# R Is there a way to make the threshold in linear regression?

I'm trying to do linear regression, but I just want to use variables with positive coefficients (I think this is called a hard threshold, but I'm not sure).

eg:

``````> summary(lm1)

Call:
lm(formula = value ~ ., data = intCollect1[, -c(1, 3)])

Residuals:
Min       1Q   Median       3Q      Max
-15.6518  -0.2089  -0.0227   0.2035  15.2235

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)     0.099763   0.024360   4.095 4.22e-05 ***
modelNum3802    0.208867   0.008260  25.285  < 2e-16 ***
modelNum8000   -0.086258   0.013104  -6.582 4.65e-11 ***
modelNum8001   -0.058225   0.010741  -5.421 5.95e-08 ***
modelNum8002   -0.001813   0.012087  -0.150 0.880776
modelNum8003   -0.083646   0.011015  -7.594 3.13e-14 ***
modelNum8004    0.002521   0.010729   0.235 0.814254
modelNum8005    0.301286   0.011314  26.630  < 2e-16 ***
```

```

In the above regression, I would like to use models 3802, 8004, and 8005. Is there a way to do this without copying and pasting each variable name?

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Instead of using, `lm`

Minimize the sum of the squares of replication errors by keeping your linear coefficients positive.

Such problems can be solved with the help `lsei`

of the package `limSolve`

. Looking at your example, it looks something like this:

``````x.variables <- c("modelNum3802", "modelNum8000", ...)
num.var <- length(x.variables)

lsei(A = intCollect1[, x.variables],
B = intCollect1\$value,
G = diag(num.var),
H = rep(0, num.var))
```

```
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I found a `nnls`

(non-negative least square) package to look out for.

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You can also reformulate your linear regression model as follows: label ~ sum (exp (\ alpha_i) f_i)

optimization target would be sum_j (label_j - sum_i (exp (\ alpha_i) f_i)) ^ 2

This has no closed form solution, but can be effectively resolved since it is convex in \ alpha_i.

Once you compute \ alpha_i's, you can rewrite them as regular linear model regressors by expressing them.

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