The Diffusion Decision Model

Model file to estimate the Diffusion Decision Model (DDM) in EMC2.

Usage

DDM()

Value

A model list with all the necessary functions for EMC2 to sample

Details

Model files are almost exclusively used in design().

Default values are used for all parameters that are not explicitly listed in the formula argument of design().They can also be accessed with DDM()$p_types.

Parameter	Transform	Natural scale	Default	Mapping	Interpretation
v	-	[-Inf, Inf]	1		Mean evidence-accumulation rate (drift rate)
a	log	[0, Inf]	log(1)		Boundary separation
t0	log	[0, Inf]	log(0)		Non-decision time
s	log	[0, Inf]	log(1)		Within-trial standard deviation of drift rate
Z	probit	[0, 1]	qnorm(0.5)	z = Z x a	Relative start point (bias)
SZ	probit	[0, 1]	qnorm(0)	sz = 2 x SZ x min(a x Z, a x (1-Z))	Relative between-trial variation in start point
sv	log	[0, Inf]	log(0)		Between-trial standard deviation of drift rate
st0	log	[0, Inf]	log(0)		Between-trial variation (range) in non-decision time

a, t0, sv, st0, s are sampled on the log scale because these parameters are strictly positive, Z, SZ and DP are sampled on the probit scale because they should be strictly between 0 and 1.

Z is estimated as the ratio of bias to one boundary where 0.5 means no bias. DP comprises the difference in non-decision time for each response option.

Conventionally, s is fixed to 1 to satisfy scaling constraints.

See Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: theory and data for two-choice decision tasks. Neural computation, 20(4), 873-922. doi:10.1162/neco.2008.12-06-420.

Examples

design_DDMaE <- design(data = forstmann,model=DDM,
                           formula =list(v~0+S,a~E, t0~1, s~1, Z~1, sv~1, SZ~1),
                           constants=c(s=log(1)))
#> Parameter(s) st0 not specified in formula and assumed constant.
#> 
#>  Sampled Parameters: 
#> [1] "v_Sleft"     "v_Sright"    "a"           "a_Eneutral"  "a_Eaccuracy"
#> [6] "t0"          "Z"           "sv"          "SZ"         
#> 
#>  Design Matrices: 
#> $v
#>      S v_Sleft v_Sright
#>   left       1        0
#>  right       0        1
#> 
#> $a
#>         E a a_Eneutral a_Eaccuracy
#>     speed 1          0           0
#>   neutral 1          1           0
#>  accuracy 1          0           1
#> 
#> $t0
#>  t0
#>   1
#> 
#> $s
#>  s
#>  1
#> 
#> $Z
#>  Z
#>  1
#> 
#> $sv
#>  sv
#>   1
#> 
#> $SZ
#>  SZ
#>   1
#> 
#> $st0
#>  st0
#>    1
#> 
# For all parameters that are not defined in the formula, default values are assumed
# (see Table above).