Use this tag for regression models (*q.v.*) that are nonlinear functions of the *parameters* (not the data!).
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18 views
GRM or mixed effect models
I need your help.
In experiment I have measured the grow of one plant on 40 locations. At one location different number of plants were measured, but always the same species. The distribution of ...
5
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1answer
95 views
Regression for a model of form $y=ax^k$?
I have a dataset which is statistics from a web discussion forum. I'm looking at the distribution of the number of replies a topic is expected to have. In particular, I've created a dataset which has ...
1
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1answer
29 views
Standard errors of regression coefficients based on sample size
For any particular nonlinear regression: $$Y_i = f(\mathbb{x_i},\theta) + \epsilon_i, i=1,...,n$$ I currently have standard errors for each of the $\theta_j$ obtained via the Gauss-Newton algorithm
...
3
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1answer
54 views
Nonlinear regression: Confidence intervals on transformed or untransformed parameters?
Suppose I am using a standard inhibition model to find biochemical parameters that fit my data. The equation is:
$y = \frac{A}{{1 + \exp \left( {\ln \left[ S \right] - \ln IC_{50}} \right)}} $
where ...
2
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0answers
20 views
Can parameter uncertainties be salvaged when the residuals are correlated?
I have a nonlinear physical model for which I'm trying to determine parameter uncertainties using Monte Carlo. Instead of describing the nitty-gritty details, I will use a series of figures:
...
0
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0answers
71 views
What method is better to model percentage response with each subject measured two times and heteroscedastic error?
The response was calculated as $\frac{Control-Observation}{Control}*100\%$. Raw values of $Control$ and $Observation$ are not available, I have only calculated values. Each value was measured twice. ...
0
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1answer
32 views
user-defined correlation matrix in r package nlme with negative values
I have a nonlinear model with residuals that are negatively autocorrelated at short distances.
I can find no spatial correlation structures in nlme that can easily handle negative autocorrelation ...
0
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1answer
35 views
Sequential problem for n=1, non linear regression
I am trying to understand an example in my stats course notes, the example relates to calculating the best value for the next experiment.
The function of the line is very simple:
$$ln(Y_i) = ...
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2answers
104 views
Formula for non-linear regression in R
I want to know if it is possible for a library in R to evaluate the association of independent variables and create a formula? I am trying to come up with a model to predict power consumption of a ...
2
votes
1answer
128 views
Fit a smooth approximation line
I have a simulated data set and I want to fit a "smooth approximation line" like the image I have provided.
1- Is it possible to do this in Excel or Matlab? May I have a pointer on how to do it?
...
1
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1answer
58 views
Select outliers with standard deviation after a nonlinear regression
I've performed an non linear regression with 3 variables and 5 parameters, using Wolfram Mathematica.
Now I want to detect the outliers that are far from 2*(standard deviation) of my function.
I've ...
0
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0answers
21 views
Ideas and issues related to parameter estimation
MPSV paper describes the method of parameter estimation. I have a set of measurements obtained from hardware. It is a vector of 1000 data samples representing a measurement.I need to formulate a model ...
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0answers
25 views
Zero to one proportion data, with quadratic term?
I have a data set with the following:
N = 60;
x = developmental stage (range 25 to 44);
y = proportion of 10 minute trial performing a behavior (range 0 to 0.81; 30 zeros)
A scatterplot produces a ...
1
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2answers
249 views
How to perform an exponential regression with multiple variables in R
I am an R noob, so I'm hoping this question isn't a dumb one.
I'd like to perform an exponential regression with multiple independent variables (similar to the LOGEST function in Excel)
I'm trying ...
2
votes
2answers
160 views
Constrained least squares estimation
I need to fit a regression model using least squares in R with the constraint that the parameters are positive. they DON'T need to sum to one. because some times parameter sum exceeds one.
Can ...
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0answers
78 views
Finding starting values for nls for critical exponential function
I'm trying to fit a critical exponential function using nls. The function is of the form $y = a+ (b + cx)r^x$ and has a single maximum/minimum, a single inflection ...
3
votes
2answers
86 views
Formulation of a nearly linear model
I try to fit a model of the following form
$$
Y = (\beta X - Z)^+ + \epsilon,
$$
where $Y,Z \ge 0$ and $X,Y,Z \in \mathbb{R}$ and $(x)^+ = \max(x,0)$.
Note that $Y,X$ and $Z$ come from a sample, ...
1
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1answer
89 views
Can I use a non-linear mixed model for data containing both linear and quadratic relationship?
I have dataset with both linear and quadratic relationships for my response variable among individuals. My dataset includes individuals sampled from two populations (9 individuals from population A ...
0
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0answers
31 views
How to estimate parameters for a nonlinear model with parameters both inside and outside of trigonometric functions?
For the given set of data $y(t)$ I have a model $y(t) = c_1 cos(\omega t) + c_2 sin(\omega t) + c_3$
How can I estimate parameters $c_1,c_2,c_3$ and $\omega$?
1
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1answer
88 views
Using regression splines for values outside of the calibration range
in my question on a load forecast model using temperature data as covariates I was advised to use regression splines. This really seems to be a/the solution.
Now I face the following problem: if I ...
3
votes
0answers
106 views
Relaxing the parallel lines assumption in a proportional odds model
I tried to specify a partial proportional odds regression in STATA using the gologit2 command.
However, gologit2 runs ...
2
votes
0answers
72 views
Exponent for non-linear regression (in R)?
I have a non-linear reglationship and I want to find the best way to determine the value for the exponent $\gamma$ in the following regression:
$y = \beta x ^ \gamma$
I would preferably like to do ...
6
votes
1answer
358 views
fitting an exponential function using least squares vs. generalized linear model vs. nonlinear least squares
I have a data set that represents exponential decay. I would like to fit an exponential function $y = Be^{ax}$ to this data. I've tried log transforming the response variable and then using least ...
0
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0answers
36 views
Methods for probability estimates
I am trying to learn about methods for learning probability estimates.
I understand how to use logistic regression for that, but I wonder if there are more complex nonlinear methods of the vein of ...
0
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0answers
46 views
How to handle data which contains 0 in a log transformation regression using R tool [duplicate]
Possible Duplicate:
How should I transform non-negative data including zeros?
I want to perform log transformation regression in R tool but the problem is that I don't know how to handle ...
1
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2answers
42 views
Bootstrapping x and y of curve maximum
I have a longitudinal dataset-- a series of measurements were collected each individual in the study, and the individuals fall into several treatment groups (normal untreated, mutant untreated, normal ...
2
votes
2answers
161 views
Model selection with nonlinear fitting? Statistical tests seem ambiguous
I'm working on fitting an exponential model
$\mathrm{Flux} = A+Bt+F\left(\exp(t_0-t/T_r) + \exp(t-t_0/T_f)\right)^{-1}+...$
to astronomical data (a light curve).
$A$, $B$, $F$, $t_0$, $T_r$, and ...
2
votes
0answers
59 views
Gauss-Newton method for MA parameter estimation
Please check my solution below for estimating Moving Average parameter using the Gauss-Newton (Linearization) method. I consider MA(1).
MA(1) model:
$$z_t=a_t-\theta_1a_{t-1}.$$
Solution:
The ...
5
votes
1answer
165 views
Regression estimator where exponents are freely varying?
Is there a regression estimation methodology that can estimate the following:
$$Y_t = \alpha + \beta X_t^x + \gamma Z_t^z + \epsilon_t$$
where $x,z\in \mathbb{R}$, are freely varying and are chosen ...
0
votes
1answer
177 views
How to describe characteristics of the curve fit by a four parameter non-linear regression?
I've fit a non-linear mixed effects model with a four parameter logistic function. My specific interest is in characterizing the point on the curve at which the horizontal component of the curve meets ...
1
vote
1answer
147 views
nls curve fitting of nested/shared parameters
I'm trying to fit raw data to curves, which works well on an individual basis. However, I'd like to "share" parameters (sometimes referred as nested parameters) across more than one data series. Is ...
1
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0answers
214 views
Comparing model fits or regression coefficients for nonlinear models fitted to different data sets
I have kinetic data measured under several treatments (one experiment per treatment) which can be fitted by several nonlinear two-parameter models, how can I compare whether there there are ...
4
votes
1answer
186 views
Identify the parameters of the model $Y=\exp(\beta_0 + \beta_1 X + \beta_2 Z)+u_i$
I have the model $Y_i=\exp(\beta_0 + \beta_1 X_i +\beta_2 Z_i) + u_i$ where we assume $\mathbf{E}[u_i|X_i,Z_i]=0$ and $Var(X_i)>0,Var(Z_i)>0$, and I need to show that $\beta_0,\beta_1,\beta_2$ ...
1
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0answers
52 views
Breakpoints and non linear regression
I have done some research about breakpoints (I am not a statistician) and I found out about the breakpoint, strucchange and segmented packages in R allowing to find breakpoints assuming linear model.
...
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0answers
181 views
Whether to use linear regression or not
Effects of growth hormone (GH) replacement with recombinant human GH on bone and mineral metabolism were studied in 36 GH-deficient children. Several outcomes, including serum ionized calcium levels, ...
3
votes
0answers
93 views
Shifted intercepts in logistic regression
I have a question about the effects of shifting the intercept in a logistic fit on the mean of a particular transformation of the scores.
Here is the notation I will be using for the question. The ...
6
votes
1answer
144 views
Residual, linear least squares and quality engineering
I wanted to ask this question on stackoverflow but I think it is more suitable here. If I am wrong, please tell me.
My question concerns the use in statistics to analyse physical/engineering data. As ...
0
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0answers
39 views
De-meaning data in mixed process model?
I want to run a fixed effects IV regression that is also a mixed process model. If I use the linear FE-IV estimator, I am assuming linearity, which I don't want to do. However, I do not have a ...
3
votes
2answers
172 views
Sampling weight when using regression or descriptive statistics
I came across sampling weight when I was looking into analyzing survey data.
I was wondering whether we need to take into consideration sampling weight when we are running linear/non-linear ...
1
vote
2answers
395 views
How do I do nonlinear generalized estimating equations in SPSS
Say I have two conditional media for bacteria growth: a bacteriocidal drug and control. I want to see the effect of my bacteriocide on culture growth, so I set up 6 flasks: three with drug, three ...
1
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0answers
97 views
Sum of Squares reduction test: Convergence criteria met, but not all parameters of the model estimated
Background: I am using weighted non-linear regression to model the growth of plant organs, with dummy variables for different species. I am using a sum of squares reduction test (SSRT) to compare the ...
4
votes
1answer
63 views
Posterior density of nonlinear random effects
Consider the nonlinear mixed effects model for the $j$th observation $y_{ij}$, $j=1,\dots,n_i$, $i=1,\dots,N$, of individual $i$ at time $t_{ij}$ :
$$
y_{ij} = f(\alpha_i, t_{ij}) + g(\alpha_i, ...
3
votes
1answer
123 views
How to compare results obtained by non-linear regression
Disclaimer: Statistics is not exactly something I am particularly good at. So if this is a stupid question, I do apologize
I have been using non-linear regression to analyze binding between two ...
0
votes
1answer
318 views
Cobb-Douglas production: interpret regression
If we take the logarithm of the Cobb-Douglas production function, we get:
ln(Y)=A+$\beta_1$ln(L)+$\beta_2$ln(K)+$\epsilon$ln(e)
I understand that in the production function, the coefficients ...
2
votes
0answers
66 views
dose response and lethal dose 50 analysis
I am going to perform an experiment to test for the pathogenicity of several bacterial strains. For this I will infect several animals (e.g. 5 per dose per bacterial strain) with increasing doses of ...
0
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0answers
55 views
Having problems with CATREG for big and small data sets and defining scaling level
I am facing with an interesting problem here. I have a data set containing mixed nature of independent variables (some are nominal, some are ordinal, some are scale). The dependent variable is ...
12
votes
2answers
484 views
How do I test a nonlinear association?
For plot 1, I can test the association between x and y by doing a simple correlation.
For plot 2, where the relationship is nonlinear yet there is a clear relation between x and y, how can I test ...
5
votes
1answer
255 views
Different random effects in nlme and nlmer
I estimated a nonlinear exponential $f(t)=\alpha-(\alpha-\beta)*exp(-\gamma*t)$ random effects model in R. I estimated the same model form using the identical data set but with nlme from the nlme ...
5
votes
1answer
443 views
How to read the the goodness of fit on nls of R?
I am trying to interpreting the output of nls(). I have read this post but I still don't understand how to choose the best fit. From my fits I have two outputs:
...
2
votes
1answer
124 views
Chi-squared test for nonlinear regression
In the context of a statistical signal processing problem, I have a signal model of the form $x[n]=s[n;\theta]+w[n]$ where $w[n]\sim{\cal N}(0,\sigma^2)$ and $s[n;\theta]$ depends nonlinearly on ...
