Calculating goodness of fit and choosing the right model (R) I'm trying to evaluate the value of an object, depending on his characteristics. In order to do this, I'm building the following regression model price ~ ., using similar objects and for each variable I got min 20 observations
I encountered following problem: none of the regression models worked for all my data, so I decided to use all of the followings methods:
model.lm <- lm(price ~ .)
model.lmLog <- lm(log(price) ~ .)
model.ltsReg <- ltsReg(price ~ .)
model.ltsRegLog <- lts(log(price) ~ .)
model.lmrob <- lmrob(price ~ .)
model.lmrobLog <- lmrob(log(price) ~ .)
model.lmRob <- lmRob(price ~ .)
model.lmRobLog <- lmRob(log(price) ~ .)
model.glm <- glm(price ~ .)
model.glmLog <- glm(price ~ ., family=gaussian(link="log"))

My question is: how can I decide which of this models fits best for the current data, without plotting the results?
As far as I know, the r-squared aren't trusty, because I the data is corrupted, so will be the r-squared.
Any ideas?
Thank you!
[UPDATE]
what do you think about using BIC or AIC and choosing the one with the lowest value?
what do you think about choosing the variables for the regression upon the analysis of anova?
I have 17 variables from which 10 are dummy variables, is that a problem?
 A: When you entertain more than about 3 models, model uncertainty will greatly distort your final result, especially with regard to precision, confidence intervals, and $P$-values.  AIC is generally preferred over BIC, but AIC does not solve the above problem.  I would choose a robust semi-parametric model such as proportional odds or proportional hazards (see the orm function in the R rms package).  These are $Y$-transformation invariant.  Or use AVAS to make estimation of the transformation of $Y$ part of the process (function areg.boot in rms).  Note that with 20 observations you cannot afford to model more than a couple of parameters on the right hand side of the model, and any linearity assumptions you make in doing so are questionable.
Traditional robust regression involves trimming, mean absolute deviation (MAD) minimization, etc., and it is very dependent on how $Y$ is transformed.  Robust regression also, except for MAD (quantile regression) produces hard-to-interpret estimates.  A large class of ordinal regression models is based on cumulative probabilities and allows one to directly estimate any exceedance probability or other probability of interest.  It also allows you to estimate means, and in the case of continuous $Y$, quantiles.  In rms the pertinent functions are orm, Quantile, Mean, and ExProb, the latter 3 functions being applied to a fit object produced by orm.  A detailed case study may be found at the link to course handouts at http://biostat.mc.vanderbilt.edu/rms and is covered in detail in the upcoming 2nd edition of my book Regression Modeling Strategies.  Except for the estimation of the conditional mean, ordinal regression in the cumulative probability family is completely invariant to the $Y$-transformation.
Note that when printing the result of orm the intercepts are not printed by default.  There are options for printing them, or use coef(fit).
