season: Tools for Uncovering and Estimating Seasonal Patterns.

Description

The package contains graphical methods for displaying seasonal data and regression models for detecting and estimating seasonal patterns.

Details

The regression models can be applied to normal, Poisson or binomial dependent data distributions. Tools are available for both time series data (equally spaced in time) and survey data (unequally spaced in time).

Sinusoidal (parametric) seasonal patterns are available (cosinor, nscosinor), as well as models for monthly data (monthglm), and the case-crossover method to control for seasonality (casecross).

season aims to fill an important gap in the software by providing a range of tools for analysing seasonal data. The examples are based on health data, but the functions are equally applicable to any data with a seasonal pattern.

Author(s)

Adrian Barnett <a.barnett@qut.edu.au>
Peter Baker
Oliver Hughes

Maintainer: Adrian Barnett <a.barnett@qut.edu.au>

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Australian Football League (AFL) Players' Birthdays for the 2009 Season

Description

The data are: a) the monthly frequencies of birthdays and an expected number based on monthly birth statistics for 1975 to 1991. b) all 617 players' initials and birthdays (excluding non-Australian born players).

Usage

AFL

Format

A list with the following 5 variables.

month

integer month (1 to 12)

players

number of players born in each month (12 observations)

expected

expected number of players born in each month (12 observations)

initials

player initials (617 observations)

dob

date of birth in date format (617 observations; year-month-day format)

Source

Dates of birth from Wikipedia.

Examples

data(AFL)
barplot(AFL$players, names.arg=month.abb)

Cardiovascular Deaths in Los Angeles, 1987–2000

Description

Monthly number of deaths from cardiovascular disease in people aged 75 and over in Los Angeles for the years 1987 to 2000.

Usage

CVD

Format

A data frame with 168 observations on the following 8 variables.

year

year of death

month

month of death

yrmon

a combination of year and month: year+(month-1)/12

cvd

monthly number of CVD deaths

tmpd

mean monthly temperature (degrees Fahrenheit)

pop

Los Angeles population aged 75+ in the year 2000 (this value is constant as only one year was available, but in general the population will (of course) change over time)

ndaysmonth

number of days in each month (used as an offset)

adj

adjusted number of CVD deaths per month using a standardised month length. Monthly number of CVD deaths multiplied by (365.25/12)/ndaysmonth. So the standard month length is 30.4 days.

Source

From the NMMAPS study.

References

Samet JM, Dominici F, Zeger SL, Schwartz J, Dockery DW (2000). The National Morbidity, Mortality, and Air Pollution Study, Part I: Methods and Methodologic Issues. Research Report 94, Health Effects Institute, Cambridge MA.

Examples

data(CVD)
plot(CVD$yrmon, CVD$cvd, type='o', xlab='Date',
     ylab='Number of CVD deaths per month')

Daily Cardiovascular Deaths in Los Angeles, 1987–2000

Description

Daily number of deaths from cardiovascular disease in people aged 75 and over in Los Angeles for the years 1987 to 2000.

Usage

CVDdaily

Format

A data frame with 5114 observations on the following 16 variables.

date

date of death in date format (year-month-day)

cvd

daily number of CVD deaths

dow

day of the week (character)

tmpd

daily mean temperature (degrees Fahrenheit)

o3mean

daily mean ozone (parts per billion)

o3tmean

daily trimmed mean ozone (parts per billion)

Mon

indicator variable for Monday

Tue

indicator variable for Tuesday

Wed

indicator variable for Wednesday

Thu

indicator variable for Thursday

Fri

indicator variable for Friday

Sat

indicator variable for Saturday

month

month (integer from 1 to 12)

winter

indicator variable for winter

spring

indicator variable for spring

summer

indicator variable for summer

autumn

indicator variable for autumn

Source

From the NMMAPS study.

References

Samet JM, Dominici F, Zeger SL, Schwartz J, Dockery DW (2000). The National Morbidity, Mortality, and Air Pollution Study, Part I: Methods and Methodologic Issues. Research Report 94, Health Effects Institute, Cambridge MA.

Examples

data(CVDdaily)
plot(CVDdaily$date, CVDdaily$cvd, type='p', xlab='Date',
     ylab='Number of CVD deaths')

Amplitude Adjusted Fourier Transform (AAFT)

Description

Generates random linear surrogate data of a time series with the same second-order properties.

Usage

aaft(data, nsur)

Arguments

Details

The AAFT uses phase-scrambling to create a surrogate of the time series that has a similar spectrum (and hence similar second-order statistics). The AAFT is useful for testing for non-linearity in a time series, and is used by nonlintest.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Kugiumtzis D (2000) Surrogate data test for nonlinearity including monotonic transformations, Phys. Rev. E, vol 62

Examples

data(CVD)
surr = aaft(CVD$cvd, nsur=1)
plot(CVD$cvd, type='l')
lines(surr[,1], col='red')

Case–crossover Analysis to Control for Seasonality

Description

Fits a time-stratified case–crossover to regularly spaced time series data. The function is not suitable for irregularly spaced individual data. The function only uses a time-stratified design, and other designs such as the symmetric bi-directional design, are not available.

Usage

casecross(
  formula,
  data,
  exclusion = 2,
  stratalength = 28,
  matchdow = FALSE,
  usefinalwindow = FALSE,
  matchconf = "",
  confrange = 0,
  stratamonth = FALSE
)

Arguments

Details

The case–crossover method compares “case” days when events occurred (e.g., deaths) with control days to look for differences in exposure that might explain differences in the number of cases. Control days are selected to be nearby to case days, which means that only recent changes in the independent variable(s) are compared. By only comparing recent values, any long-term or seasonal variation in the dependent and independent variable(s) can be eliminated. This elimination depends on the definition of nearby and on the seasonal and long-term patterns in the independent variable(s).

Control and case days are only compared if they are in the same stratum. The stratum is controlled by stratalength, the default value is 28 days, so that cases and controls are compared in four week sections. Smaller stratum lengths provide a closer control for season, but reduce the available number of controls. Control days that are close to the case day may have similar levels of the independent variable(s). To reduce this correlation it is possible to place an exclusion around the cases. The default is 2, which means that the smallest gap between a case and control will be 3 days.

To remove any confounding by day of the week it is possible to additionally match by day of the week (matchdow), although this usually reduces the number of available controls. This matching is in addition to the strata matching.

It is possible to additionally match case and control days by an important confounder (matchconf) in order to remove its effect. Control days are matched to case days if they are: i) in the same strata, ii) have the same day of the week if matchdow=TRUE, iii) have a value of matchconf that is within plus/minus confrange of the value of matchconf on the case day. If the range is set too narrow then the number of available controls will become too small, which in turn means the number of case days with at least one control day is compromised.

The method uses conditional logistic regression (see coxph and so the parameter estimates are odds ratios.)

The code assumes that the data frame contains a date variable (in Date format) called ‘date’.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Janes, H., Sheppard, L., Lumley, T. (2005) Case-crossover analyses of air pollution exposure data: Referent selection strategies and their implications for bias. Epidemiology 16(6), 717–726.

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

See Also

summary.casecross, coxph

Examples

# cardiovascular disease data
data(CVDdaily)
CVDdaily = subset(CVDdaily, date<=as.Date('1987-12-31')) # subset for example
# Effect of ozone on CVD death
model1 = casecross(cvd ~ o3mean+tmpd+Mon+Tue+Wed+Thu+Fri+Sat, data=CVDdaily)
summary(model1)
# match on day of the week
model2 = casecross(cvd ~ o3mean+tmpd, matchdow=TRUE, data=CVDdaily)
summary(model2)
# match on temperature to within a degree
model3 = casecross(cvd ~ o3mean+Mon+Tue+Wed+Thu+Fri+Sat, data=CVDdaily,
                   matchconf='tmpd', confrange=1)
summary(model3)

Mean and Confidence Interval for Circular Phase

Description

Calculates the mean and confidence interval for the phase based on a chain of MCMC samples.

Usage

ciPhase(theta, alpha = 0.05)

Arguments

Details

The estimates of the phase are rotated to have a centre of \pi, the point on the circumference of a unit radius circle that is furthest from zero. The mean and confidence interval are calculated on the rotated values, then the estimates are rotated back.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Fisher, N. (1993) Statistical Analysis of Circular Data. Cambridge University Press. Page 36.

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Examples

theta = rnorm(n=2000, mean=0, sd=pi/50) # 2000 normal samples, centred on zero
hist(theta, breaks=seq(-pi/8, pi/8, pi/30))
ciPhase(theta)

Function to Draw CI Polygon

Description

Internal function to draw a confidence interval for multiple times as a grey area. For internal use only.

Usage

cipolygon(time, lower, upper)

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Cosinor Regression Model for Detecting Seasonality in Yearly Data or Circadian Patterns in Hourly Data

Description

Fits a cosinor model as part of a generalized linear model.

Usage

cosinor(
  formula,
  date,
  data,
  family = gaussian(),
  alpha = 0.05,
  cycles = 1,
  rescheck = FALSE,
  type = "daily",
  offsetmonth = FALSE,
  offsetpop = NULL,
  text = TRUE
)

Arguments

Details

The cosinor model captures a seasonal pattern using a sinusoid. It is therefore suitable for relatively simple seasonal patterns that are symmetric and stationary. The default is to fit an annual seasonal pattern (cycle=1), but other higher frequencies are possible (e.g., twice per year: cycle=2). The model is fitted using a sine and cosine term that together describe the sinusoid. These parameters are added to a generalized linear model, so the model can be fitted to a range of dependent data (e.g., Normal, Poisson, Binomial). Unlike the nscosinor model, the cosinor model can be applied to unequally spaced data.

Value

Returns an object of class “Cosinor” with the following parts:

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

See Also

summary.Cosinor, plot.Cosinor

Examples

## cardiovascular disease data (offset based on number of days in...
## ...the month scaled to an average month length)
data(CVD)
res = cosinor(cvd~1, date='month', data=CVD, type='monthly',
              family=poisson(), offsetmonth=TRUE)
summary(res)
seasrescheck(res$residuals) # check the residuals
## stillbirth data
data(stillbirth)
res = cosinor(stillborn~1, date='dob', data=stillbirth,
              family=binomial(link='cloglog'))
summary(res)
plot(res)
## hourly indoor temperature data
res = cosinor(bedroom~1, date='datetime', type='hourly', data=indoor)
summary(res)
# to get the p-values for the sine and cosine estimates
summary(res$glm)

Creates an Adjacency Matrix

Description

Creates an adjacency matrix in a form suitable for using in BRugs or WinBUGS.

Usage

createAdj(matrix, filename = "Adj.txt", suffix = NULL)

Arguments

Details

Adjacency matrices are used by conditional autoregressive (CAR) models to smooth estimates according to some neighbourhood map. The basic idea is that neighbouring areas have more in common than non-neighbouring areas and so will be positively correlated.

As well as correlations in space it is possible to use CAR models to model similarities in time.

In this case the matrix represents those time points that we wish to assume to be correlated.

Value

Creates a text file named filename that contains the total number of neighbours (num), the index number of the adjacent neighbours (adj) and the weights (weights).

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Examples

# Nearest neighbour matrix for 5 time points
x = c(NA,1,NA,NA,NA)
(V = toeplitz(x))
createAdj(V)

Exercise Data from Queensland, 2005–2007

Description

Exercise data in longitudinal format from a physical activity intervention study in Logan, Queensland. Some subjects were lost to follow-up, so all three visits are not available for all subjects.

Usage

exercise

Format

A data frame with 1302 observations on the following 7 variables.

id

subject number

visit

visit number (1, 2 or 3)

date

date of interview (year-month-day)

year

year of interview

month

month of interview

bmi

body mass index at visit 1 (kg/m^2)

walking

walking time per week (in minutes) at each visit

Source

From Prof Elizabeth Eakin and colleagues, The University of Queensland, Brisbane.

References

Eakin E, et al (2009) Telephone counselling for physical activity and diet in type 2 diabetes and hypertension, Am J of Prev Med, vol 36, pages 142–9

Examples

data(exercise)
boxplot(exercise$walking ~ exercise$month)

Count the Number of Days in the Month

Description

Counts the number of days per month given a range of dates. Used to adjust monthly count data for the at-risk time period. For internal use only.

Usage

flagleap(data, report = TRUE, matchin = FALSE)

Arguments

Details

The data should contain the numeric variable called ‘year’ as a 4 digit year (e.g., 1973).

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Indoor Temperature Data

Description

The data are indoor temperatures (in degrees C) for a bedroom and living room in a house in Brisbane, Australia for the dates 10 July 2013 to 3 October 2013. Temperatures were recorded using data loggers which recorded every hour to the nearest 0.5 degrees.

Format

A data.frame with the following 3 variables.

datetime

date and time in POSIXlt format

living

the living room temperature

bedroom

the bedroom temperature

Source

Adrian G Barnett.

Examples

data(indoor)
res = cosinor(bedroom~1, date='datetime', type='hourly', data=indoor)
summary(res)

Inverse Fraction of the Year or Hour

Description

Inverts a fraction of the year or hour to a useful time scale.

Usage

invyrfraction(frac, type = "daily", text = TRUE)

Arguments

Details

Returns the day and month (for daily) or fraction of the month (for monthly) given a fraction of the year. Assumes a year length of 365.25 days for daily. When using monthly the 1st of January is 1, the 1st of December is 12, and the 31st of December is 12.9. For hourly it returns the fraction of the 24-hour clock starting from zero (midnight).

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Examples

invyrfraction(c(0, 0.5, 0.99), type='daily')
invyrfraction(c(0, 0.5, 0.99), type='monthly')
invyrfraction(c(0, 0.5, 0.99), type='hourly')

Forward and Backward Sweep of the Kalman Filter

Description

Internal function to do a forward and backward sweep of the Kalman filter, used by nscosinor. For internal use only.

Usage

kalfil(data, f, vartheta, w, tau, lambda, cmean)

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Fit a GLM with Month

Description

Fit a generalized linear model with a categorical variable of month.

Usage

monthglm(
  formula,
  data,
  family = gaussian(),
  refmonth = 1,
  monthvar = "month",
  offsetmonth = FALSE,
  offsetpop = NULL
)

Arguments

Details

Month is fitted as a categorical variable as part of a generalized linear model. Other independent variables can be added to the right-hand side of formula.

This model is useful for examining non-sinusoidal seasonal patterns. For sinusoidal seasonal patterns see cosinor.

The data frame should contain the integer months and the year as a 4 digit number. These are used to calculate the number of days in each month accounting for leap years.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

See Also

summary.monthglm, plot.monthglm

Examples

data(CVD)
mmodel = monthglm(formula=cvd~1 ,data=CVD, family=poisson(),
                  offsetpop=expression(pop/100000), offsetmonth=TRUE)
summary(mmodel)

Monthly Means

Description

Calculate the monthly mean or adjusted monthly mean for count data.

Usage

monthmean(data, resp, offsetpop = NULL, adjmonth = FALSE)

Arguments

Details

For time series recorded at monthly intervals it is often useful to examine (and plot) the average in each month. When using count data we should adjust the mean to account for the unequal number of days in the month (e.g., 31 in January and 28 or 29 in February).

This function assumes that the data set (data) contains variables for the year and month called year and month, respectively.

Value

Returns an object of class “Monthmean” with the following parts:

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

See Also

plot.Monthmean

Examples

# cardiovascular disease data
data(CVD)
mmean = monthmean(data=CVD, resp='cvd', offsetpop=expression(pop/100000), adjmonth='average')
mmean
plot(mmean)

Remove Letters and Characters from a String

Description

Remove letters and characters from a string to leave only numbers. Removes all letters (upper and lower case) and the characters “.”, “(” and “)”. For internal use only.

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Test of Non-linearity of a Time Series

Description

A bootstrap test of non-linearity in a time series using the third-order moment.

Usage

nonlintest(data, n.lag, n.boot, alpha = 0.05)

Arguments

Details

The test uses aaft to create linear surrogates with the same second-order properties, but no (third-order) non-linearity. The third-order moments (third) of these linear surrogates and the actual series are then compared from lags 0 up to n.lag (excluding the skew at the co-ordinates (0,0)). The bootstrap test works on the overall area outside the limits, and gives an indication of the overall non-linearity. The plot using region shows those co-ordinates of the third order moment that exceed the null hypothesis limits, and can be a useful clue for guessing the type of non-linearity. For example, a large value at the co-ordinates (0,1) might be caused by a bi-linear series X_t=\alpha X_{t-1}\varepsilon_{t-1} +\varepsilon_t.

Value

Returns an object of class “nonlintest” with the following parts:

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Barnett AG & Wolff RC (2005) A Time-Domain Test for Some Types of Nonlinearity, IEEE Transactions on Signal Processing, vol 53, pages 26–33

See Also

print.nonlintest, plot.nonlintest

Examples

data(CVD)
## Not run: test.res = nonlintest(data=CVD$cvd, n.lag=4, n.boot=1000)

Non-stationary Cosinor

Description

Decompose a time series using a non-stationary cosinor for the seasonal pattern.

Usage

nscosinor(
  data,
  response,
  cycles,
  niters = 1000,
  burnin = 500,
  tau,
  lambda = 1/12,
  div = 50,
  monthly = TRUE,
  alpha = 0.05
)

Arguments

Details

This model is designed to decompose an equally spaced time series into a trend, season(s) and noise. A seasonal estimate is estimated as s_t=A_t\cos(\omega_t-P_t), where t is time, A_t is the non-stationary amplitude, P_t is the non-stationary phase and \omega_t is the frequency.

A non-stationary seasonal pattern is one that changes over time, hence this model gives potentially very flexible seasonal estimates.

The frequency of the seasonal estimate(s) are controlled by cycle. The cycles should be specified in units of time. If the data is monthly, then setting lambda=1/12 and cycles=12 will fit an annual seasonal pattern. If the data is daily, then setting lambda= 1/365.25 and cycles=365.25 will fit an annual seasonal pattern. Specifying cycles= c(182.6,365.25) will fit two seasonal patterns, one with a twice-annual cycle, and one with an annual cycle.

The estimates are made using a forward and backward sweep of the Kalman filter. Repeated estimates are made using Markov chain Monte Carlo (MCMC). For this reason the model can take a long time to run. To give stable estimates a reasonably long sample should be used (niters), and the possibly poor initial estimates should be discarded (burnin).

Value

Returns an object of class “nsCosinor” with the following parts:

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Barnett, A.G., Dobson, A.J. (2004) Estimating trends and seasonality in coronary heart disease Statistics in Medicine. 23(22) 3505–23.

See Also

plot.nsCosinor, summary.nsCosinor

Examples

data(CVD)
# model to fit an annual pattern to the monthly cardiovascular disease data
f = c(12)
tau = c(10,50)
## Not run: res12 = nscosinor(data=CVD, response='adj', cycles=f, niters=5000,
         burnin=1000, tau=tau)
summary(res12)
plot(res12)

## End(Not run)

Initial Values for Non-stationary Cosinor

Description

Creates initial values for the non-stationary cosinor decomposition nscosinor. For internal use only.

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Periodogram

Description

Estimated periodogram using the fast Fourier transform (fft).

Usage

peri(data, adjmean = TRUE, plot = TRUE)

Arguments

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Examples

data(CVD)
p = peri(CVD$cvd)

Phase from Cosinor Estimates

Description

Calculate the phase given the estimated sine and cosine values from a cosinor model.

Usage

phasecalc(cosine, sine)

Arguments

Details

Returns the phase in radians, in the range [0,2\pi). The phase is the peak in the sinusoid.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Fisher, N.I. (1993) Statistical Analysis of Circular Data. Cambridge University Press, Cambridge. Page 31.

Examples

phasecalc(cosine=0, sine=1) # pi/2

Plot the Results of a Cosinor

Description

Plots the fitted sinusoid from a Cosinor object produced by cosinor.

Usage

## S3 method for class 'Cosinor'
plot(x, ...)

Arguments

Details

The code produces the fitted sinusoid based on the intercept and sinusoid. The y-axis is on the scale of probability if the link function is ‘logit’ or ‘cloglog’. If the analysis was based on monthly data then month is shown on the x-axis. If the analysis was based on daily data then time is shown on the x-axis.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

cosinor, summary.Cosinor, seasrescheck

Plot of Monthly Mean Estimates

Description

Plots estimated monthly means.

Usage

## S3 method for class 'Monthmean'
plot(x, ...)

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

monthmean

Plot of Monthly Estimates

Description

Plots the estimated from a generalized linear model with a categorical variable of month.

Usage

## S3 method for class 'monthglm'
plot(x, alpha = 0.05, ylim = NULL, ...)

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

monthglm

Examples

data(CVD)
mmodel = monthglm(formula=cvd~1, data=CVD, family=poisson(),
                  offsetpop=expression(pop/100000), offsetmonth=TRUE, refmonth=6)
plot(mmodel)

Plot the Results of the Non-linear Test

Description

Creates a contour plot of the region of the third-order moment outside the test limits generated by nonlintest.

Usage

## S3 method for class 'nonlintest'
plot(x, plot = TRUE, ...)

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

nonlintest

Plot the Results of a Non-stationary Cosinor

Description

Plots the trend and season(s) from a nsCosinor object produced by nscosinor.

Usage

## S3 method for class 'nsCosinor'
plot(x, ...)

Arguments

Details

The code produces the season(s) and trend estimates.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

nscosinor

Circular Plot

Description

Circular plot of a monthly variable.

Usage

plotCircle(months, dp = 1, ...)

Arguments

Details

This circular plot can be useful for estimates of an annual seasonal pattern. Darker shades of grey correspond to larger numbers.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Examples

plotCircle(months=seq(1,12,1),dp=0)

Circular Plot Using Segments

Description

A circular plot useful for visualising monthly or weekly data.

Usage

plotCircular(
  area1,
  area2 = NULL,
  spokes = NULL,
  scale = 0.8,
  labels,
  stats = TRUE,
  dp = 1,
  clockwise = TRUE,
  spoke.col = "black",
  lines = FALSE,
  centrecirc = 0.03,
  main = "",
  xlab = "",
  ylab = "",
  pieces.col = c("white", "gray"),
  length = FALSE,
  legend = TRUE,
  auto.legend = list(x = "bottomright", fill = NULL, labels = NULL, title = ""),
  ...
)

Arguments

Details

A circular plot can be useful for spotting the shape of the seasonal pattern. This function can be used to plot any circular patterns, e.g., weekly or monthly. The number of segments will be the length of the variable area1.

The plots are also called rose diagrams, with the segments then called ‘petals’.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Fisher, N.I. (1993) Statistical Analysis of Circular Data. Cambridge University Press, Cambridge.

Examples

# months (dummy data)
plotCircular(area1=seq(1,12,1), scale=0.7, labels=month.abb, dp=0)
# weeks (random data)
daysoftheweek = c('Monday','Tuesday','Wednesday','Thursday','Friday',
'Saturday','Sunday')
weekfreq = table(round(runif(100, min=1, max=7)))
plotCircular(area1=weekfreq, labels=daysoftheweek, dp=0)
# Observed number of AFL players with expected values
data(AFL)
plotCircular(area1=AFL$players, area2=AFL$expected, scale=0.72,
  labels=month.abb, dp=0, lines=TRUE, legend=FALSE)
plotCircular(area1=AFL$players, area2=AFL$expected, scale=0.72,
  labels=month.abb, dp=0, lines=TRUE, pieces.col=c("green","red"),
  auto.legend=list(labels=c("Obs","Exp"), title="# players"),
  main="Observed and Expected AFL players")

Plot Results by Month

Description

Plots results by month.

Usage

plotMonth(data, resp, panels = 12, ...)

Arguments

Details

Assumes the data frame contains variables called year and month.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Examples

data(CVD)
plotMonth(data=CVD, resp='cvd', panels=12)

Print the Results of a Cosinor

Description

The default print method for a Cosinor object produced by cosinor.

Usage

## S3 method for class 'Cosinor'
print(x, ...)

Arguments

Details

Uses print.glm.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

cosinor, summary.Cosinor, glm

Print the Results from Monthmean

Description

Print the monthly means from a Monthmean object produced by monthmean.

Usage

## S3 method for class 'Monthmean'
print(x, digits = 1, ...)

Arguments

Details

The code prints the monthly mean estimates.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

monthmean

Print the Results of a Case-Crossover Model

Description

The default print method for a casecross object produced by casecross.

Usage

## S3 method for class 'casecross'
print(x, ...)

Arguments

Details

Uses print.coxph.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

casecross, summary.casecross, coxph

Print monthglm

Description

Print monthglm

Usage

## S3 method for class 'monthglm'
print(x, ...)

Arguments

Print the Results of the Non-linear Test

Description

The default print method for a nonlintest object produced by nonlintest.

Usage

## S3 method for class 'nonlintest'
print(x, ...)

Arguments

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

nonlintest, plot.nonlintest

Print the Results of a Non-stationary Cosinor

Description

The default print method for a nsCosinor object produced by nscosinor.

Usage

## S3 method for class 'nsCosinor'
print(x, ...)

Arguments

Details

Prints out the model call, number of MCMC samples, sample size and residual summary statistics.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

nscosinor, summary.nsCosinor

printing a summary of a Cosinor

Description

printing a summary of a Cosinor

Usage

## S3 method for class 'summary.Cosinor'
print(x, ...)

Arguments

printing a summary of a month.glm

Description

printing a summary of a month.glm

Usage

## S3 method for class 'summary.monthglm'
print(x, ...)

Arguments

printing a summary of an nscosinor

Description

printing a summary of an nscosinor

Usage

## S3 method for class 'summary.nscosinor'
print(x, ...)

Arguments

Random Inverse Gamma Distribution

Description

Internal function to simulate a value from an inverse Gamma distribution, used by nscosinor. See the MCMCpack library. For internal use only.

Arguments

Schizophrenia Births in Australia, 1930–1971

Description

Monthly number of babies born with schizophrenia in Australia from 1930 to 1971. The national number of births and number of cases are missing for January 1960 are missing.

Usage

schz

Format

A data frame with 504 observations on the following 6 variables.

year

year of birth

month

month of birth

yrmon

a combination of year and month: year+(month-1)/12

NBirths

monthly number of births in Australia, used as an offset

SczBroad

monthly number of schizophrenia births using the broad diagnostic criteria

SOI

southern oscillation index

Source

From Prof John McGrath and colleagues, The University of Queensland, Brisbane.

Examples

data(schz)
plot(schz$yrmon, schz$SczBroad, type='o', xlab='Date',
     ylab='Number of schizophrenia births')

Seasonal Residual Checks

Description

Tests the residuals for any remaining seasonality.

Usage

seasrescheck(res)

Arguments

Details

Plots: i) histogram of the residuals, ii) a scatter plot against residual order, iii) the autocovariance, iv) the cumulative periodogram (see cpgram)

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Examples

# cardiovascular disease data
# (use an offset of the scaled number of days in a month)
data(CVD)
model = cosinor(cvd~1, date='month', data=CVD, type='monthly',
                family=poisson(), offsetmonth=TRUE)
seasrescheck(resid(model))

Plot a Sinusoid

Description

Plots a sinusoid over 0 to 2\pi.

Usage

sinusoid(amplitude, frequency, phase, ...)

Arguments

Details

Sinusoidal curves are useful for modelling seasonal data. A sinusoid is plotted using the equation: A\cos(ft-P), t=0,\ldots,2 \pi, where A is the amplitude, f is the frequency, t is time and P is the phase.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Examples

sinusoid(amplitude=1, frequency=1, phase=1)

Stillbirths in Queensland, 1998–2000

Description

Monthly number of stillbirths in Australia from 1998 to 2000. It is a rare event; there are 352 stillbirths out of 60,110 births. To preserve confidentiality the day of birth has been randomly re-ordered.

Usage

stillbirth

Format

A data frame with 60,110 observations on the following 7 variables.

dob

date of birth (year-month-day)

year

year of birth

month

month of birth

yrmon

a combination of year and month: year+(month-1)/12

seifa

SEIFA score, an area level measure of socioeconomic status in quintiles

gestation

gestation in weeks

stillborn

stillborn (yes/no); 1=Yes, 0=No

Source

From Queensland Health.

Examples

data(stillbirth)
table(stillbirth$month, stillbirth$stillborn)

Summary for a Cosinor

Description

The default print method for a Cosinor object produced by cosinor.

Usage

## S3 method for class 'Cosinor'
summary(object, digits = 2, ...)

Arguments

Details

Summarises the sinusoidal seasonal pattern and tests whether there is statistically significant seasonal or circadian pattern (assuming a smooth sinusoidal pattern). The amplitude describes the average height of the sinusoid, and the phase describes the location of the peak. The scale of the amplitude depends on the link function. For logistic regression the amplitude is given on a probability scale. For Poisson regression the amplitude is given on an absolute scale.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

cosinor, plot.Cosinor, invyrfraction

Summary of the Results of a Case-crossover Model

Description

The default summary method for a casecross object produced by casecross.

Usage

## S3 method for class 'casecross'
summary(object, ...)

Arguments

Details

Shows the number of control days, the average number of control days per case days, and the parameter estimates.

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

casecross

Summary for a Monthglm

Description

The default summary method for a monthglm object produced by monthglm.

Usage

## S3 method for class 'monthglm'
summary(object, ...)

Arguments

Details

The estimates are the mean, 95% confidence interval, Z-value and associated p-value (comparing each month to the reference month). If Poisson regression was used then the estimates are shown as rate ratios. If logistic regression was used then the estimates are shown as odds ratios.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

monthglm, plot.monthglm

Summary for a Non-stationary Cosinor

Description

The default summary method for a nsCosinor object produced by nscosinor.

Usage

## S3 method for class 'nsCosinor'
summary(object, ...)

Arguments

Details

The amplitude describes the average height of each seasonal cycle, and the phase describes the location of the peak. The results for the phase are given in radians (0 to 2\pi), they can be transformed to the time scale using the invyrfraction making sure to first divide by 2\pi.

The larger the standard deviation for the seasonal cycles, the greater the non-stationarity. This is because a larger standard deviation means more change over time.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

See Also

nscosinor, plot.nsCosinor

Third-order Moment

Description

Estimated third order moment for a time series.

Usage

third(data, n.lag, centre = TRUE, outmax = TRUE, plot = TRUE)

Arguments

Details

The third-order moment is the extension of the second-order moment (essentially the autocovariance). The equation for the third order moment at lags (j,k) is: n^{-1}\sum X_t X_{t+j} X_{t+k}. The third-order moment is useful for testing for non-linearity in a time series, and is used by nonlintest.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Examples

data(CVD)
third(CVD$cvd, n.lag=12)

Walter and Elwood's Test of Seasonality

Description

Tests for a seasonal pattern in Binomial data.

Usage

wtest(cases, offset, data, alpha = 0.05)

Arguments

Details

A test of whether monthly data has a sinusoidal seasonal pattern. The test has low power compared with the cosinor test.

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

References

Walter, S.D., Elwood, J.M. (1975) A test for seasonality of events with a variable population at risk. British Journal of Preventive and Social Medicine 29, 18–21.

Barnett, A.G., Dobson, A.J. (2010) Analysing Seasonal Health Data. Springer.

Examples

data(stillbirth)
# tabulate the total number of births and the number of stillbirths
freqs = table(stillbirth$month,stillbirth$stillborn)
data = list()
data$trials = as.numeric(freqs[,1]+freqs[,2])
data$success = as.numeric(freqs[,2])
# test for a seasonal pattern in stillbirth
test = wtest(cases='success', offset='trials', data=data)

Fraction of the Year

Description

Calculate the fraction of the year for a date variable (after accounting for leap years) or for month.

Usage

yrfraction(date, type = "daily")

Arguments

Details

Returns the fraction of the year in the range [0,1).

Value

Author(s)

Adrian Barnett a.barnett@qut.edu.au

Examples

# create fractions for the start, middle and end of the year
date = as.Date(c(0, 181, 364), origin='1991-01-01')
# create fractions based on these dates
yrfraction(date)
yrfraction(1:12, type='monthly')