How Many Imputations Do You Need? A Two-stage Calculation Using a Quadratic Rule

When using multiple imputation, users often want to know how many imputations they need. An old answer is that 2–10 imputations usually suffice, but this recommendation only addresses the efficiency of point estimates. You may need more imputations if, in addition to efficient point estimates, you also want standard error ( SE) estimates that would not change (much) if you imputed the data again. For replicable SE estimates, the required number of imputations increases quadratically with the fraction of missing information (not linearly, as previous studies have suggested). I recommend a two-stage procedure in which you conduct a pilot analysis using a small-to-moderate number of imputations, then use the results to calculate the number of imputations that are needed for a final analysis whose SE estimates will have the desired level of replicability. I implement the two-stage procedure using a new SAS macro called %mi_combine and a new Stata command called how_many_imputations.

Steering without Representation with the Use of Active Fixation

This paper demonstrates the use of active fixation on both fixed and moving fixation points to guide a robot vehicle by means of a steering rule which, at large distances, sets the steering angle directly proportional to the deviation of gaze direction from translation direction. Steering a motor vehicle around a winding but otherwise uncluttered road has been observed by Land and Lee to involve repeated periods of visual fixation upon the tangent point of the inside of each bend. We suggest that proportional rule devised for steering in the robotic example appears applicable to the observed human performance data, providing an alternative explanation to the quadratic rule proposed by Land and Lee.

Dependence of Ultrasonic Nonlinear Parameter B/A on Fat

This study deals with the relationship between the magnitude of acoustic nonlinearity, sound speed of tissues and the amount of fat present in them. A two-component model, i.e., nonfat and fat, has been assumed and equations that relate the nonlinear parameter (B/A) of a medium to the properties of its components have been derived for two cases. In the first case, the density and sound speed are the same for the two components; B/A is a linear function of fat concentration. To represent this case, mixtures of egg white and yolk were studied. Even though the differences in density and sound speed of the two egg components were within 1 percent of each other, B/A showed a deviation from linearity. In the second case, i.e., when the density and sound speed of the two components are not equal, a quadratic equation has been derived using mixture laws. Livers, fats, egg mixtures, and oil data were used to represent this case. B/A increased quadratically with fat concentration. The presence of proteins on the binary aqueous/fat mixtures modified the quadratic rule.