| Title: | Effects under Linear, Logistic and Poisson Regression Models with Transformed Variables |
|---|---|
| Description: | Computation of effects under linear, logistic and Poisson regression models with transformed variables. Logarithm and power transformations are allowed. Effects can be displayed both numerically and graphically in both the original and the transformed space of the variables. |
| Authors: | Jose Barrera-Gomez and Xavier Basagana |
| Maintainer: | Jose Barrera-Gomez <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.1.5 |
| Built: | 2024-11-04 06:05:04 UTC |
| Source: | https://github.com/cran/tlm |
Computation of effects under linear, logistic and Poisson regression models with transformed variables. Logarithm and power transformations are allowed. Effects can be displayed both numerically and graphically in both the original and the transformed space of the variables.
| Package: | tlm |
| Type: | Package |
| Version: | 0.1.5 |
| Date: | 2017-04-07 |
| License: | GPL (>=2) |
| URL: | http://www.creal.cat/xbasagana/software.html |
| LazyLoad: | yes |
Jose Barrera-Gomez and Xavier Basagana
Maintainer: Jose Barrera-Gomez <[email protected]>
Barrera-Gomez J, Basagana X. Models with transformed variables: interpretation and software. Epidemiology. 2015;26(2):e16-17.
# linear regression model with log-log tansformation: data(feld1) head(feld1) modcat <- tlm(y = logroom, x = logmattress, z = cat, ypow = 0, xpow = 0, data = feld1) # print and summary: modcat summary(modcat) # plotting the fitted model in the original space: plot(modcat, xname = "Mattress levels", yname = "room levels") # plotting the fitted model in the transformed space (and adding the observations): plot(modcat, xname = "Mattress levels", yname = "room levels", type = "transformed", observed = TRUE) # diagnosis plot for the fitted model: plot(modcat, type = "diagnosis") # Expected geometric mean of the response, adjusting for variable 'cat': MY(modcat) # Expected mean of the transformed response, adjusting for variable 'cat': MY(modcat, space = "transformed") # Information on how to interpret effects: effectInfo(modcat) # Summary effect (default effect): effect(modcat)# linear regression model with log-log tansformation: data(feld1) head(feld1) modcat <- tlm(y = logroom, x = logmattress, z = cat, ypow = 0, xpow = 0, data = feld1) # print and summary: modcat summary(modcat) # plotting the fitted model in the original space: plot(modcat, xname = "Mattress levels", yname = "room levels") # plotting the fitted model in the transformed space (and adding the observations): plot(modcat, xname = "Mattress levels", yname = "room levels", type = "transformed", observed = TRUE) # diagnosis plot for the fitted model: plot(modcat, type = "diagnosis") # Expected geometric mean of the response, adjusting for variable 'cat': MY(modcat) # Expected mean of the transformed response, adjusting for variable 'cat': MY(modcat, space = "transformed") # Information on how to interpret effects: effectInfo(modcat) # Summary effect (default effect): effect(modcat)
Simulated data for birth weight and cord serum cotinine levels in 351 newborns.
data(cotinine)data(cotinine)
A data frame with 351 observations on the following 4 variables.
cotininenumeric cord serum cotinine level in the mother (ng/ml).
logcotininelogarithm of cotinine.
weightnumeric birth weight (g).
underweighta factor with levels no and yes, indicating underweight (weight < 2500 g).
Data were simulated to emulate true data pattern observed in a real study (see ‘References’).
See ‘References’.
Pichini S et al. Cord serum cotinine as a biomarker of fetal exposure to cigarette smoke at the end of pregnancy. Environmental Health Perspectives. 2000;108(11):1079-1083.
data(cotinine) par(las = 1, mfrow = c(2, 2)) with(cotinine, plot(cotinine, weight)) with(cotinine, plot(logcotinine, weight)) with(cotinine, boxplot(cotinine ~ underweight)) with(cotinine, boxplot(logcotinine ~ underweight))data(cotinine) par(las = 1, mfrow = c(2, 2)) with(cotinine, plot(cotinine, weight)) with(cotinine, plot(logcotinine, weight)) with(cotinine, boxplot(cotinine ~ underweight)) with(cotinine, boxplot(logcotinine ~ underweight))
This function estimates the effect of a explanatory variable of interest on a response variable, under a fitted linear, logistic or Poisson regression model with transformed variables. The effect is estimated in the original scale of the variables.
effect(object, x1 = NULL, x2 = NULL, c = NULL, q = NULL, r = NULL, npoints = NULL, level = 0.95, nboot = 999, seed = 4321, verbose = TRUE) ## S3 method for class 'effect' print(x, ...)effect(object, x1 = NULL, x2 = NULL, c = NULL, q = NULL, r = NULL, npoints = NULL, level = 0.95, nboot = 999, seed = 4321, verbose = TRUE) ## S3 method for class 'effect' print(x, ...)
object |
an object of class " |
x1 |
numeric. The values of the explanatory variable where the effect should be computed. See ‘Details’. |
x2 |
numeric. The alternative values of the explanatory variable (changing from |
c |
numeric. The additive change in the explanatory variable. See ‘Details’. |
q |
numeric. The multiplicative change in the explanatory variable. See ‘Details’. |
r |
numeric. The percent change in the explanatory variable. See ‘Details’. |
npoints |
numeric. The number of points where the effect should be computed. See ‘Details’. |
level |
numeric. Confidence level for the effect estimate. Default is 0.95. |
nboot |
numeric. The number of non parametric bootstrap samples to compute confidence intervals. Default is 999. See ‘Details’. |
seed |
numeric. A single value, the seed for bootstrapping. Default is 4321. |
verbose |
logical. Whether to print detailed progress on R prompt. Default is |
x |
an object of class " |
... |
further additional arguments passed to the method |
In order to compute the effect, both the initial and the final values of the explanatory should be provided. It can be done in several ways. For instance, providing, x1 and x2; x1 and one of c, q or r; x1, npoints and one of c, q or r. Only one of the arguments c, q or r is used, prevailing c and then q. If no enough argument are passed, the interquartile range will be considered and a summary effect should be computed, if it exists.
Confidence intervals are computed by transforming the endpoints of the intervals in the transformed scale when it is possible, while non-parametric bootstrap is used otherwise.
effect |
point estimate and confidence interval for the effect size. |
info |
information on how to interpret the effect. Used by the function |
Barrera-Gomez J and Basagana X.
Barrera-Gomez J, Basagana X. Models with transformed variables: interpretation and software. Epidemiology. 2015;26(2):e16-17.
tlm, effectInfo, MY.
### Linear model with log transformation in the response variable: data(imt) head(imt) # model fitting: modimt <- tlm(y = logimt, x = age, data = imt, ypow = 0) modimt # information on interpreting the effect: effectInfo(modimt) # the function effect provides as default the expected change in IMT # for an additive change in age equal to the interquartile range: effect(modimt) # other effects: (minage <- min(imt$age)) (maxage <- max(imt$age)) effect(modimt, c = maxage - minage) ## Not run: effect(modimt, x1 = minage, r = 50, npoints = 3) ## End(Not run)### Linear model with log transformation in the response variable: data(imt) head(imt) # model fitting: modimt <- tlm(y = logimt, x = age, data = imt, ypow = 0) modimt # information on interpreting the effect: effectInfo(modimt) # the function effect provides as default the expected change in IMT # for an additive change in age equal to the interquartile range: effect(modimt) # other effects: (minage <- min(imt$age)) (maxage <- max(imt$age)) effect(modimt, c = maxage - minage) ## Not run: effect(modimt, x1 = minage, r = 50, npoints = 3) ## End(Not run)
This function provides information on interpreting effects in linear, logistic and Poisson models with transformed variables. Specifically, if a summary measure for the effect exists, the function details how to obtain it.
effectInfo(object) ## S3 method for class 'effectInfo' print(x, ...)effectInfo(object) ## S3 method for class 'effectInfo' print(x, ...)
object |
an object of class " |
x |
an object of class " |
... |
further additional arguments for the |
beta |
regression coefficient estimate in the fitted model which is associated to the effect of the explanatory variable of interest on the response variable. |
Xincrease |
type of change in the exploratory variable of interest (additive or realtive) for which a summary effect exists. |
effecttype |
type of effect on the response variable for which a summary effect exists. |
effectsize |
formula for the summary effect size, if any. |
furtherinfo |
further information about how to interpret effects. |
Barrera-Gomez J and Basagana X.
Barrera-Gomez J, Basagana X. Models with transformed variables: interpretation and software. Epidemiology. 2015;26(2):e16-17.
### Linear model with log transformation in the explanatory variable: data(cotinine) head(cotinine) # model fitting: modcot <- tlm(y = weight, x = logcotinine, data = cotinine, xpow = 0) modcot # information on interpreting the effect: effectInfo(modcot) ### Linear model with no summary measure of effect: data(glucose) head(glucose) # transformations Y^(-2) and X^(-1/2): modgluco <- tlm(y = inv2glu, x = inv12tri, data = glucose, ypow = -2, xpow = -1/2) modgluco effectInfo(modgluco)### Linear model with log transformation in the explanatory variable: data(cotinine) head(cotinine) # model fitting: modcot <- tlm(y = weight, x = logcotinine, data = cotinine, xpow = 0) modcot # information on interpreting the effect: effectInfo(modcot) ### Linear model with no summary measure of effect: data(glucose) head(glucose) # transformations Y^(-2) and X^(-1/2): modgluco <- tlm(y = inv2glu, x = inv12tri, data = glucose, ypow = -2, xpow = -1/2) modgluco effectInfo(modgluco)
Simulated data for cat allergen concentrations (Fel d 1) in 471 homes, measured in both the living room and the bed mattress.
data(feld1)data(feld1)
A data frame with 471 observations on the following 5 variables.
mattressnumeric Feld d 1 concentration in the bed mattress (g/g).
roomnumeric Feld d 1 concentration in the living room (g/g).
logmattresslogarithm of mattress.
logroomlogarithm of room.
cata factor with levels no and yes, indicating cat ownership.
Data were simulated to emulate true data pattern observed in a real study (see ‘References’).
See ‘References’.
Basagana X et al. Domestic aeroallergen levels in Barcelona and Menorca (Spain). Pediatric Allergy and Immunology. 2002;13(6):412-417.
data(feld1) par(las = 1, mfrow = c(1, 2)) with(feld1, plot(mattress, room, col = as.numeric(cat))) with(feld1, plot(logmattress, logroom, col = as.numeric(cat)))data(feld1) par(las = 1, mfrow = c(1, 2)) with(feld1, plot(mattress, room, col = as.numeric(cat))) with(feld1, plot(logmattress, logroom, col = as.numeric(cat)))
Simulated data for glucose and triglycerides levels in blood in 400 adults.
data(glucose)data(glucose)
A data frame with 400 observations on the following 4 variables.
triglynumeric triglycerides levels in blood (mg/dl).
gluconumeric glucose levels in blood (mg/dl).
inv12trinumeric reciprocal of the square root of trigly (i.e., -1/2 power transformation).
inv2glunumeric reciprocal of the gluco square (i.e., -2 power transformation).
Data were simulated to emulate true data pattern observed in a real study (see ‘References’).
See ‘References’.
Rivera M et al. Association between long-term exposure to traffic-related air pollution and subclinical atherosclerosis: the REGICOR Study. Environmental Health Perspectives. 2013;121(2):223-230.
data(glucose) par(las = 1, mfrow = c(1, 2)) with(glucose, plot(trigly, gluco)) with(glucose, plot(inv12tri, inv2glu))data(glucose) par(las = 1, mfrow = c(1, 2)) with(glucose, plot(trigly, gluco)) with(glucose, plot(inv12tri, inv2glu))
Simulated data for intima media thickness of the carotid artery and age in 2784 adults.
data(imt)data(imt)
A data frame with 2784 observations on the following 3 variables.
agenumeric age of the individual (years).
imtnumeric intima media thickness of the carotid artery (mm).
logimtlogarithm of imt.
Data were simulated to emulate true data pattern observed in a real study (see ‘References’).
See ‘References’.
Rivera M et al. Association between long-term exposure to traffic-related air pollution and subclinical atherosclerosis: the REGICOR Study. Environmental Health Perspectives. 2013;121(2):223-230.
data(imt) par(las = 1, mfrow = c(1, 2)) with(imt, plot(age, imt)) with(imt, plot(age, logimt))data(imt) par(las = 1, mfrow = c(1, 2)) with(imt, plot(age, imt)) with(imt, plot(age, logimt))
This function computes expected measures of the response variable under a linear, logistic or Poisson regression fitted model with transformed variables. Measures can be calculated in both the original and the transformed space. The function automatically provides the name of the measure depending on the fitted model.
MY(object, x = NULL, npoints = 10, space = c("original", "transformed"), level = 0.95) ## S3 method for class 'MY' print(x, ...)MY(object, x = NULL, npoints = 10, space = c("original", "transformed"), level = 0.95) ## S3 method for class 'MY' print(x, ...)
object |
an object of class " |
x |
for |
npoints |
numeric. If |
space |
character. If " |
level |
numeric. The confidence level for measures. Default is 0.95. |
... |
further additional arguments for the |
In order to compute adjusted measures, all explanatory variables in the model different than the explanatory variable of interest are set at their means.
If space is "original", then the mean (for Poisson response) or the probability (for binary response) is computed. For gaussian response, the mean is computed if the response variable is not transformed; otherwise, the geometric mean (for log transformation in the response) or the median (for power transformation) is computed.
If space is "transformed", then the mean (for Poisson response or transformed gaussian response), or the logodds (for binary response) is computed.
If x is NULL, the measure is computed in npoints values of the explanatory variable of interest. Those values are choosen to be in arithmetic progression in the given space, inside the observed range of the explanatory variable.
M |
adjusted measure of the response variable. See ‘Details’. |
ymeasure |
the type of measure for |
space |
space where measures has been computed (" |
ypow |
numeric power transformation assumed in the response variable. See |
xpow |
numeric power transformation assumed in the explanatory variable of interest. See |
Barrera-Gomez J and Basagana X.
Barrera-Gomez J, Basagana X. Models with transformed variables: interpretation and software. Epidemiology. 2015;26(2):e16-17.
tlm, effectInfo, effect.
data(feld1) head(feld1) # Linear model with log-log transformation, adjusting for variable 'cat': modcat <- tlm(y = logroom, x = logmattress, z = cat, data = feld1, ypow = 0, xpow = 0) summary(modcat) # Geometric mean of the response as a function of the explanatory variable, # adjusted for 'cat': MY(modcat) MY(modcat, npoints = 3) # computed at 1st and 3rd quartiles of the explanatory variable: MY(modcat, x = quantile(feld1$mattress, probs = c(1, 3)/4)) # Mean of the log(response) as a function of the log explanatory variable, # adjusted for 'cat': MY(modcat, space = "transformed")data(feld1) head(feld1) # Linear model with log-log transformation, adjusting for variable 'cat': modcat <- tlm(y = logroom, x = logmattress, z = cat, data = feld1, ypow = 0, xpow = 0) summary(modcat) # Geometric mean of the response as a function of the explanatory variable, # adjusted for 'cat': MY(modcat) MY(modcat, npoints = 3) # computed at 1st and 3rd quartiles of the explanatory variable: MY(modcat, x = quantile(feld1$mattress, probs = c(1, 3)/4)) # Mean of the log(response) as a function of the log explanatory variable, # adjusted for 'cat': MY(modcat, space = "transformed")
summary method for an object created by the the function tlm.
## S3 method for class 'tlm' summary(object, ...) ## S3 method for class 'summary.tlm' print(x, ...)## S3 method for class 'tlm' summary(object, ...) ## S3 method for class 'summary.tlm' print(x, ...)
object |
an object of class " |
x |
an object of class " |
... |
further additional arguments for |
Essentially, the output of summary.lm or summary.glm is displayed. In addition, further information on the fitted model is also displayed.
model |
the fitted model in the transformed space. |
ypow |
the value of |
xpow |
the value of |
summary |
the summary of the fitted model provide by |
Barrera-Gomez J and Basagana X.
Barrera-Gomez J, Basagana X. Models with transformed variables: interpretation and software. Epidemiology. 2015;26(2):e16-17.
### linear model with log-log transformation: data(feld1) modcat <- tlm (y = logroom, x = logmattress, z = cat, data = feld1, ypow = 0, xpow = 0) modcat summary(modcat)### linear model with log-log transformation: data(feld1) modcat <- tlm (y = logroom, x = logmattress, z = cat, data = feld1, ypow = 0, xpow = 0) modcat summary(modcat)
This function fits a linear, logistic or Poisson regression model with transformed variables and creates an object which can be used to extract effects of the explanatory variable of interest on the response variable, in the original scale of the variables.
tlm(y, x, z = "none", family = gaussian, data, ypow = 1, xpow = 1, ...) ## S3 method for class 'tlm' print(x, ...) ## S3 method for class 'tlm' plot(x, type = c("original", "transformed", "diagnosis"), observed = FALSE, xname = "x", yname = "y", level = 0.95, ...)tlm(y, x, z = "none", family = gaussian, data, ypow = 1, xpow = 1, ...) ## S3 method for class 'tlm' print(x, ...) ## S3 method for class 'tlm' plot(x, type = c("original", "transformed", "diagnosis"), observed = FALSE, xname = "x", yname = "y", level = 0.95, ...)
y |
name of the response variable (unquoted). |
x |
name of the explanatory variable of interest (unquoted). |
z |
additional explanatory variables in the model. Default is " |
family |
the link function. For linear model, |
data |
a |
ypow |
numeric power transformation already done in |
xpow |
numeric power transformation already done in |
type |
character indicating the type of plot for the fitted model. If " |
observed |
logical indicating whether the observations should be added to the plot. Assumed to be |
xname |
character. The name of the |
yname |
character. The name of the |
level |
numeric. Confidence level for the prediction of the measure of |
... |
further additional arguments passed to |
z can be any expression allowed as a right-hand-side in
formula. However, expressions involving the variable
passed in x are not allowed. To include all the remaining
variables in data, use just a period (.).
The transformations already done in y and x are passed by
ypow and xpow, respectively. They should be a
number. Default is 1 (no transformation). The value 0 corresponds to the
logarithmic transformation. If family is not gaussian,
y is assumed non transformed. If x is categorical or
presents only two different values, the value of xpow is assumed to be 1. If x presents only two different values, it is considered as a binary variable.
model |
the fitted model in the transformed space. |
ypow |
the value of |
xpow |
the value of |
Barrera-Gomez J and Basagana X.
Barrera-Gomez J, Basagana X. Models with transformed variables: interpretation and software. Epidemiology. 2015;26(2):e16-17.
### Linear model with log-log transformation: data(feld1) head(feld1) # model fitting in the transformed space: modcat <- tlm (y = logroom, x = logmattress, z = cat, data = feld1, ypow = 0, xpow = 0) modcat summary(modcat) # plot of the geometric mean of the response (original space), adjusting for 'cat': plot(modcat, xname = "Mattress levels", yname = "room levels") # plot of the mean of the log of response (transformed space), adjusting for 'cat' and # adding the observations: plot(modcat, type = "transformed", xname = "mattress levels", yname = "room levels", observed = TRUE) # diagnosis plot: plot(modcat, type = "diagnosis") ### The same model but now considering 'cat' as the explanatory variable of interest: modcat2 <- tlm (y = logroom, x = cat, z = logmattress, data = feld1, ypow = 0) summary(modcat2) # plot of the geometric mean of the response (original space), adjusting # for mattress levels: plot(modcat2, xname = "Cat", yname = "room levels") # plot of the mean of the log of response (transformed space), adjusting # for mattress levels: plot(modcat2, type = "transformed", xname = "Cat", yname = "room levels")### Linear model with log-log transformation: data(feld1) head(feld1) # model fitting in the transformed space: modcat <- tlm (y = logroom, x = logmattress, z = cat, data = feld1, ypow = 0, xpow = 0) modcat summary(modcat) # plot of the geometric mean of the response (original space), adjusting for 'cat': plot(modcat, xname = "Mattress levels", yname = "room levels") # plot of the mean of the log of response (transformed space), adjusting for 'cat' and # adding the observations: plot(modcat, type = "transformed", xname = "mattress levels", yname = "room levels", observed = TRUE) # diagnosis plot: plot(modcat, type = "diagnosis") ### The same model but now considering 'cat' as the explanatory variable of interest: modcat2 <- tlm (y = logroom, x = cat, z = logmattress, data = feld1, ypow = 0) summary(modcat2) # plot of the geometric mean of the response (original space), adjusting # for mattress levels: plot(modcat2, xname = "Cat", yname = "room levels") # plot of the mean of the log of response (transformed space), adjusting # for mattress levels: plot(modcat2, type = "transformed", xname = "Cat", yname = "room levels")