means the parallelism assumption is only applied to \(X_2\), \(X_5\) and the intercept. 2. parallel = TRUE ~ -1 and parallel = TRUE ~ 0 mean the parallelism assumption is applied to no variables at all. Similarly, parallel = FALSE ~ -1 and parallel = FALSE ~ 0 mean the parallelism assumption is applied to all the variables including the intercept. 3. parallel = FALSE ~ x2 - 1 and parallel = FALSE ~ x2 + 0 applies the parallelism constraint to all terms (including the intercept) except for \(X_2\). 4. parallel = FALSE ~ x2 * x3 probably will not work. Instead, expand it out manually to get parallel = FALSE ~ x2 + x3 + x2:x3, and that should work. That's because the main formula processes or expands the "*" operator but parallel does not. 5. To check whether parallel has done what was expected, type coef(fit, matrix = TRUE) or constraints(fit) for confirmation.

This argument is common in VGAM family functions for categorical responses, e.g., cumulative, acat, cratio, sratio. For the proportional odds model (cumulative) having parallel constraints applied to each explanatory variable (except for the intercepts) means the fitted probabilities do not become negative or greater than 1. However this parallelism or proportional-odds assumption ought to be checked.

nsimEIM

Some VGAM family functions use simulation to obtain an approximate expected information matrix (EIM). For those that do, the nsimEIM argument specifies the number of random variates used per observation; the mean of nsimEIM random variates is taken. Thus nsimEIM controls the accuracy and a larger value may be necessary if the EIMs are not positive-definite. For intercept-only models (y ~ 1) the value of nsimEIM can be smaller (since the common value used is also then taken as the mean over the observations), especially if the number of observations is large.

Some VGAM family functions provide two algorithms for estimating the EIM. If applicable, set nsimEIM = NULL to choose the other algorithm.

imethod

An integer with value 1 or 2 or 3 or ... which specifies the initialization method for some parameters or a specific parameter. If failure to converge occurs try the next higher value, and continue until success. For example, imethod = 1 might be the method of moments, and imethod = 2 might be another method. If no value of imethod works then it will be necessary to use arguments such as isigma. For many VGAM family functions it is advisable to try this argument with all possible values to safeguard against problems such as converging to a local solution. VGAM family functions with this argument usually correspond to a model or distribution that is relatively hard to fit successfully, therefore care is needed to ensure the global solution is obtained. So using all possible values that this argument supplies is a good idea.

VGAM family functions such genpoisson2 recycle imethod to be of length 2 corresponding to the 2 parameters. In the future, this feature will be extended to other family functions to confer more flexibility.

bhhh

The BHHH method has now been implemented in vglm.control so it works at a much wider level rather than being family function specific. What is below are remnants of some dated information that may be deleted in the future.

Logical. Use the BHHH method? Although VGAM is primarily based on Fisher scoring, the EIM for some models cannot be derived or be computed. For those, the Berndt-Hall-Hall-Hausman algorithm might be implemented or be an alternative. Being an approximation, The results should not differ much if \(n\) is very large, however for small \(n\) the difference can be substantial, e.g., Greene (2012).

oim.bhhh

Numeric. Shrinkage factor between the BHHH working weights and the OIM. Is used only if bhhh = TRUE and valid values are in \([0, 1]\). So oim.bhhh = 0.9 should be very similar to Newton–Raphson. Individual negative Hessian matrices may be negative-definite depending on the response, hence it is necessary for the IRLS algorithm to shrink them towards a positive-definite matrix, such as that provided by the BHHH method.

Form2

Formula. Using applied to models with \(M=2\). Specifies the terms for \(\eta_2\) and the other terms belong to \(\eta_1\). It is a way to partition the X matrix into two sets of covariates, where they are assigned to each \(\eta_j\) separately. This argument sets up constraint matrices rbind(0, 1) for terms in Form2 and rbind(1, 0) for setdiff(formula, Form2) so to speak. Note that sometimes this argument is only accessed if vfl = TRUE. Arguments such as Form1 and Form3 are also possible in VGAM family functions because the \(\eta_j\) which is likely to be modelled more simply is chosen for convenience.

vfl

A single logical. This stands for variance factorized loglinear (VFL) model. If TRUE then usually some other argument such as Form2 or parallel is used to partition the main vglm formula into two sets of covariates. For some families such as negbinomial this enables overdispersion to be modelled conveniently via a loglinear model, given the mean. It is necessary to read the online help regarding each VGAM family function because each one may different from others. To fit some VFL models it is necessary to make a copy of existing covariates by creating new variable names and then adding it to the main formula.

A good question is: why is vfl necessary? Wouldn't Form2 be sufficient? Setting vfl = TRUE enables some internal checking such as avoiding conflicts. For example, it is often necessary to set zero = NULL and parallel = FALSE, otherwise there would be contradictions.

type.fitted

Character. Type of fitted value returned by the fitted() methods function. The first choice is always the default. The available choices depends on what kind of family function it is. Using the first few letters of the chosen choice is okay. See fittedvlm for more details.

The choice "Qlink" refers to quantile-links, which was introduced in December 2018 in VGAMextra 0.0-2 for several 1-parameter distributions. Here, either the loglink or logitlink or identitylink of the quantile is the link function (and the choice is dependent on the support of the distribution), and link functions end in "Qlink". A limited amount of support is provided for such links, e.g., fitted(fit) are the fitted quantiles, which is the same as predict(fit, type = "response"). However, fitted(fit, percentiles = 77) will not work.

percentiles

Numeric vector, with values between 0 and 100 (although it is not recommended that exactly 0 or 100 be inputted). Used only if type.fitted = "quantiles" or type.fitted = "percentiles", then this argument specifies the values of these quantiles. The argument name tries to reinforce that the values lie between 0 and 100. See fittedvlm for more details.

probs.x, probs.y

Numeric, with values in (0, 1). The probabilites that define quantiles with respect to some vector, usually an x or y of some sort. This is used to create two subsets of data corresponding to `low' and `high' values of x or y. Each value is separately fed into the probs argument of quantile. If the data set size is small then it may be necessary to increase/decrease slightly the first/second values respectively.

lss

Logical. This stands for the ordering: location, scale and shape. Should the ordering of the parameters be in this order? Almost all VGAM family functions have this order by default, but in order to match the arguments of existing R functions, one might need to set lss = FALSE. For example, the arguments of weibullR are scale and shape, whereas rweibull are shape and scale. As a temporary measure (from VGAM 0.9-7 onwards but prior to version 1.0-0), some family functions such as sinmad have an lss argument without a default. For these, setting lss = FALSE will work. Later, lss = TRUE will be the default. Be careful for the dpqr-type functions, e.g., rsinmad.

Thresh

Thresholds is another name for the intercepts, e.g., for categorical models. They may be constrained by functions such as CM.equid and CM.qnorm. The string "CM." and the Thresh argument is pasted and then that function is called to obtain the constraint matrix for the intercept term. So Thresh = "free", Thresh = "equid", Thresh = "qnorm", Thresh = "symm0", Thresh = "symm1" etc. are possibilities. Families that use this include multinomial, cratio, sratio, cumulative, acat. The associated arguments are Trev, Tref and Intercept. Since Intercept = NULL always, this signifies using the "CM." function default.

whitespace

Logical. Should white spaces (" ") be used in the labelling of the linear/additive predictors? Setting TRUE usually results in more readability but it occupies more columns of the output.

oim

Logical. Should the observed information matrices (OIMs) be used for the working weights? In general, setting oim = TRUE means the Newton-Raphson algorithm, and oim = FALSE means Fisher-scoring. The latter uses the EIM, and is usually recommended. If oim = TRUE then nsimEIM is ignored.

nrfs

Numeric, a value in \([0, 1]\). Experimental argument for allowing a mixture of Newton-Raphson and Fisher scoring. The working weights are taken as a linear combination of the two. If nrfs = 0 then Newton-Raphson is used, i.e., the OIM is wholly used. If nrfs = 1 then Fisher scoring is used, i.e., the EIM is wholly used. If convergence is successful then one might expect Newton-Raphson to be faster than Fisher scoring because the former has an order-2 convergence rate while the latter has a linear rate.

,

multiple.responses

Logical. Some VGAM family functions allow a multivariate or vector response. If so, then usually the response is a matrix with columns corresponding to the individual response variables. They are all fitted simultaneously. Arguments such as parallel may then be useful to allow for relationships between the regressions of each response variable. If multiple.responses = TRUE then sometimes the response is interpreted differently, e.g., posbinomial chooses the first column of a matrix response as success and combines the other columns as failure, but when multiple.responses = TRUE then each column of the response matrix is the number of successes and the weights argument is of the same dimension as the response and contains the number of trials.

This argument should be generally ignored.

byrow.arg

Logical. Some VGAM family functions that handle multiple responses have arguments that allow input to be fed in which affect all the responses, e.g., imu for initalizing a mu parameter. In such cases it is sometime more convenient to input one value per response by setting byrow.arg = TRUE; then values are recycled in order to form a matrix of the appropriate dimension. This argument matches byrow in matrix; in fact it is fed into such using matrix(..., byrow = byrow.arg). This argument has no effect when there is one response.

ishrinkage

Shrinkage factor \(s\) used for obtaining initial values. Numeric, between 0 and 1. In general, the formula used is something like \(s \mu + (1-s) y\) where \(\mu\) is a measure of central tendency such as a weighted mean or median, and \(y\) is the response vector. For example, the initial values are slight perturbations of the mean towards the actual data. For many types of models this method seems to work well and is often reasonably robust to outliers in the response. Often this argument is only used if the argument imethod is assigned a certain value.

nointercept

An integer-valued vector specifying which linear/additive predictors have no intercepts. Any values must be from the set {1,2,...,\(M\)}. A value of NULL means no such constraints.

bred

Logical. Some VGAM family functions will allow bias-reduction based on the work by Kosmidis and Firth. Sometimes half-stepping is a good idea; set stepsize = 0.5 and monitor convergence by setting trace = TRUE.

Some VGAM family functions (such as normal.vcm) implement models with potentially lots of parameter link functions. These two arguments allow many such links and extra arguments to be inputted more easily. One has something like link.list = list ("(Default)" = "identitylink", x2 = "loglink", x3 = "logofflink") and earg.list = list ("(Default)" = list(), x2 = list(), x3 = "list(offset = -1)"). Then any unnamed terms will have the default link with its corresponding extra argument. Note: the multilogitlink link is also possible, and if so, at least two instances of it are necessary. Then the last term is the baseline/reference group.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Warning

The zero argument is supplied for convenience but conflicts can arise with other arguments, e.g., the constraints argument of vglm and vgam. See Example 5 below for an example. If not sure, use, e.g., constraints(fit) and coef(fit, matrix = TRUE) to check the result of a fit fit.

The arguments zero and nointercept can be inputted with values that fail. For example, multinomial(zero = 2, nointercept = 1:3) means the second linear/additive predictor is identically zero, which will cause a failure.

Be careful about the use of other potentially contradictory constraints, e.g., multinomial(zero = 2, parallel = TRUE ~ x3). If in doubt, apply constraints() to the fitted object to check.

VGAM family functions with the nsimEIM may have inaccurate working weight matrices. If so, then the standard errors of the regression coefficients may be inaccurate. Thus output from summary(fit), vcov(fit), etc. may be misleading.

Changes relating to the lss argument have very important consequences and users must beware. Good programming style is to rely on the argument names and not on the order.

Details

Full details will be given in documentation yet to be written, at a later date! A general recommendation is to set trace = TRUE whenever any model fitting is done, since monitoring convergence is usually very informative.

References

Yee, T. W. (2015). Vector Generalized Linear and Additive Models: With an Implementation in R. New York, USA: Springer.

Kosmidis, I. and Firth, D. (2009). Bias reduction in exponential family nonlinear models. Biometrika, 96, 793–804.

Berndt, E. K., Hall, B. H., Hall, R. E. and Hausman, J. A. (1974). Estimation and inference in nonlinear structural models, Annals of Economic and Social Measurement, 3–4, 653–665.

Greene, W. H. (2012). Econometric Analysis, 7th Edition. Prentice Hall: Harlow, Essex, UK.

Miranda-Soberanis, V. F. and Yee, T. W. (2019). New link functions for distribution–specific quantile regression based on vector generalized linear and additive models. Journal of Probability and Statistics, 5, 1–11.

See also

Links, vglm, vgam, vglmff-class, UtilitiesVGAM, multilogitlink, multinomial, VGAMextra.

Author

T. W. Yee

Examples

# Example 1
cumulative()
#> Family:  cumulative 
#> Informal classes: cumulative, VGAMordinal, VGAMcategorical 
#> 
#> Cumulative logitlink model
#> 
#> Links:   logitlink(P[Y<=j])
cumulative(link = "probitlink", reverse = TRUE, parallel = TRUE)
#> Family:  cumulative 
#> Informal classes: cumulative, VGAMordinal, VGAMcategorical 
#> 
#> Cumulative probitlink model
#> 
#> Links:   probitlink(P[Y>=j+1])

# Example 2
wdata <- data.frame(x2 = runif(nn <- 1000))
wdata <- transform(wdata,
         y = rweibull(nn, shape = 2 + exp(1 + x2), scale = exp(-0.5)))
fit <- vglm(y ~ x2,
            weibullR(lshape = "logofflink(offset = -2)", zero = 2),
# Was:      weibullR(lshape =  logofflink(offset = -2) , zero = 2),
            data = wdata)
coef(fit, mat = TRUE)
#>             loglink(scale) logofflink(shape, offset = -2)
#> (Intercept)    -0.48337769                       1.419395
#> x2             -0.03176123                       0.000000
fit@misc$earg
#> $scale
#> $scale$theta
#> 
#> 
#> $scale$bvalue
#> NULL
#> 
#> $scale$inverse
#> [1] FALSE
#> 
#> $scale$deriv
#> [1] 0
#> 
#> $scale$short
#> [1] TRUE
#> 
#> $scale$tag
#> [1] FALSE
#> 
#> attr(,"function.name")
#> [1] "loglink"
#> 
#> $shape
#> $shape$theta
#> 
#> 
#> $shape$offset
#> -2
#> 
#> $shape$inverse
#> [1] FALSE
#> 
#> $shape$deriv
#> [1] 0
#> 
#> $shape$short
#> [1] TRUE
#> 
#> $shape$tag
#> [1] FALSE
#> 
#> attr(,"function.name")
#> [1] "logofflink"
#> 

# Example 3; multivariate (multiple) response
if (FALSE) { # \dontrun{
ndata <- data.frame(x = runif(nn <- 500))
ndata <- transform(ndata,
           y1 = rnbinom(nn, exp(1), mu = exp(3+x)),  # k is size
           y2 = rnbinom(nn, exp(0), mu = exp(2-x)))
fit <- vglm(cbind(y1, y2) ~ x, negbinomial(zero = -2), ndata)
coef(fit, matrix = TRUE)
} # }
# Example 4
if (FALSE) { # \dontrun{
# fit1 and fit2 are equivalent
fit1 <- vglm(ymatrix ~ x2 + x3 + x4 + x5,
             cumulative(parallel = FALSE ~ 1 + x3 + x5), cdata)
fit2 <- vglm(ymatrix ~ x2 + x3 + x4 + x5,
             cumulative(parallel = TRUE ~ x2 + x4), cdata)
} # }

# Example 5
udata <- data.frame(x2 = rnorm(nn <- 200))
udata <- transform(udata,
           x1copy = 1,  # Copy of the intercept
           x3 = runif(nn),
           y1 = rnorm(nn, 1 - 3*x2, sd = exp(1 + 0.2*x2)),
           y2 = rnorm(nn, 1 - 3*x2, sd = exp(1)))
args(uninormal)
#> function (lmean = "identitylink", lsd = "loglink", lvar = "loglink", 
#>     var.arg = FALSE, imethod = 1, isd = NULL, parallel = FALSE, 
#>     vfl = FALSE, Form2 = NULL, smallno = 1e-05, zero = if (var.arg) "var" else "sd") 
#> NULL
fit1 <- vglm(y1 ~ x2, uninormal, udata)            # This is okay
fit2 <- vglm(y2 ~ x2, uninormal(zero = 2), udata)  # This is okay
fit4 <- vglm(y2 ~ x2 + x1copy + x3,
             uninormal(zero = NULL, vfl = TRUE,
                       Form2 = ~ x1copy + x3 - 1), udata)
coef(fit4,  matrix = TRUE)  # VFL model
#>                   mean loglink(sd)
#> (Intercept)  0.9048329   0.0000000
#> x2          -3.2372814   0.0000000
#> x1copy       0.0000000   0.9350089
#> x3           0.0000000   0.1173070

# This creates potential conflict
clist <- list("(Intercept)" = diag(2), "x2" = diag(2))
fit3 <- vglm(y2 ~ x2, uninormal(zero = 2), data = udata,
             constraints = clist)  # Conflict!
coef(fit3, matrix = TRUE)  # Shows that clist[["x2"]] was overwritten,
#>                  mean loglink(sd)
#> (Intercept)  0.910496   0.9968751
#> x2          -3.234083   0.0000000
constraints(fit3)  # i.e., 'zero' seems to override the 'constraints' arg
#> $`(Intercept)`
#>      [,1] [,2]
#> [1,]    1    0
#> [2,]    0    1
#> 
#> $x2
#>      [,1]
#> [1,]    1
#> [2,]    0
#> 

# Example 6 ('whitespace' argument)
pneumo <- transform(pneumo, let = log(exposure.time))
fit1 <- vglm(cbind(normal, mild, severe) ~ let,
             sratio(whitespace = FALSE, parallel = TRUE), pneumo)
fit2 <- vglm(cbind(normal, mild, severe) ~ let,
             sratio(whitespace = TRUE,  parallel = TRUE), pneumo)
head(predict(fit1), 2)  # No white spaces
#>   logitlink(P[Y=1|Y>=1]) logitlink(P[Y=2|Y>=2])
#> 1               4.653177               3.970682
#> 2               2.447440               1.764945
head(predict(fit2), 2)  # Uses white spaces
#>   logitlink(P[Y = 1|Y >= 1]) logitlink(P[Y = 2|Y >= 2])
#> 1                   4.653177                   3.970682
#> 2                   2.447440                   1.764945

# Example 7 ('zero' argument with character input)
set.seed(123); n <- 1000
ldata <- data.frame(x2 = runif(n))
ldata <- transform(ldata, y1 = rlogis(n, loc = 5*x2, scale = exp(2)))
ldata <- transform(ldata, y2 = rlogis(n, loc = 5*x2, scale = exp(1*x2)))
ldata <- transform(ldata, w1 = runif(n))
ldata <- transform(ldata, w2 = runif(n))
fit7 <- vglm(cbind(y1, y2) ~ x2,
#        logistic(zero = "location1"),  # location1 is intercept-only
#        logistic(zero = "location2"),
#        logistic(zero = "location*"),  # Not okay... all is unmatched
#        logistic(zero = "scale1"),
#        logistic(zero = "scale2"),
#        logistic(zero = "scale"),  # Both scale parameters are matched
         logistic(zero = c("location", "scale2")),  # All but scale1
#        logistic(zero = c("LOCAT", "scale2")),  # Only scale2 is matched
#        logistic(zero = c("LOCAT")),  # Nothing is matched
#        trace = TRUE,
#        weights = cbind(w1, w2),
         weights = w1,
         data = ldata)
coef(fit7, matrix = TRUE)
#>             location1 loglink(scale1) location2 loglink(scale2)
#> (Intercept)  2.724712       1.9049773  2.206739       0.6750725
#> x2           0.000000       0.1538263  0.000000       0.0000000