Assesses order of ante-dependence for repeated measures data (M.S. Ridout & R.W. Payne).
Options
TREATMENTSTRUCTURE = formula |
Treatment formula for the model at each time; if this is not set, the default is taken from the setting (which must already have been defined) of the TREATMENTSTRUCTURE directive |
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BLOCKSTRUCTURE = formula |
Block formula for the model at each time; if this is not set, the default is taken from any existing setting specified by the BLOCKSTRUCTURE directive and if neither has been set the design is assumed to be unstratified (i.e. to have a single error term) |
MAXORDER = scalar |
Maximum order against which to test; default is maximum possible order |
FACTORIAL = scalar |
Limit on the number of factors in a treatment term |
TIME = factor |
Indicates the time of each observation when there is a single DATA variate |
Parameter
DATA = variates |
Data observations either in a list of variates (one for each time), or a single variate (with TIME set to a factor indicating the time of each observation) |
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Description
A repeated measures experiment is one in which the same set of units, or subjects, is observed at a sequence of times to investigate treatment effects over a period of time. The set of variates observed at the successive times is said to have an ante-dependence structure of order r if each ith variate (i>r), given the preceding r, is independent of all further preceding variates (Gabriel 1961, 1962). Procedure ANTORDER
calculates statistics to assist in the selection of an appropriate order of ante-dependence structure for sets of repeated measures data, using the method of Kenward (1987). Once the order of ante-dependence structure has been established, the individual variates can be analysed individually by analysis of covariance, adjusting for the r previous variates, to assess the times at which treatment effects occurred. Also, procedure ANTTEST
can be used to perform overall tests of treatment effects.
The model for the analysis is specified by options of the procedure. TREATMENTSTRUCTURE
specifies a model formula to define the treatment terms in the analysis; if this is unset, ANTORDER
will use the model already defined by the TREATMENTSTRUCTURE
directive, or will fail if that too has not been set. BLOCKSTRUCTURE
defines the underlying structure of the design, and ANTORDER
will use the model (if any) previously defined by the BLOCKSTRUCTURE
directive if this is not set; these can both be omitted if there is only one error term (i.e. if the design is unstratified). Option MAXORDER
specifies the maximum order of ante-dependence structure to be tested; by default, this is taken as the maximum possible order (the smaller of the number of times minus one or the number of residual degrees at each time; see Kenward 1987). The FACTORIAL
option can be used to set a limit on the number of factors in the terms generated from the treatment formula.
The data are specified by the DATA
parameter in one of two ways. The first is to supply a list of variates, each one containing the measurements made on the subjects at one of the successive occasions on which they were observed.
The second possibility is to supply a single DATA
variate containing the data from all the times. The TIME
option must then be set to a factor indicating the time of each observation. The block and treatment factors must be defined to match the DATA
variate, and each subject should be represented by a unique combination of the block factors. If not, Genstat prints a warning and assumes that the subjects occur in the same order within each time.
The data may contain missing values but these should represent “dropouts”: that is, once subjects start to record missing values, their observations should continue to be missing at all subsequent times.
Options: TREATMENTSTRUCTURE
, BLOCKSTRUCTURE
, MAXORDER
, FACTORIAL
, TIME
.
Parameter: DATA
.
Method
The procedure uses the method of Kenward (1987) to calculate the statistics using residual sums of squares from analysis of covariance. For further details of ante-dependence see Gabriel (1961, 1962).
Action with RESTRICT
Any restriction on the DATA
variates will be applied to all of them.
References
Gabriel, K.R. (1961). The model of ante-dependence for data of biological growth. Bulletin Institut International Statistique (Paris), 39, 253-264, (33rd session).
Gabriel, K.R. (1962). Ante-dependence analysis of an ordered set of variables. Annals of Mathematical Statistics, 33, 201-212.
Kenward, M.G. (1987). A method for comparing profiles of repeated measurements, Applied Statistics, 36, 296-308.
See also
Directive: VSTRUCTURE
.
Procedures: ANTTEST
, ANTMVESTIMATE
.
Commands for: Repeated measurements.
Example
CAPTION 'ANTORDER example',\ 'Data from Kenward (1987, Appl. Statist., 36, 296-308).';\ STYLE=meta,plain POINTER [NVALUES=11] Weight VARIATE [NVALUES=60] Weight[1...11] FACTOR [LEVELS=2; VALUES=30(1,2)] Treatmnt READ Weight[1...11] 210 215 230 244 259 266 277 292 292 290 264 230 240 258 277 277 293 300 323 327 340 343 226 233 248 277 297 313 322 340 354 365 362 233 239 253 277 292 310 318 333 336 353 338 238 241 262 282 300 314 319 331 338 348 338 225 228 237 261 271 288 300 316 319 333 330 224 225 239 257 268 290 304 313 310 318 318 237 241 255 276 293 307 312 336 336 344 328 237 224 234 239 256 266 276 300 302 293 269 233 239 259 283 294 313 320 347 348 362 352 217 222 235 256 267 285 295 317 315 308 301 228 223 246 266 277 287 300 312 308 328 333 241 247 268 290 309 323 336 348 359 372 370 221 221 240 253 273 282 292 307 306 317 318 217 220 235 259 262 276 284 305 303 315 317 214 221 237 256 271 283 287 314 316 320 298 224 231 241 256 265 283 295 314 313 328 334 200 203 221 236 248 262 276 294 291 311 310 238 232 252 268 285 298 303 320 324 320 327 230 222 243 253 268 284 290 316 314 330 330 217 224 242 265 284 302 309 324 328 338 334 209 209 221 238 256 267 281 295 301 309 289 224 227 245 267 279 294 312 328 329 297 297 230 231 244 261 272 283 294 318 320 333 338 216 218 223 243 259 270 270 290 301 314 297 231 239 254 276 294 304 317 335 333 319 307 207 216 228 255 275 285 296 314 319 330 330 227 236 251 264 276 287 297 315 309 313 294 221 232 251 274 284 295 300 323 319 333 322 233 238 254 266 282 294 295 310 320 327 326 233 224 245 258 271 287 287 287 290 293 297 231 238 260 273 290 300 311 313 317 321 326 232 237 245 265 285 298 304 319 317 334 329 239 246 268 288 308 309 327 324 327 336 341 215 216 239 264 282 299 307 321 328 332 337 236 226 242 255 263 277 290 299 300 308 310 219 229 246 265 279 292 299 299 298 300 290 231 245 270 292 302 321 322 334 323 337 337 230 228 243 255 272 276 277 289 289 300 303 232 240 247 263 275 286 294 302 308 319 326 234 237 259 289 311 324 342 347 355 368 368 237 235 258 263 282 304 318 327 336 349 353 229 234 254 276 294 315 323 341 346 352 357 220 227 248 273 290 308 322 326 330 342 343 232 241 255 276 293 309 310 330 326 329 330 210 225 242 260 272 277 273 295 292 305 306 229 241 252 265 274 285 303 308 315 328 328 204 198 217 233 251 258 272 283 279 295 298 220 221 236 260 274 295 300 301 310 318 316 233 234 250 268 280 298 308 319 318 336 333 234 234 254 274 294 306 318 334 343 349 350 200 207 217 238 252 267 284 282 282 284 288 220 213 229 252 254 273 293 289 294 292 298 225 239 254 269 289 308 313 324 327 347 344 236 245 257 271 294 307 317 327 328 328 325 231 231 237 261 274 285 291 301 307 315 320 208 211 238 254 267 287 306 312 320 337 338 232 248 261 285 292 307 312 323 318 328 329 233 241 252 273 301 316 332 336 339 348 345 221 219 231 251 270 272 287 294 292 292 299 : ANTORDER [TREATMENTSTRUCTURE=Treatmnt; MAXORDER=10] Weight[]